s_id
stringlengths 10
10
| p_id
stringlengths 6
6
| u_id
stringlengths 10
10
| date
stringlengths 10
10
| language
stringclasses 1
value | original_language
stringclasses 11
values | filename_ext
stringclasses 1
value | status
stringclasses 1
value | cpu_time
int64 0
100
| memory
stringlengths 4
6
| code_size
int64 15
14.7k
| code
stringlengths 15
14.7k
| problem_id
stringlengths 6
6
| problem_description
stringlengths 358
9.83k
| input
stringlengths 2
4.87k
| output
stringclasses 807
values | __index_level_0__
int64 1.1k
1.22M
|
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
s002692553
|
p00008
|
u392970366
|
1596670285
|
Python
|
Python3
|
py
|
Accepted
| 50
|
5596
| 254
|
while True:
try:
n = int(input())
except:
break
ans = 0
for a in range(10):
for b in range(10):
for c in range(10):
d = n - (a + b + c)
ans += 0 <= d <= 9
print(ans)
|
p00008
|
<H1>Sum of 4 Integers</H1>
<p>
Write a program which reads an integer <var>n</var> and identifies the number of combinations of <var>a, b, c</var> and <var>d</var> (0 ≤ <var>a, b, c, d</var> ≤ 9) which meet the following equality:<br>
<br>
<var>a + b + c + d = n</var><br>
<br>
For example, for <var>n</var> = 35, we have 4 different combinations of (<var>a, b, c, d</var>): (<var>8, 9, 9, 9</var>), (<var>9, 8, 9, 9</var>), (<var>9, 9, 8, 9</var>), and (<var>9, 9, 9, 8</var>).
</p>
<H2>Input</H2>
<p>
The input consists of several datasets. Each dataset consists of <var>n</var> (1 ≤ <var>n</var> ≤ 50) in a line. The number of datasets is less than or equal to 50.
</p>
<H2>Output</H2>
<p>
Print the number of combination in a line.
</p>
<H2>Sample Input</H2>
<pre>
35
1
</pre>
<H2>Output for the Sample Input</H2>
<pre>
4
4
</pre>
|
35
1
|
4
4
| 5,102
|
s436919250
|
p00008
|
u309196579
|
1596606764
|
Python
|
Python3
|
py
|
Accepted
| 50
|
5592
| 254
|
while True:
try:
n = int(input())
except:
break
ans = 0
for a in range(10):
for b in range(10):
for c in range(10):
d = n - (a + b + c)
ans += 0 <= d <= 9
print(ans)
|
p00008
|
<H1>Sum of 4 Integers</H1>
<p>
Write a program which reads an integer <var>n</var> and identifies the number of combinations of <var>a, b, c</var> and <var>d</var> (0 ≤ <var>a, b, c, d</var> ≤ 9) which meet the following equality:<br>
<br>
<var>a + b + c + d = n</var><br>
<br>
For example, for <var>n</var> = 35, we have 4 different combinations of (<var>a, b, c, d</var>): (<var>8, 9, 9, 9</var>), (<var>9, 8, 9, 9</var>), (<var>9, 9, 8, 9</var>), and (<var>9, 9, 9, 8</var>).
</p>
<H2>Input</H2>
<p>
The input consists of several datasets. Each dataset consists of <var>n</var> (1 ≤ <var>n</var> ≤ 50) in a line. The number of datasets is less than or equal to 50.
</p>
<H2>Output</H2>
<p>
Print the number of combination in a line.
</p>
<H2>Sample Input</H2>
<pre>
35
1
</pre>
<H2>Output for the Sample Input</H2>
<pre>
4
4
</pre>
|
35
1
|
4
4
| 5,103
|
s462512391
|
p00008
|
u187074069
|
1595929176
|
Python
|
Python3
|
py
|
Accepted
| 20
|
5592
| 320
|
while True:
try:
n = int(input())
if n > 18:
n = 36 - n
ans = (n+1)*(n+2)*(n+3)/6
if n >= 10:
n = n - 10
ans = ans - 2*(n+1)*(n+2)*(n+3)/3
if n < 0:
ans = 0
print(int(ans))
except EOFError:
break
|
p00008
|
<H1>Sum of 4 Integers</H1>
<p>
Write a program which reads an integer <var>n</var> and identifies the number of combinations of <var>a, b, c</var> and <var>d</var> (0 ≤ <var>a, b, c, d</var> ≤ 9) which meet the following equality:<br>
<br>
<var>a + b + c + d = n</var><br>
<br>
For example, for <var>n</var> = 35, we have 4 different combinations of (<var>a, b, c, d</var>): (<var>8, 9, 9, 9</var>), (<var>9, 8, 9, 9</var>), (<var>9, 9, 8, 9</var>), and (<var>9, 9, 9, 8</var>).
</p>
<H2>Input</H2>
<p>
The input consists of several datasets. Each dataset consists of <var>n</var> (1 ≤ <var>n</var> ≤ 50) in a line. The number of datasets is less than or equal to 50.
</p>
<H2>Output</H2>
<p>
Print the number of combination in a line.
</p>
<H2>Sample Input</H2>
<pre>
35
1
</pre>
<H2>Output for the Sample Input</H2>
<pre>
4
4
</pre>
|
35
1
|
4
4
| 5,104
|
s591757975
|
p00008
|
u260980560
|
1588728631
|
Python
|
Python3
|
py
|
Accepted
| 40
|
5592
| 343
|
for line in open(0).readlines():
N = int(line)
lim = min(9, N)
ans = 0
if 0 <= N <= 36:
for a in range(0, lim+1):
for b in range(0, lim+1):
for c in range(0, lim+1):
d = N - a - b - c
if 0 <= d <= lim:
ans += 1
print(ans)
|
p00008
|
<H1>Sum of 4 Integers</H1>
<p>
Write a program which reads an integer <var>n</var> and identifies the number of combinations of <var>a, b, c</var> and <var>d</var> (0 ≤ <var>a, b, c, d</var> ≤ 9) which meet the following equality:<br>
<br>
<var>a + b + c + d = n</var><br>
<br>
For example, for <var>n</var> = 35, we have 4 different combinations of (<var>a, b, c, d</var>): (<var>8, 9, 9, 9</var>), (<var>9, 8, 9, 9</var>), (<var>9, 9, 8, 9</var>), and (<var>9, 9, 9, 8</var>).
</p>
<H2>Input</H2>
<p>
The input consists of several datasets. Each dataset consists of <var>n</var> (1 ≤ <var>n</var> ≤ 50) in a line. The number of datasets is less than or equal to 50.
</p>
<H2>Output</H2>
<p>
Print the number of combination in a line.
</p>
<H2>Sample Input</H2>
<pre>
35
1
</pre>
<H2>Output for the Sample Input</H2>
<pre>
4
4
</pre>
|
35
1
|
4
4
| 5,105
|
s798823325
|
p00008
|
u230927103
|
1586444927
|
Python
|
Python3
|
py
|
Accepted
| 50
|
5596
| 333
|
while True:
try:
count = 0
n = int(input())
for a in range(10):
for b in range(10):
for c in range(10):
d = n - a - b - c
if (d >= 0 and d <= 9):
count += 1
print(count)
except EOFError:
break
|
p00008
|
<H1>Sum of 4 Integers</H1>
<p>
Write a program which reads an integer <var>n</var> and identifies the number of combinations of <var>a, b, c</var> and <var>d</var> (0 ≤ <var>a, b, c, d</var> ≤ 9) which meet the following equality:<br>
<br>
<var>a + b + c + d = n</var><br>
<br>
For example, for <var>n</var> = 35, we have 4 different combinations of (<var>a, b, c, d</var>): (<var>8, 9, 9, 9</var>), (<var>9, 8, 9, 9</var>), (<var>9, 9, 8, 9</var>), and (<var>9, 9, 9, 8</var>).
</p>
<H2>Input</H2>
<p>
The input consists of several datasets. Each dataset consists of <var>n</var> (1 ≤ <var>n</var> ≤ 50) in a line. The number of datasets is less than or equal to 50.
</p>
<H2>Output</H2>
<p>
Print the number of combination in a line.
</p>
<H2>Sample Input</H2>
<pre>
35
1
</pre>
<H2>Output for the Sample Input</H2>
<pre>
4
4
</pre>
|
35
1
|
4
4
| 5,106
|
s570402281
|
p00008
|
u933957884
|
1572692191
|
Python
|
Python3
|
py
|
Accepted
| 80
|
5612
| 186
|
import sys; print("\n".join(str(sum(1 for n in [int(in_n)] for a in range(10) for b in range(a, a+10) for c in range(b, b+10) for d in range(c, c+10) if d == n)) for in_n in sys.stdin))
|
p00008
|
<H1>Sum of 4 Integers</H1>
<p>
Write a program which reads an integer <var>n</var> and identifies the number of combinations of <var>a, b, c</var> and <var>d</var> (0 ≤ <var>a, b, c, d</var> ≤ 9) which meet the following equality:<br>
<br>
<var>a + b + c + d = n</var><br>
<br>
For example, for <var>n</var> = 35, we have 4 different combinations of (<var>a, b, c, d</var>): (<var>8, 9, 9, 9</var>), (<var>9, 8, 9, 9</var>), (<var>9, 9, 8, 9</var>), and (<var>9, 9, 9, 8</var>).
</p>
<H2>Input</H2>
<p>
The input consists of several datasets. Each dataset consists of <var>n</var> (1 ≤ <var>n</var> ≤ 50) in a line. The number of datasets is less than or equal to 50.
</p>
<H2>Output</H2>
<p>
Print the number of combination in a line.
</p>
<H2>Sample Input</H2>
<pre>
35
1
</pre>
<H2>Output for the Sample Input</H2>
<pre>
4
4
</pre>
|
35
1
|
4
4
| 5,107
|
s895452239
|
p00008
|
u586792237
|
1564929728
|
Python
|
Python3
|
py
|
Accepted
| 30
|
5596
| 239
|
a = [0 for i in range(51)]
for i in range(10):
for j in range(10):
for k in range(10):
for l in range(10):
a[i + j + k + l] += 1
while True:
try:
n = int(input())
print(a[n])
except EOFError:
break
|
p00008
|
<H1>Sum of 4 Integers</H1>
<p>
Write a program which reads an integer <var>n</var> and identifies the number of combinations of <var>a, b, c</var> and <var>d</var> (0 ≤ <var>a, b, c, d</var> ≤ 9) which meet the following equality:<br>
<br>
<var>a + b + c + d = n</var><br>
<br>
For example, for <var>n</var> = 35, we have 4 different combinations of (<var>a, b, c, d</var>): (<var>8, 9, 9, 9</var>), (<var>9, 8, 9, 9</var>), (<var>9, 9, 8, 9</var>), and (<var>9, 9, 9, 8</var>).
</p>
<H2>Input</H2>
<p>
The input consists of several datasets. Each dataset consists of <var>n</var> (1 ≤ <var>n</var> ≤ 50) in a line. The number of datasets is less than or equal to 50.
</p>
<H2>Output</H2>
<p>
Print the number of combination in a line.
</p>
<H2>Sample Input</H2>
<pre>
35
1
</pre>
<H2>Output for the Sample Input</H2>
<pre>
4
4
</pre>
|
35
1
|
4
4
| 5,108
|
s507590470
|
p00008
|
u821561321
|
1564923201
|
Python
|
Python3
|
py
|
Accepted
| 30
|
5600
| 193
|
e=[0]*51
for a in range(10):
for b in range(10):
for c in range(10):
for d in range(10):
e[sum([a,b,c,d])]+=1
while 1:
try:
print(e[int(input())])
except:
break
|
p00008
|
<H1>Sum of 4 Integers</H1>
<p>
Write a program which reads an integer <var>n</var> and identifies the number of combinations of <var>a, b, c</var> and <var>d</var> (0 ≤ <var>a, b, c, d</var> ≤ 9) which meet the following equality:<br>
<br>
<var>a + b + c + d = n</var><br>
<br>
For example, for <var>n</var> = 35, we have 4 different combinations of (<var>a, b, c, d</var>): (<var>8, 9, 9, 9</var>), (<var>9, 8, 9, 9</var>), (<var>9, 9, 8, 9</var>), and (<var>9, 9, 9, 8</var>).
</p>
<H2>Input</H2>
<p>
The input consists of several datasets. Each dataset consists of <var>n</var> (1 ≤ <var>n</var> ≤ 50) in a line. The number of datasets is less than or equal to 50.
</p>
<H2>Output</H2>
<p>
Print the number of combination in a line.
</p>
<H2>Sample Input</H2>
<pre>
35
1
</pre>
<H2>Output for the Sample Input</H2>
<pre>
4
4
</pre>
|
35
1
|
4
4
| 5,109
|
s972251868
|
p00008
|
u607723579
|
1564814490
|
Python
|
Python3
|
py
|
Accepted
| 30
|
5604
| 306
|
ans = [0 for i in range(51)]
for i in range(10):
for j in range(10):
for k in range(10):
for l in range(10):
ans[i+j+k+l] += 1
#for i in range(50+1):
# print(i, ans[i])
while True:
try:
print(ans[int(input())])
except EOFError:
break
|
p00008
|
<H1>Sum of 4 Integers</H1>
<p>
Write a program which reads an integer <var>n</var> and identifies the number of combinations of <var>a, b, c</var> and <var>d</var> (0 ≤ <var>a, b, c, d</var> ≤ 9) which meet the following equality:<br>
<br>
<var>a + b + c + d = n</var><br>
<br>
For example, for <var>n</var> = 35, we have 4 different combinations of (<var>a, b, c, d</var>): (<var>8, 9, 9, 9</var>), (<var>9, 8, 9, 9</var>), (<var>9, 9, 8, 9</var>), and (<var>9, 9, 9, 8</var>).
</p>
<H2>Input</H2>
<p>
The input consists of several datasets. Each dataset consists of <var>n</var> (1 ≤ <var>n</var> ≤ 50) in a line. The number of datasets is less than or equal to 50.
</p>
<H2>Output</H2>
<p>
Print the number of combination in a line.
</p>
<H2>Sample Input</H2>
<pre>
35
1
</pre>
<H2>Output for the Sample Input</H2>
<pre>
4
4
</pre>
|
35
1
|
4
4
| 5,110
|
s412345148
|
p00008
|
u614095715
|
1560533257
|
Python
|
Python3
|
py
|
Accepted
| 30
|
5644
| 193
|
import itertools
import sys
com = [0] * 51
r10 = range(10)
for a,b,c,d in itertools.product(r10,r10,r10,r10):
com[a+b+c+d] += 1
for line in sys.stdin.readlines():
print(com[int(line)])
|
p00008
|
<H1>Sum of 4 Integers</H1>
<p>
Write a program which reads an integer <var>n</var> and identifies the number of combinations of <var>a, b, c</var> and <var>d</var> (0 ≤ <var>a, b, c, d</var> ≤ 9) which meet the following equality:<br>
<br>
<var>a + b + c + d = n</var><br>
<br>
For example, for <var>n</var> = 35, we have 4 different combinations of (<var>a, b, c, d</var>): (<var>8, 9, 9, 9</var>), (<var>9, 8, 9, 9</var>), (<var>9, 9, 8, 9</var>), and (<var>9, 9, 9, 8</var>).
</p>
<H2>Input</H2>
<p>
The input consists of several datasets. Each dataset consists of <var>n</var> (1 ≤ <var>n</var> ≤ 50) in a line. The number of datasets is less than or equal to 50.
</p>
<H2>Output</H2>
<p>
Print the number of combination in a line.
</p>
<H2>Sample Input</H2>
<pre>
35
1
</pre>
<H2>Output for the Sample Input</H2>
<pre>
4
4
</pre>
|
35
1
|
4
4
| 5,111
|
s089923946
|
p00008
|
u506537276
|
1560143603
|
Python
|
Python3
|
py
|
Accepted
| 30
|
5596
| 244
|
a = [0 for i in range(51)]
for i in range(10):
for j in range(10):
for k in range(10):
for l in range(10):
a[i + j + k + l] += 1
while True:
try:
n = int(input())
print(a[n])
except EOFError:
break
|
p00008
|
<H1>Sum of 4 Integers</H1>
<p>
Write a program which reads an integer <var>n</var> and identifies the number of combinations of <var>a, b, c</var> and <var>d</var> (0 ≤ <var>a, b, c, d</var> ≤ 9) which meet the following equality:<br>
<br>
<var>a + b + c + d = n</var><br>
<br>
For example, for <var>n</var> = 35, we have 4 different combinations of (<var>a, b, c, d</var>): (<var>8, 9, 9, 9</var>), (<var>9, 8, 9, 9</var>), (<var>9, 9, 8, 9</var>), and (<var>9, 9, 9, 8</var>).
</p>
<H2>Input</H2>
<p>
The input consists of several datasets. Each dataset consists of <var>n</var> (1 ≤ <var>n</var> ≤ 50) in a line. The number of datasets is less than or equal to 50.
</p>
<H2>Output</H2>
<p>
Print the number of combination in a line.
</p>
<H2>Sample Input</H2>
<pre>
35
1
</pre>
<H2>Output for the Sample Input</H2>
<pre>
4
4
</pre>
|
35
1
|
4
4
| 5,112
|
s409324128
|
p00008
|
u406093358
|
1555463373
|
Python
|
Python
|
py
|
Accepted
| 100
|
4648
| 286
|
import sys
for line in sys.stdin:
n = int(line)
cnt = 0
for i in range(0, 10):
for j in range(0, 10):
for k in range(0, 10):
for p in range(0, 10):
if i+j+k+p == n:
cnt += 1
break
if i+j+k == n: break
if i+j == n: break
if i == n: break
print cnt
|
p00008
|
<H1>Sum of 4 Integers</H1>
<p>
Write a program which reads an integer <var>n</var> and identifies the number of combinations of <var>a, b, c</var> and <var>d</var> (0 ≤ <var>a, b, c, d</var> ≤ 9) which meet the following equality:<br>
<br>
<var>a + b + c + d = n</var><br>
<br>
For example, for <var>n</var> = 35, we have 4 different combinations of (<var>a, b, c, d</var>): (<var>8, 9, 9, 9</var>), (<var>9, 8, 9, 9</var>), (<var>9, 9, 8, 9</var>), and (<var>9, 9, 9, 8</var>).
</p>
<H2>Input</H2>
<p>
The input consists of several datasets. Each dataset consists of <var>n</var> (1 ≤ <var>n</var> ≤ 50) in a line. The number of datasets is less than or equal to 50.
</p>
<H2>Output</H2>
<p>
Print the number of combination in a line.
</p>
<H2>Sample Input</H2>
<pre>
35
1
</pre>
<H2>Output for the Sample Input</H2>
<pre>
4
4
</pre>
|
35
1
|
4
4
| 5,113
|
s748709492
|
p00008
|
u195186080
|
1550733079
|
Python
|
Python3
|
py
|
Accepted
| 50
|
5600
| 421
|
def calc(n, x):
# n個の数(0~9)の和でxが作れるかどうかを判別する
if n == 1:
if x <= 9:
return 1
else:
return 0
else:
num = 0
for i in range(10):
if x-i < 0:
continue
num += calc(n-1, x-i)
return num
while True:
try:
print(calc(4, int(input())))
except:
exit(0)
|
p00008
|
<H1>Sum of 4 Integers</H1>
<p>
Write a program which reads an integer <var>n</var> and identifies the number of combinations of <var>a, b, c</var> and <var>d</var> (0 ≤ <var>a, b, c, d</var> ≤ 9) which meet the following equality:<br>
<br>
<var>a + b + c + d = n</var><br>
<br>
For example, for <var>n</var> = 35, we have 4 different combinations of (<var>a, b, c, d</var>): (<var>8, 9, 9, 9</var>), (<var>9, 8, 9, 9</var>), (<var>9, 9, 8, 9</var>), and (<var>9, 9, 9, 8</var>).
</p>
<H2>Input</H2>
<p>
The input consists of several datasets. Each dataset consists of <var>n</var> (1 ≤ <var>n</var> ≤ 50) in a line. The number of datasets is less than or equal to 50.
</p>
<H2>Output</H2>
<p>
Print the number of combination in a line.
</p>
<H2>Sample Input</H2>
<pre>
35
1
</pre>
<H2>Output for the Sample Input</H2>
<pre>
4
4
</pre>
|
35
1
|
4
4
| 5,114
|
s716785144
|
p00008
|
u350155409
|
1547293441
|
Python
|
Python3
|
py
|
Accepted
| 20
|
5600
| 204
|
import sys
n = [0]*51
for i in range(10):
for j in range(10):
for k in range(10):
for l in range(10):
n[i+j+k+l] += 1
for i in sys.stdin:
print(n[int(i)])
|
p00008
|
<H1>Sum of 4 Integers</H1>
<p>
Write a program which reads an integer <var>n</var> and identifies the number of combinations of <var>a, b, c</var> and <var>d</var> (0 ≤ <var>a, b, c, d</var> ≤ 9) which meet the following equality:<br>
<br>
<var>a + b + c + d = n</var><br>
<br>
For example, for <var>n</var> = 35, we have 4 different combinations of (<var>a, b, c, d</var>): (<var>8, 9, 9, 9</var>), (<var>9, 8, 9, 9</var>), (<var>9, 9, 8, 9</var>), and (<var>9, 9, 9, 8</var>).
</p>
<H2>Input</H2>
<p>
The input consists of several datasets. Each dataset consists of <var>n</var> (1 ≤ <var>n</var> ≤ 50) in a line. The number of datasets is less than or equal to 50.
</p>
<H2>Output</H2>
<p>
Print the number of combination in a line.
</p>
<H2>Sample Input</H2>
<pre>
35
1
</pre>
<H2>Output for the Sample Input</H2>
<pre>
4
4
</pre>
|
35
1
|
4
4
| 5,115
|
s024283853
|
p00008
|
u080014366
|
1547036763
|
Python
|
Python3
|
py
|
Accepted
| 90
|
5596
| 318
|
def count(a):#関数「count」を定義
count = 0
if a<=36:
for i in range(10):#()内は0から一つ前までの数
for j in range(10):
for k in range(10):
for l in range(10):
if i+j+k+l==a:
count +=1
print(count)
while True:
try:
a=int(input())
count(a)
except EOFError:
break
|
p00008
|
<H1>Sum of 4 Integers</H1>
<p>
Write a program which reads an integer <var>n</var> and identifies the number of combinations of <var>a, b, c</var> and <var>d</var> (0 ≤ <var>a, b, c, d</var> ≤ 9) which meet the following equality:<br>
<br>
<var>a + b + c + d = n</var><br>
<br>
For example, for <var>n</var> = 35, we have 4 different combinations of (<var>a, b, c, d</var>): (<var>8, 9, 9, 9</var>), (<var>9, 8, 9, 9</var>), (<var>9, 9, 8, 9</var>), and (<var>9, 9, 9, 8</var>).
</p>
<H2>Input</H2>
<p>
The input consists of several datasets. Each dataset consists of <var>n</var> (1 ≤ <var>n</var> ≤ 50) in a line. The number of datasets is less than or equal to 50.
</p>
<H2>Output</H2>
<p>
Print the number of combination in a line.
</p>
<H2>Sample Input</H2>
<pre>
35
1
</pre>
<H2>Output for the Sample Input</H2>
<pre>
4
4
</pre>
|
35
1
|
4
4
| 5,116
|
s068219139
|
p00008
|
u717526540
|
1541637392
|
Python
|
Python3
|
py
|
Accepted
| 50
|
5588
| 278
|
while(1):
try:
n = int(input())
except:
break
cnt = 0
for a in range(10):
for b in range(10):
for c in range(10):
d = n - a - b - c
if 0 <= d < 10:
cnt += 1
print(cnt)
|
p00008
|
<H1>Sum of 4 Integers</H1>
<p>
Write a program which reads an integer <var>n</var> and identifies the number of combinations of <var>a, b, c</var> and <var>d</var> (0 ≤ <var>a, b, c, d</var> ≤ 9) which meet the following equality:<br>
<br>
<var>a + b + c + d = n</var><br>
<br>
For example, for <var>n</var> = 35, we have 4 different combinations of (<var>a, b, c, d</var>): (<var>8, 9, 9, 9</var>), (<var>9, 8, 9, 9</var>), (<var>9, 9, 8, 9</var>), and (<var>9, 9, 9, 8</var>).
</p>
<H2>Input</H2>
<p>
The input consists of several datasets. Each dataset consists of <var>n</var> (1 ≤ <var>n</var> ≤ 50) in a line. The number of datasets is less than or equal to 50.
</p>
<H2>Output</H2>
<p>
Print the number of combination in a line.
</p>
<H2>Sample Input</H2>
<pre>
35
1
</pre>
<H2>Output for the Sample Input</H2>
<pre>
4
4
</pre>
|
35
1
|
4
4
| 5,117
|
s738138248
|
p00008
|
u853158149
|
1521965057
|
Python
|
Python3
|
py
|
Accepted
| 30
|
5604
| 244
|
num = [0 for i in range(51)]
for a in range(10):
for b in range(10):
for c in range(10):
for d in range(10):
num[a+b+c+d] += 1
while 1:
try:
print(num[int(input())])
except:
break
|
p00008
|
<H1>Sum of 4 Integers</H1>
<p>
Write a program which reads an integer <var>n</var> and identifies the number of combinations of <var>a, b, c</var> and <var>d</var> (0 ≤ <var>a, b, c, d</var> ≤ 9) which meet the following equality:<br>
<br>
<var>a + b + c + d = n</var><br>
<br>
For example, for <var>n</var> = 35, we have 4 different combinations of (<var>a, b, c, d</var>): (<var>8, 9, 9, 9</var>), (<var>9, 8, 9, 9</var>), (<var>9, 9, 8, 9</var>), and (<var>9, 9, 9, 8</var>).
</p>
<H2>Input</H2>
<p>
The input consists of several datasets. Each dataset consists of <var>n</var> (1 ≤ <var>n</var> ≤ 50) in a line. The number of datasets is less than or equal to 50.
</p>
<H2>Output</H2>
<p>
Print the number of combination in a line.
</p>
<H2>Sample Input</H2>
<pre>
35
1
</pre>
<H2>Output for the Sample Input</H2>
<pre>
4
4
</pre>
|
35
1
|
4
4
| 5,118
|
s273576601
|
p00008
|
u197615660
|
1374476960
|
Python
|
Python
|
py
|
Accepted
| 20
|
4212
| 212
|
while True:
try:
n = int(raw_input())
judge = 0
for i in range(10):
for j in range(10):
for k in range(10):
if -1 < n - i - j - k < 10:
judge += 1
print judge
except EOFError:
break
|
p00008
|
<H1>Sum of 4 Integers</H1>
<p>
Write a program which reads an integer <var>n</var> and identifies the number of combinations of <var>a, b, c</var> and <var>d</var> (0 ≤ <var>a, b, c, d</var> ≤ 9) which meet the following equality:<br>
<br>
<var>a + b + c + d = n</var><br>
<br>
For example, for <var>n</var> = 35, we have 4 different combinations of (<var>a, b, c, d</var>): (<var>8, 9, 9, 9</var>), (<var>9, 8, 9, 9</var>), (<var>9, 9, 8, 9</var>), and (<var>9, 9, 9, 8</var>).
</p>
<H2>Input</H2>
<p>
The input consists of several datasets. Each dataset consists of <var>n</var> (1 ≤ <var>n</var> ≤ 50) in a line. The number of datasets is less than or equal to 50.
</p>
<H2>Output</H2>
<p>
Print the number of combination in a line.
</p>
<H2>Sample Input</H2>
<pre>
35
1
</pre>
<H2>Output for the Sample Input</H2>
<pre>
4
4
</pre>
|
35
1
|
4
4
| 5,119
|
s862542423
|
p00009
|
u957021183
|
1504684684
|
Python
|
Python3
|
py
|
Accepted
| 80
|
14372
| 757
|
# Aizu Problem 0009: Prime Number
#
import sys, math, os, bisect
# read input:
PYDEV = os.environ.get('PYDEV')
if PYDEV=="True":
sys.stdin = open("sample-input.txt", "rt")
def primes2(n):
""" Input n>=6, Returns a list of primes, 2 <= p < n """
n, correction = n-n%6+6, 2-(n%6>1)
sieve = [True] * (n//3)
for i in range(1,int(n**0.5)//3+1):
if sieve[i]:
k=3*i+1|1
sieve[ k*k//3 ::2*k] = [False] * ((n//6-k*k//6-1)//k+1)
sieve[k*(k-2*(i&1)+4)//3::2*k] = [False] * ((n//6-k*(k-2*(i&1)+4)//6-1)//k+1)
return [2,3] + [3*i+1|1 for i in range(1,n//3-correction) if sieve[i]]
primes = primes2(10**6)
for line in sys.stdin:
n = int(line)
idx = bisect.bisect_right(primes, n)
print(idx)
|
p00009
|
<H1>Prime Number</H1>
<p>
Write a program which reads an integer <var>n</var> and prints the number of prime numbers which are less than or equal to <var>n</var>. A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2, 3, 5 and 7.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. Each dataset has an integer <var>n</var> (1 ≤ <var>n</var> ≤ 999,999) in a line.
</p>
<p>
The number of datasets is less than or equal to 30.
</p>
<H2>Output</H2>
<p>
For each dataset, prints the number of prime numbers.
</p>
<H2>Sample Input</H2>
<pre>
10
3
11
</pre>
<H2>Output for the Sample Input</H2>
<pre>
4
2
5
</pre>
|
10
3
11
|
4
2
5
| 5,120
|
s707025188
|
p00010
|
u995990363
|
1530848494
|
Python
|
Python3
|
py
|
Accepted
| 20
|
5696
| 1,196
|
import math
class P(object):
def __init__(self, x, y):
self.x = x
self.y = y
def width(self, p):
return math.sqrt((self.x - p.x)**2 + (self.y - p.y)**2)
def __repr__(self):
return '{0:.3f} {1:.3f}'.format(self.x, self.y)
def calc_cos(a,b,c):
return (b**2 + c**2 - a**2) / (2*b*c)
def calc_sin(c):
return math.sqrt(1 - c**2)
def calc_2sin(s,c):
return 2 * s * c
def run():
n = int(input())
for _ in range(n):
x1, y1, x2, y2, x3, y3 = list(map(float, input().split()))
p1, p2, p3 = P(x1, y1), P(x2, y2), P(x3, y3)
a, b, c = p1.width(p2), p2.width(p3), p3.width(p1)
cosA, cosB, cosC = calc_cos(a,b,c), calc_cos(b,c,a), calc_cos(c,a,b)
sinA, sinB, sinC = calc_sin(cosA), calc_sin(cosB), calc_sin(cosC)
sin2A, sin2B, sin2C = calc_2sin(sinA, cosA), calc_2sin(sinB, cosB), calc_2sin(sinC, cosC)
r = a / sinA / 2
x = (p1.x * sin2B + p2.x * sin2C + p3.x * sin2A) / (sin2A + sin2B + sin2C)
y = (p1.y * sin2B + p2.y * sin2C + p3.y * sin2A) / (sin2A + sin2B + sin2C)
print('{0:.3f} {1:.3f} {2:.3f}'.format(x,y,r))
if __name__ == '__main__':
run()
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,121
|
s888023198
|
p00010
|
u244742296
|
1409825937
|
Python
|
Python3
|
py
|
Accepted
| 30
|
6984
| 1,688
|
# -*- coding: utf-8 -*-
import cmath
class Point(object):
def __init__(self, x, y):
self.point = complex(x, y)
def __str__(self):
return "x = {0}, y = {1}".format(self.point.real, self.point.imag)
class Triangle(Point):
def __init__(self, a, b, c):
self.a = a
self.b = b
self.c = c
# ３辺の長さ
self.edgeA = abs(b.point-c.point)
self.edgeB = abs(c.point-a.point)
self.edgeC = abs(a.point-b.point)
# ３角の大きさ
self.angleA = Triangle.angle(self.edgeA, self.edgeB, self.edgeC)
self.angleB = Triangle.angle(self.edgeB, self.edgeC, self.edgeA)
self.angleC = Triangle.angle(self.edgeC, self.edgeA, self.edgeB)
# 角度を求める
def angle(A, B, C):
return cmath.acos( (B*B+C*C-A*A)/(2*B*C) )
# 外接円の半径
def circumscribedCircleRadius(self):
return abs((self.edgeA/cmath.sin(self.angleA))/2)
# 外心
def circumscribedCircleCenter(self):
A = cmath.sin(2*self.angleA)
B = cmath.sin(2*self.angleB)
C = cmath.sin(2*self.angleC)
X = (self.a.point.real*A + self.b.point.real*B + self.c.point.real*C) / (A+B+C)
Y = (self.a.point.imag*A + self.b.point.imag*B + self.c.point.imag*C) / (A+B+C)
return complex(X, Y)
n = int(input())
for i in range(n):
line = list(map(float, input().split()))
p1 = Point(line[0], line[1])
p2 = Point(line[2], line[3])
p3 = Point(line[4], line[5])
T = Triangle(p1, p2, p3)
center = T.circumscribedCircleCenter()
print("{0:.3f} {1:.3f} {2:.3f}".format(center.real, center.imag, T.circumscribedCircleRadius()))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,122
|
s693920046
|
p00010
|
u579833671
|
1410771915
|
Python
|
Python
|
py
|
Accepted
| 20
|
4428
| 556
|
import math
n = input()
for i in range(n):
p = map(float, raw_input().split())
x1, y1, x2, y2, x3, y3 = p[0], p[1], p[2], p[3], p[4], p[5]
px = ((y1- y3) * (y1**2 - y2**2 + x1**2 - x2**2) - (y1 - y2) * (y1**2 - y3**2 + x1**2 - x3**2)) / (2 * (y1 - y3) * (x1 - x2) - 2 * (y1 - y2) * (x1 - x3))
py = ((x1- x3) * (x1**2 - x2**2 + y1**2 - y2**2) - (x1 - x2) * (x1**2 - x3**2 + y1**2 - y3**2)) / (2 * (x1 - x3) * (y1 - y2) - 2 * (x1 - x2) * (y1 - y3))
r = math.sqrt((x1 - px)**2 + (y1 - py)**2)
print("%.3f %.3f %.3f" % (px, py, r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,123
|
s031239253
|
p00010
|
u506132575
|
1416114717
|
Python
|
Python
|
py
|
Accepted
| 20
|
4376
| 777
|
#!/usr/bin/env python
# -*- coding: utf-8 -*-
import sys
def calc_det(lis):
return lis[0]*lis[3]-lis[1]*lis[2]
def sq(x):
return x*x
for s in sys.stdin:
d = map(float, s.split() )
if len(d) == 1:
continue
x1,y1,x2,y2,x3,y3 = d[0],d[1],d[2],d[3],d[4],d[5]
d11 = 2*(x3-x2)
d12 = 2*(y3-y2)
d21 = 2*(x2-x1)
d22 = 2*(y2-y1)
x11 = sq(x3)-sq(x2)+sq(y3)-sq(y2)
x21 = sq(x2)-sq(x1)+sq(y2)-sq(y1)
y12 = x11
y22 = x21
x0 = calc_det( [x11,d12,x21,d22] )/calc_det( [d11,d12,d21,d22] )
y0 = calc_det( [d11,y12,d21,y22] )/calc_det( [d11,d12,d21,d22] )
r = ( (x0-x1)**2 + (y0-y1)**2 )**0.5
print "%.3f %.3f %.3f" % (x0,y0,r)
'''
Bibliography
３点を通る円の半径を求む（#７）
http://www.geocities.jp/jtqsw192/FIG/313r/3point_r.htm
'''
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,124
|
s889427989
|
p00010
|
u567380442
|
1424262005
|
Python
|
Python3
|
py
|
Accepted
| 30
|
6776
| 743
|
import sys
f = sys.stdin
def take2(iterable):
while True:
yield next(iterable), next(iterable)
#外積
def cross(v1, v2):
return v1.real * v2.imag - v1.imag * v2.real
# 線分13と線分24の交点を求める
def get_intersection(p1,p2,p3,p4):
a1 = p4 - p2
b1 = p2 - p3
b2 = p1 - p2
s1 = cross(a1, b2) / 2
s2 = cross(a1, b1) / 2
return p1 + (p3 - p1) * s1 / (s1 + s2)
n = int(f.readline())
for i in range(n):
p1, p2, p3 = [x + y * 1j for x, y in take2(map(float, f.readline().split()))]
p12 = (p1 + p2) / 2
p13 = (p1 + p3) / 2
pxy = get_intersection(p12,p13,p12 + (p2 - p1) * 1j,p13 + (p1 - p3) * 1j)
r = abs(pxy - p1)
print('{:.3f} {:.3f} {:.3f}'.format(pxy.real,pxy.imag,r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,125
|
s351931260
|
p00010
|
u540744789
|
1426158084
|
Python
|
Python
|
py
|
Accepted
| 10
|
4496
| 731
|
import math
for i in range(input()):
x1,y1,x2,y2,x3,y3=map(float,raw_input().split(" "))
if y2==y1 or y3==y1:
if y2==y1:
a2=-(x3-x1)/(y3-y1)
b2=((y3+y1)-a2*(x1+x3))/2.0
a,b,c,d,e,f=1.0,0.0,(x1+x2)/2.0,-a2,1.0,b2
else:
a1=-(x2-x1)/(y2-y1)
b1=((y2+y1)-a1*(x1+x2))/2.0
a,b,c,d,e,f=-a1,1.0,b1,1.0,0.0,(x1+x3)/2.0
else:
a1=-(x2-x1)/(y2-y1)
a2=-(x3-x1)/(y3-y1)
b1=((y2+y1)-a1*(x1+x2))/2.0
b2=((y3+y1)-a2*(x1+x3))/2.0
a,b,c,d,e,f=-a1,1.0,b1,-a2,1.0,b2
py=(a*f-c*d)/(a*e-b*d)
px=(c*e-f*b)/(a*e-b*d)
r=math.sqrt((px-x1)**2 + (py-y1)**2)
print "{0:.3f} {1:.3f} {2:.3f}".format(px,py,r)
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,126
|
s580932409
|
p00010
|
u879226672
|
1431621030
|
Python
|
Python
|
py
|
Accepted
| 20
|
4412
| 457
|
# coding: utf-8
import math
for i in range(int(raw_input())):
x1, y1, x2, y2, x3, y3 = map(float,raw_input().split())
px = ((y1-y3)*(y1**2 -y2**2 +x1**2 -x2**2) -(y1-y2)*(y1**2 -y3**2 +x1**2 -x3**2)) / (2*(y1-y3)*(x1-x2)-2*(y1-y2)*(x1-x3))
py = ((x1-x3)*(x1**2 -x2**2 +y1**2 -y2**2) -(x1-x2)*(x1**2 -x3**2 +y1**2 -y3**2)) / (2*(x1-x3)*(y1-y2)-2*(x1-x2)*(y1-y3))
r = math.sqrt((x1-px)**2 + (y1-py)**2)
print "%.3f %.3f %.3f" % (px, py, r)
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,127
|
s989196126
|
p00010
|
u067299340
|
1432816763
|
Python
|
Python
|
py
|
Accepted
| 20
|
4376
| 471
|
def calc(l):
A1=2*(l[1][0]-l[0][0])
B1=2*(l[1][1]-l[0][1])
C1=l[0][0]**2-l[1][0]**2+l[0][1]**2-l[1][1]**2
A2=2*(l[2][0]-l[0][0])
B2=2*(l[2][1]-l[0][1])
C2=l[0][0]**2-l[2][0]**2+l[0][1]**2-l[2][1]**2
X=(B1*C2-B2*C1)/(A1*B2-A2*B1)
Y=(C1*A2-C2*A1)/(A1*B2-A2*B1)
R=((X-l[0][0])**2+(Y-l[0][1])**2)**0.5
return tuple(map(round, [X,Y,R], [3]*3))
l=[zip(*[iter(map(float,raw_input().split()))]*2) for i in range(input())]
for ll in l:
print "%.3f %.3f %.3f"%(calc(ll))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,128
|
s090858081
|
p00010
|
u067299340
|
1432817040
|
Python
|
Python
|
py
|
Accepted
| 10
|
4336
| 354
|
def calc(a,b,c,d,e,f):
A1=2*(c-a)
B1=2*(d-b)
C1=a**2-c**2+b**2-d**2
A2=2*(e-a)
B2=2*(f-b)
C2=a*a-e*e+b*b-f*f
X=(B1*C2-B2*C1)/(A1*B2-A2*B1)
Y=(C1*A2-C2*A1)/(A1*B2-A2*B1)
R=((X-a)**2+(Y-b)**2)**0.5
return tuple(map(round, [X,Y,R], [3]*3))
l=[map(float,raw_input().split()) for i in range(input())]
for ll in l:
print "%.3f %.3f %.3f"%(calc(*ll))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,129
|
s386023601
|
p00010
|
u067299340
|
1432817248
|
Python
|
Python
|
py
|
Accepted
| 20
|
4336
| 317
|
def calc(a,b,c,d,e,f):
A=2*(c-a)
B=2*(d-b)
C=a*a-c*c+b*b-d*d
D=2*(e-a)
E=2*(f-b)
F=a*a-e*e+b*b-f*f
N=(A*E-D*B)
X=(B*F-E*C)/N
Y=(C*D-F*A)/N
R=((X-a)**2+(Y-b)**2)**0.5
return tuple(map(round,[X,Y,R],[3]*3))
l=[map(float,raw_input().split())for i in range(input())]
for k in l:print"%.3f %.3f %.3f"%(calc(*k))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,130
|
s122823497
|
p00010
|
u067299340
|
1432817322
|
Python
|
Python
|
py
|
Accepted
| 10
|
4332
| 312
|
def calc(a,b,c,d,e,f):
A=2*(c-a)
B=2*(d-b)
C=a*a-c*c+b*b-d*d
D=2*(e-a)
E=2*(f-b)
F=a*a-e*e+b*b-f*f
N=(A*E-D*B)
X=(B*F-E*C)/N
Y=(C*D-F*A)/N
return tuple(map(round,[X,Y,((X-a)**2+(Y-b)**2)**0.5],[3]*3))
l=[map(float,raw_input().split())for i in range(input())]
for k in l:print"%.3f %.3f %.3f"%(calc(*k))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,131
|
s543355455
|
p00010
|
u067299340
|
1432817587
|
Python
|
Python
|
py
|
Accepted
| 10
|
4332
| 302
|
def g(a,b,c,d,e,f):
A=2*(c-a)
B=2*(d-b)
C=a*a-c*c+b*b-d*d
D=2*(e-a)
E=2*(f-b)
F=a*a-e*e+b*b-f*f
N=(A*E-D*B)
X=(B*F-E*C)/N
Y=(C*D-F*A)/N
return tuple(map(round,[X,Y,((X-a)**2+(Y-b)**2)**0.5],[3]*3))
for k in [map(float,raw_input().split())for i in range(input())]:print"%.3f %.3f %.3f"%(g(*k))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,132
|
s152540471
|
p00010
|
u379956761
|
1434726722
|
Python
|
Python3
|
py
|
Accepted
| 30
|
6824
| 531
|
#!/usr/bin/env python
#-*- coding:utf-8 -*-
import sys
import math
n = int(input())
for data in sys.stdin:
x1, y1, x2, y2, x3, y3 = map(float, data.split())
a1 = x2 - x1
b1 = y2 - y1
a2 = x3 - x1
b2 = y3 - y1
px = (b2 * (a1 * a1 + b1 * b1) - b1 * (a2 * a2 + b2 * b2)) / (2 * (a1 * b2 - a2 * b1))
py = (a1 * (a2 * a2 + b2 * b2) - a2 * (a1 * a1 + b1 * b1)) / (2 * (a1 * b2 - a2 * b1))
r = math.sqrt(px * px + py * py)
px += x1
py += y1
print("{0:.3f} {1:.3f} {2:.3f}".format(px, py, r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,133
|
s773101625
|
p00010
|
u722431421
|
1439559123
|
Python
|
Python
|
py
|
Accepted
| 10
|
4360
| 685
|
# coding: utf-8
#Problem Name: Circumscrived Circle of a Triangle
#ID: tabris
#Mail: t123037@kaiyodai.ac.jp
def __det(matrix):
return matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0]
def __sqdist(p1,p2):
return ((p1[0] - p2[0])**2 + (p1[1] - p2[1])**2)**.5
n = int(raw_input())
for i in range(n):
x1,y1,x2,y2,x3,y3 = map(float,raw_input().split(' '))
det = __det([[(x2-x1),(y2-y1)],[(x3-x1),(y3-y1)]])
c1 = (x1**2-x2**2+y1**2-y2**2)/2
c2 = (x1**2-x3**2+y1**2-y3**2)/2
px = __det([[c1,(y1-y2)],[c2,(y1-y3)]])/det
py = __det([[(x1-x2),c1],[(x1-x3),c2]])/det
r = __sqdist([x1,y1],[px,py])
print '{0:.3f} {1:.3f} {2:.3f}'.format(px,py,r)
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,134
|
s040160979
|
p00010
|
u722431421
|
1439560398
|
Python
|
Python
|
py
|
Accepted
| 10
|
4360
| 685
|
# coding: utf-8
#Problem Name: Circumscrived Circle of a Triangle
#ID: tabris
#Mail: t123037@kaiyodai.ac.jp
def __det(matrix):
return matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0]
def __sqdist(p1,p2):
return ((p1[0] - p2[0])**2 + (p1[1] - p2[1])**2)**.5
n = int(raw_input())
for i in range(n):
x1,y1,x2,y2,x3,y3 = map(float,raw_input().split(' '))
det = __det([[(x2-x1),(y2-y1)],[(x3-x1),(y3-y1)]])
c1 = (x2**2-x1**2+y2**2-y1**2)/2
c2 = (x3**2-x1**2+y3**2-y1**2)/2
px = __det([[c1,(y2-y1)],[c2,(y3-y1)]])/det
py = __det([[(x2-x1),c1],[(x3-x1),c2]])/det
r = __sqdist([x1,y1],[px,py])
print '{0:.3f} {1:.3f} {2:.3f}'.format(px,py,r)
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,135
|
s182973471
|
p00010
|
u140201022
|
1443010856
|
Python
|
Python
|
py
|
Accepted
| 10
|
6568
| 457
|
n=int(raw_input())
for i in range(n):
x1,y1,x2,y2,x3,y3=map(float,raw_input().split())
a=((x1-x2)**2+(y1-y2)**2)**0.5
b=((x1-x3)**2+(y1-y3)**2)**0.5
c=((x2-x3)**2+(y2-y3)**2)**0.5
s=(a+b+c)/2
ss=(s*(s-a)*(s-b)*(s-c))**0.5
sina=2*ss/b/c
r=a/sina/2
a*=a
b*=b
c*=c
px=(a*(b+c-a)*x3+b*(a+c-b)*x2+c*(a+b-c)*x1)/16/ss**2
py=(a*(b+c-a)*y3+b*(a+c-b)*y2+c*(a+b-c)*y1)/16/ss**2
print '%.3f %.3f %.3f'%(px,py,r)
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,136
|
s416647942
|
p00010
|
u802625365
|
1447077872
|
Python
|
Python
|
py
|
Accepted
| 10
|
6480
| 731
|
import math
for i in range(input()):
x1,y1,x2,y2,x3,y3=map(float,raw_input().split(" "))
if y2==y1 or y3==y1:
if y2==y1:
a2=-(x3-x1)/(y3-y1)
b2=((y3+y1)-a2*(x1+x3))/2.0
a,b,c,d,e,f=1.0,0.0,(x1+x2)/2.0,-a2,1.0,b2
else:
a1=-(x2-x1)/(y2-y1)
b1=((y2+y1)-a1*(x1+x2))/2.0
a,b,c,d,e,f=-a1,1.0,b1,1.0,0.0,(x1+x3)/2.0
else:
a1=-(x2-x1)/(y2-y1)
a2=-(x3-x1)/(y3-y1)
b1=((y2+y1)-a1*(x1+x2))/2.0
b2=((y3+y1)-a2*(x1+x3))/2.0
a,b,c,d,e,f=-a1,1.0,b1,-a2,1.0,b2
py=(a*f-c*d)/(a*e-b*d)
px=(c*e-f*b)/(a*e-b*d)
r=math.sqrt((px-x1)**2 + (py-y1)**2)
print "{0:.3f} {1:.3f} {2:.3f}".format(px,py,r)
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,137
|
s095321992
|
p00010
|
u777299405
|
1447135791
|
Python
|
Python3
|
py
|
Accepted
| 20
|
7680
| 513
|
import math
n = int(input())
for i in range(n):
x1, y1, x2, y2, x3, y3 = map(float, input().split())
a1 = x1 ** 2 - x2 ** 2 + y1 ** 2 - y2 ** 2
a2 = y1 ** 2 - y3 ** 2 + x1 ** 2 - x3 ** 2
px = ((y1 - y3) * a1 - (y1 - y2) * a2) / \
(2 * (y1 - y3) * (x1 - x2) - 2 * (y1 - y2) * (x1 - x3))
py = ((x1 - x3) * a1 - (x1 - x2) * a2) / \
(2 * (x1 - x3) * (y1 - y2) - 2 * (x1 - x2) * (y1 - y3))
r = math.hypot(x1 - px, y1 - py)
print("{0:.3f} {1:.3f} {2:.3f}".format(px, py, r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,138
|
s373464496
|
p00010
|
u529386725
|
1453716676
|
Python
|
Python3
|
py
|
Accepted
| 30
|
7568
| 553
|
N = int(input()) #num of test case
for i in range(N):
#one test case
x1, y1, x2, y2, x3, y3 = map(float, input().split())
#vertices
a = complex(x1, y1)
b = complex(x2, y2)
c = complex(x3, y3)
#make c = 0 by parallel transformation
a -= c
b -= c
z0 = abs(a)**2 * b - abs(b)**2 * a
z0 /= a.conjugate() * b - a * b.conjugate()
#inverse parallel transformation
z = z0 + c
zx = "{0:.3f}".format(z.real)
zy = "{0:.3f}".format(z.imag)
r = "{0:.3f}".format(abs(z0))
print(zx, zy, r)
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,139
|
s725716370
|
p00010
|
u512342660
|
1455035612
|
Python
|
Python
|
py
|
Accepted
| 10
|
6436
| 715
|
#! -*- coding:utf-8 -*-
import math
n = input()
for x in xrange(n):
x1,y1,x2,y2,x3,y3 = map(float,raw_input().split())
a1 = 2.0*(x2-x1)
b1 = 2.0*(y2-y1)
x12 = x1**2
y12 = y1**2
c1 = x12-x2**2+y12-y2**2
a2 = 2.0*(x3-x1)
b2 = 2.0*(y3-y1)
c2 = x12-x3**2+y12-y3**2
denom=(a1*b2-a2*b1)
# print "x1^2 : "+str(x12)
# print "y1^2 : "+str(y12)
# print "a1 : "+str(a1)
# print "b1 : "+str(b1)
# print "c1 : "+str(c1)
# print "a2 : "+str(a2)
# print "b2 : "+str(b2)
# print "c2 : "+str(c2)
# print "denom : "+str(denom)
x = (b1*c2-b2*c1)/denom
y = (c1*a2-c2*a1)/denom
r = math.sqrt((x-x1)**2+(y-y1)**2)
print "%.3f %.3f %.3f"%(x,y,r)
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,140
|
s991435630
|
p00010
|
u867824281
|
1456973282
|
Python
|
Python
|
py
|
Accepted
| 10
|
6488
| 731
|
import math
for i in range(input()):
x1,y1,x2,y2,x3,y3=map(float,raw_input().split(" "))
if y2==y1 or y3==y1:
if y2==y1:
a2=-(x3-x1)/(y3-y1)
b2=((y3+y1)-a2*(x1+x3))/2.0
a,b,c,d,e,f=1.0,0.0,(x1+x2)/2.0,-a2,1.0,b2
else:
a1=-(x2-x1)/(y2-y1)
b1=((y2+y1)-a1*(x1+x2))/2.0
a,b,c,d,e,f=-a1,1.0,b1,1.0,0.0,(x1+x3)/2.0
else:
a1=-(x2-x1)/(y2-y1)
a2=-(x3-x1)/(y3-y1)
b1=((y2+y1)-a1*(x1+x2))/2.0
b2=((y3+y1)-a2*(x1+x3))/2.0
a,b,c,d,e,f=-a1,1.0,b1,-a2,1.0,b2
py=(a*f-c*d)/(a*e-b*d)
px=(c*e-f*b)/(a*e-b*d)
r=math.sqrt((px-x1)**2 + (py-y1)**2)
print "{0:.3f} {1:.3f} {2:.3f}".format(px,py,r)
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,141
|
s506594358
|
p00010
|
u766477342
|
1457531280
|
Python
|
Python3
|
py
|
Accepted
| 30
|
7668
| 518
|
for i in range(int(input())):
x1, y1, x2, y2, x3, y3 = list(map(float,input().split()))
a = x2 - x1
b = y2 - y1
c = (x1**2 - x2**2) + (y1**2 - y2**2)
d = x3 - x1
e = y3 - y1
f = (x1**2 - x3**2) + (y1**2 - y3**2)
l = (e*c - b*f) / (a*e - b*d)
m = (c*d - f*a) / (b*d - a*e)
n = -(x1**2 + y1**2 + l*x1 + m*y1)
import math
px = round(-l/2, 3)
py = round(-m/2, 3)
r = round(math.sqrt(l**2 + m**2 - 4*n ) / 2, 3)
print("{:.3f} {:.3f} {:.3f}".format(px, py, r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,142
|
s751255268
|
p00010
|
u650459696
|
1458379386
|
Python
|
Python3
|
py
|
Accepted
| 30
|
7732
| 580
|
def circum(x1,y1,x2,y2,x3,y3):
a1 = 2 * (x2 - x1)
b1 = 2 * (y2 - y1)
c1 = x1 ** 2 - x2 ** 2 + y1 ** 2 - y2 ** 2
a2 = 2 * (x3 - x1)
b2 = 2 * (y3 - y1)
c2 = x1 ** 2 - x3 ** 2 + y1 ** 2 - y3 ** 2
X = (b1 * c2 - b2 * c1)/(a1 * b2 - a2 * b1)
Y = (c1 * a2 - c2 * a1)/(a1 * b2 - a2 * b1)
R = ((x1 - X) ** 2 + (y1 - Y) ** 2) ** 0.5
return map(lambda n: round(n,3), [X,Y,R])
N = int(input())
ans = []
for i in range(N):
ans.append(circum(*list(map(float,input().split()))))
for i in range(N):
print('{0:.3f} {1:.3f} {2:.3f}'.format(*ans[i]))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,143
|
s938879104
|
p00010
|
u148101999
|
1459229246
|
Python
|
Python
|
py
|
Accepted
| 20
|
6504
| 612
|
import sys
def calc_det(lis):
return lis[0]*lis[3]-lis[1]*lis[2]
def sq(x):
return x*x
for s in sys.stdin:
d = map(float, s.split() )
if len(d) == 1:
continue
x1,y1,x2,y2,x3,y3 = d[0],d[1],d[2],d[3],d[4],d[5]
d11 = 2*(x3-x2)
d12 = 2*(y3-y2)
d21 = 2*(x2-x1)
d22 = 2*(y2-y1)
x11 = sq(x3)-sq(x2)+sq(y3)-sq(y2)
x21 = sq(x2)-sq(x1)+sq(y2)-sq(y1)
y12 = x11
y22 = x21
x0 = calc_det( [x11,d12,x21,d22] )/calc_det( [d11,d12,d21,d22] )
y0 = calc_det( [d11,y12,d21,y22] )/calc_det( [d11,d12,d21,d22] )
r = ( (x0-x1)**2 + (y0-y1)**2 )**0.5
print "%.3f %.3f %.3f" % (x0,y0,r)
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,144
|
s520573129
|
p00010
|
u915343634
|
1459349618
|
Python
|
Python3
|
py
|
Accepted
| 30
|
7672
| 534
|
#!/usr/bin/env python
#-*- coding:utf-8 -*-
import sys
import math
n = int(input())
for data in sys.stdin:
x1, y1, x2, y2, x3, y3 = map(float, data.split())
a1 = x2 - x1
b1 = y2 - y1
a2 = x3 - x1
b2 = y3 - y1
px = (b2 * (a1 * a1 + b1 * b1) - b1 * (a2 * a2 + b2 * b2)) / (2 * (a1 * b2 - a2 * b1))
py = (a1 * (a2 * a2 + b2 * b2) - a2 * (a1 * a1 + b1 * b1)) / (2 * (a1 * b2 - a2 * b1))
r = math.sqrt(px * px + py * py)
px += x1
py += y1
print("{0:.3f} {1:.3f} {2:.3f}".format(px, py, r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,145
|
s605000142
|
p00010
|
u130979865
|
1459902454
|
Python
|
Python
|
py
|
Accepted
| 10
|
6524
| 908
|
# -*- coding: utf-8 -*-
import math
class Point_Class():
def __init__(self, x, y):
self.x = x
self.y = y
def calcCenter(p1, p2, p3):
p = ((p1.y-p2.y)*(p3.x*p3.x+p1.y*p2.y)+(p2.y-p3.y)*(p1.x*p1.x+p2.y*p3.y)+(p3.y-p1.y)*(p2.x*p2.x+p3.y*p1.y)) / ((-2)*(p1.y*(p2.x-p3.x)+p2.y*(p3.x-p1.x)+p3.y*(p1.x-p2.x)))
q = ((p1.x-p2.x)*(p3.y*p3.y+p1.x*p2.x)+(p2.x-p3.x)*(p1.y*p1.y+p2.x*p3.x)+(p3.x-p1.x)*(p2.y*p2.y+p3.x*p1.x)) / ((-2)*(p1.x*(p2.y-p3.y)+p2.x*(p3.y-p1.y)+p3.x*(p1.y-p2.y)))
return Point_Class(p, q)
def calcRadius(p, pc):
return math.sqrt(pow((p.x-pc.x), 2)+pow((p.y-pc.y), 2))
n = int(raw_input())
for i in range(n):
x1, y1, x2, y2, x3, y3 = map(float, raw_input().split())
p1 = Point_Class(x1, y1)
p2 = Point_Class(x2, y2)
p3 = Point_Class(x3, y3)
pc = calcCenter(p1, p2, p3)
r = calcRadius(p1, pc)
print "%.3f %.3f %.3f" %(pc.x, pc.y, r)
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,146
|
s023453487
|
p00010
|
u966364923
|
1460037425
|
Python
|
Python3
|
py
|
Accepted
| 30
|
7940
| 1,684
|
def perpendicular_bisector(p, q):
x = (q[0] - p[0])
y = (q[1] - p[1])
return (2 * x, 2 * y, p[0]**2-q[0]**2+p[1]**2-q[1]**2)
def gauss_jordan_elimination(Array):
# N???M??????Array
N = len(Array)
if N == 0:
return (True, Array)
else:
M = len(Array[0])
A = []
for i in range(len(Array)):
A.append(Array[i][:])
pivot = 0
L = min(N, M)
while pivot < L:
pivot_v = A[pivot][pivot]
pivot_row = pivot
for i in range(pivot + 1, L):
v = max(A[i][pivot], -A[i][pivot])
if pivot_v < v:
pivot_row = i
pivot_v = v
if pivot_row > pivot:
for i in range(M):
A[pivot][i], A[pivot_row][i] = A[pivot_row][i], A[pivot][i]
if pivot_v == 0:
return ('False', A)
inv_pivot = 1 / A[pivot][pivot]
A[pivot][pivot] = 1
for i in range(pivot + 1, M):
A[pivot][i] *= inv_pivot
for i in range(N):
if i == pivot:
continue
t = -1 * A[i][pivot]
A[i][pivot] = 0
for j in range(pivot + 1, M):
A[i][j] += t * A[pivot][j]
pivot += 1
return ('True', A)
n = int(input())
for _ in range(n):
x1, y1, x2, y2, x3, y3 = map(float, input().split())
a = list(perpendicular_bisector((x1, y1), (x2, y2)))
b = list(perpendicular_bisector((x1, y1), (x3, y3)))
c = [a, b]
state, c = gauss_jordan_elimination(c)
x = -c[0][2]
y = -c[1][2]
r = ((x - x1)**2 + (y - y1)**2)**0.5
print('{0:.3f} {1:.3f} {2:.3f}'.format(round(x, 3), round(y, 3), round(r, 3)))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,147
|
s595740441
|
p00010
|
u572790226
|
1460122876
|
Python
|
Python3
|
py
|
Accepted
| 30
|
7820
| 1,232
|
from math import sqrt
def circle(x1, y1, x2, y2, x3, y3):
if x1 == 0:
dx = 1
x1 = x1 + dx
x2 = x2 + dx
x3 = x3 + dx
else:
dx = 0
if y2 == 0:
dy = 1
y1 = y1 + dy
y2 = y2 + dy
y3 = y3 + dy
else:
dy = 0
A = [[x1, y1, 1, 1, 0, 0],[x2, y2, 1, 0, 1, 0],[x3, y3, 1, 0, 0, 1]]
# print(A)
for i in range(3):
A[0] = [x/A[0][0] for x in A[0]]
A[1] = [A[1][j] - A[1][0] * A[0][j] for j in range(6)]
A[2] = [A[2][j] - A[2][0] * A[0][j] for j in range(6)]
# print(A)
for j in range(3):
A[j] = A[j][1:] + A[j][:1]
A = A[1:] + A[:1]
# print(A)
for i in range(3):
A[i] = A[i][:3]
# print(A)
V = [-x1**2-y1**2, -x2**2-y2**2, -x3**2-y3**2]
M = [(A[i][0] * V[0] + A[i][1] * V[1] + A[i][2] * V[2]) for i in range(3)]
xcenter = -0.5 * M[0] - dx
ycenter = -0.5 * M[1] - dy
radius = sqrt((M[0]**2) /4 + (M[1]**2) /4 - M[2])
return xcenter, ycenter, radius
n = int(input())
for line in range(n):
x1, y1, x2, y2, x3, y3 = map(float, input().split())
xc, yc, ra = circle(x1, y1, x2, y2, x3, y3)
print('%.3f %.3f %.3f' % (xc, yc, ra))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,148
|
s273583003
|
p00010
|
u146816547
|
1469285358
|
Python
|
Python
|
py
|
Accepted
| 10
|
6536
| 490
|
import math
n = int(raw_input())
for i in range(n):
x1, y1, x2, y2, x3, y3 = map(float, raw_input().split())
px = ((y2 - y3)*(x1*x1 + y1*y1) + (y3 - y1)*(x2*x2 + y2*y2) + (y1 - y2)*(x3*x3 + y3*y3))/(2*(x1*(y2 - y3) + x2*(y3 - y1) + x3*(y1 - y2)))
py = ((x2 - x3)*(x1*x1 + y1*y1) + (x3 - x1)*(x2*x2 + y2*y2) + (x1 - x2)*(x3*x3 + y3*y3))/(2*(y1*(x2 - x3) + y2*(x3 - x1) + y3*(x1 - x2)))
r = math.sqrt(pow((x1 - px), 2) + pow((y1 - py), 2))
print "%.3f %.3f %.3f" % (px, py, r)
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,149
|
s974707088
|
p00010
|
u896025703
|
1469537864
|
Python
|
Python3
|
py
|
Accepted
| 20
|
7768
| 512
|
import math
def solve(a,b,c,d,e,f):
x = - (d*(f**2+e**2-b**2-a**2) + b*(-f**2-e**2) + b**2*f + a**2*f + d**2*(b-f) + c**2*(b-f)) / (c*(2*f-2*b) - 2*a*f + 2*b*e + d*(2*a-2*e))
y = (c*(f**2+e**2-b**2-a**2) + a*(-f**2-e**2) + b**2*e + a**2*e + d**2*(a-e) + c**2*(a-e)) / (c*(2*f-2*b) - 2*a*f + 2*b*e + d*(2*a - 2*e))
r = math.hypot(x-a, y-b)
return x,y,r
n = int(input())
for _ in range(n):
a,b,c,d,e,f = map(float, input().split())
x,y,r = solve(a,b,c,d,e,f)
print("{:.3f} {:.3f} {:.3f}".format(x, y, r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,150
|
s701215159
|
p00010
|
u648595404
|
1469702541
|
Python
|
Python3
|
py
|
Accepted
| 20
|
7824
| 483
|
import math
n = int(input())
for i in range(n):
x1,y1,x2,y2,x3,y3 = map(float,input().split())
a1,b1,c1 = 2*(x2-x1),2*(y2-y1), (x1**2 - x2 **2 + y1 ** 2 - y2 ** 2)
a2,b2,c2 = 2*(x3-x1), 2*(y3-y1), (x1**2 - x3 **2 + y1 ** 2 - y3 ** 2)
p1 = (b1*c2 - b2*c1)/(a1*b2 - a2*b1)
p2 = (c1*a2 - c2*a1)/(a1*b2 - a2*b1)
r = math.hypot(x1-p1, y1-p2)
temp = [p1,p2,r]
ans = map(lambda x:round(x,3),temp)
print("%03.3f %03.3f %03.3f"%(temp[0],temp[1],temp[2]))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,151
|
s034249254
|
p00010
|
u582608581
|
1470393346
|
Python
|
Python3
|
py
|
Accepted
| 30
|
7660
| 508
|
import math
def Cramer(c):
den = c[0]*c[4] - c[1]*c[3]
return [(c[2]*c[4] - c[1]*c[5]) / den, (c[0]*c[5] - c[2]*c[3]) / den]
n = eval(input())
for i in range(n):
c = [eval(item) for item in input().split()]
sol = Cramer([2*(c[0] - c[2]),\
2*(c[1] - c[3]),\
c[0]**2 + c[1]**2 - c[2]**2 - c[3]**2,\
2*(c[0] - c[4]),\
2*(c[1] - c[5]),\
c[0]**2 + c[1]**2 - c[4]**2 - c[5]**2])
r = math.sqrt((sol[0] - c[0])**2+(sol[1] - c[1])**2)
print('%.3f %.3f %.3f' %(sol[0], sol[1], r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,152
|
s794785392
|
p00010
|
u358919705
|
1471820775
|
Python
|
Python3
|
py
|
Accepted
| 30
|
7596
| 487
|
for _ in range(int(input())):
x1, y1, x2, y2, x3, y3 = map(float, input().split())
d = 2 * (x2 * y3 - x3 * y2 + x3 * y1 - x1 * y3 + x1 * y2 - x2 * y1)
px = ((y2 - y3) * (x1 ** 2 + y1 ** 2) + (y3 - y1) * (x2 ** 2 + y2 ** 2) + (y1 - y2) * (x3 ** 2 + y3 ** 2)) / d
py = -1 * ((x2 - x3) * (x1 ** 2 + y1 ** 2) + (x3 - x1) * (x2 ** 2 + y2 ** 2) + (x1 - x2) * (x3 ** 2 + y3 ** 2)) / d
print('{0:.3f} {1:.3f} {2:.3f}'.format(px, py, ((x1 - px) ** 2 + (y1 - py) ** 2) ** 0.5))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,153
|
s333881423
|
p00010
|
u358919705
|
1471821390
|
Python
|
Python3
|
py
|
Accepted
| 20
|
7664
| 289
|
for _ in[0]*int(input()):
a,d,b,e,c,f=map(float,input().split())
z=2*(b*f-c*e+c*d-a*f+a*e-b*d)
x=((e-f)*(a**2+d**2)+(f-d)*(b**2+e**2)+(d-e)*(c**2+f**2))/z
y=((c-b)*(a**2+d**2)+(a-c)*(b**2+e**2)+(b-a)*(c**2+f**2))/z
print('{0:.3f} {1:.3f} {2:.3f}'.format(x,y,((a-x)**2+(d-y)**2)**0.5))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,154
|
s466402039
|
p00010
|
u659302741
|
1477740619
|
Python
|
Python3
|
py
|
Accepted
| 30
|
7776
| 970
|
import math
def simultaneous_equasion(a, b, c, d, e, f):
"??£???????¨????"
det = a * d - b * c
a11 = d / det
a12 = - b / det
a21 = - c / det
a22 = a / det
return a11 * e + a12 * f, a21 * e + a22 * f
n = int(input())
for i in range(n):
x1, y1, x2, y2, x3, y3 = map(float, input().split())
# ?????????O??¨????????¨???OP1 ^ 2 = OP2 ^ 2
# (x - x1) ^ 2 + (y - y1) ^ 2 = (x - x2) ^ 2 + (y - y2) ^ 2
# - 2 * x * x1 + x1 ^ 2 - 2 * y * y1 + y1 ^ 2 = - 2 * x * x2 + x2 ^ 2 - 2 * y * y2 + y2 ^ 2
# 2 * (x1 - x2) * x + 2 * (y1 - y2) * y = x1 ^ 2 + y2 ^ 2 - x2 ^ 2 - y2 ^ 2
a = 2 * (x1 - x2)
b = 2 * (y1 - y2)
c = 2 * (x1 - x3)
d = 2 * (y1 - y3)
e = x1 ** 2 + y1 ** 2 - x2 ** 2 - y2 ** 2
f = x1 ** 2 + y1 ** 2 - x3 ** 2 - y3 ** 2
px, py = simultaneous_equasion(a, b, c, d, e, f)
r = math.sqrt((px - x1) ** 2 + (py - y1) ** 2)
print("%.3f %.3f %.3f" % (round(px, 3), round(py, 3), round(r, 3)))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,155
|
s667130325
|
p00010
|
u149199817
|
1478146853
|
Python
|
Python3
|
py
|
Accepted
| 30
|
7764
| 1,424
|
# -*- coding: utf-8 -*-
import sys
def length(a, b):
return ((a[0] - b[0])**2 + (a[1] - b[1])**2)**0.5
def solve_sim_equ(a, b, c, d, e, f):
'''
From Problem 0004.
This function solves following equation.
ax + by = c
dx + ey = f
'''
if a==0 and d==0:
if b==0 and e==0:
return 0., 0.
if b != 0:
return 0., c/b+0.
else:
return 0., f/e+0.
elif b==0 and e==0:
if a != 0:
return 0., d/a+0.
else:
return 0., a/d+0.
if b == 0:
a, d = d, a
b, e = e, b
c, f = f, c
g = e / b
x = (g*c - f) / (g*a - d)
y = (c - a*x) / b
return x+0., y+0.
def circumscribed_circle(x, y, z):
def get_equ_coef(p, q):
h_x = (p[0] + q[0]) / 2
h_y = (p[1] + q[1]) / 2
a = q[1] - p[1]
b = p[0] - q[0]
c = b * h_x - a * h_y
return b, -a, c
coef = get_equ_coef(x, y) + get_equ_coef(y, z)
center = solve_sim_equ(*coef)
r = length(center, x)
return center, r
def main():
N = int(input())
for i in range(N):
vs = [float(v) for v in input().split()]
a = (vs[0], vs[1])
b = (vs[2], vs[3])
c = (vs[4], vs[5])
center, r = circumscribed_circle(a, b, c)
print('{0:.3f} {1:.3f} {2:.3f}'.format(center[0], center[1], r))
if __name__ == '__main__':
main()
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,156
|
s398805927
|
p00010
|
u252368621
|
1479000288
|
Python
|
Python3
|
py
|
Accepted
| 40
|
7816
| 693
|
import math
n=int(input())
for i in range(n):
deta=[float(i) for i in input().split()]
h1=math.sqrt((deta[2]-deta[0])**2+(deta[3]-deta[1])**2)
h2=math.sqrt((deta[4]-deta[2])**2+(deta[5]-deta[3])**2)
h3=math.sqrt((deta[0]-deta[4])**2+(deta[1]-deta[5])**2)
sub=(h1+h2+h3)/2
s=math.sqrt(sub*(sub-h1)*(sub-h2)*(sub-h3))
sum=((h1*h2*h3)/s)/4
a=2*deta[2]-2*deta[0]
b=2*deta[3]-2*deta[1]
c=-(deta[0]**2+deta[1]**2-(deta[2]**2)-(deta[3]**2))
d=2*deta[4]-2*deta[2]
e=2*deta[5]-2*deta[3]
f=-(deta[2]**2+deta[3]**2-(deta[4]**2)-(deta[5]**2))
x=(e*c-b*f)/(a*e-b*d)
y=(a*f-c*d)/(a*e-b*d)
print("{0:.3f} {1:.3f} {2:.3f}".format(x,y,sum))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,157
|
s737007763
|
p00010
|
u922871577
|
1479280435
|
Python
|
Python
|
py
|
Accepted
| 10
|
6520
| 509
|
import math
n = input()
for i in xrange(n):
x1, y1, x2, y2, x3, y3 = map(float, raw_input().split())
p = ((y1-y3)*(y1**2 - y2**2 + x1**2 - x2**2) - \
(y1-y2)*(y1**2 - y3**2 + x1**2 - x3**2)) / \
(2*(y1-y3)*(x1-x2)-2*(y1-y2)*(x1-x3))
q = ((x1-x3)*(x1**2 - x2**2 + y1**2 - y2**2) - \
(x1-x2)*(x1**2 - x3**2 + y1**2 - y3**2)) / \
(2*(x1-x3)*(y1-y2)-2*(x1-x2)*(y1-y3))
print '%.3f %.3f %.3f'%(round(p,3), round(q,3), round(math.sqrt((x1-p)**2+(y1-q)**2), 3))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,158
|
s933546471
|
p00010
|
u123687446
|
1480672642
|
Python
|
Python3
|
py
|
Accepted
| 20
|
7624
| 470
|
from math import sqrt
n = int(input())
for i in range(n):
x1,y1,x2,y2,x3,y3 = list(map(float, input().split()))
c = 2*((x2 - x1)*(y3 - y1) - (y2 - y1)*(x3 - x1))
ox = ((y3 - y1)*(x2**2 - x1**2 + y2**2 - y1**2) + (y1 - y2)*(x3**2 - x1**2 + y3**2 - y1**2))/c
oy = ((x1 - x3)*(x2**2 - x1**2 + y2**2 - y1**2) + (x2 - x1)*(x3**2 - x1**2 + y3**2 - y1**2))/c
r = sqrt((x1-ox)**2+(y1-oy)**2)
print("{0:.3f} {1:.3f} {2:.3f}".format(ox+0.0, oy+0.0, r+0.0))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,159
|
s187920197
|
p00010
|
u301729341
|
1481011872
|
Python
|
Python3
|
py
|
Accepted
| 30
|
7756
| 599
|
import math
n = int(input())
for i in range(n):
x1,y1,x2,y2,x3,y3 = map(float,input().split())
a = 2*(x2 - x1)
b = 2*(y2 - y1)
c = x2**2 + y2**2 - x1**2 -y1**2
d = 2*(x3 - x1)
e = 2*(y3 - y1)
f = x3**2 + y3**2 - x1**2 -y1**2
x = (c*e - f*b)/(a*e - b*d)
y = (c*d - f*a)/(b*d - e*a)
r = math.sqrt((x1 - x)**2 + (y1 - y)**2)
x = round(x,3)
y = round(y,3)
r = round(r,3)
if x == -0.0:
x = 0.0
if y == -0.0:
y = 0.0
print("{0:.3f}".format(x),end = ' ')
print("{0:.3f}".format(y),end = ' ')
print("{0:.3f}".format(r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,160
|
s135004720
|
p00010
|
u811733736
|
1481252091
|
Python
|
Python3
|
py
|
Accepted
| 20
|
7940
| 1,598
|
from math import cos, sin, sqrt, radians, degrees, acos, fabs
if __name__ == '__main__':
epsilon = 1e-9
# ??????????????\???
num = int(input())
for i in range(num):
x1, y1, x2, y2, x3, y3 = [float(x) for x in input().split(' ')]
# ??????????????§????§???¢???cos???????±???????arccos??§?§???????????????????
a = sqrt((x1-x2)**2 + (y1-y2)**2)
b = sqrt((x2-x3)**2 + (y2-y3)**2)
c = sqrt((x1-x3)**2 + (y1-y3)**2)
cosA = (b**2+c**2-a**2)/(2*b*c)
# ???????§???????????????°?????£????????????????????\????????????????±????????????¨?????§?????????
r = a / sin(acos(cosA)) / 2
"""
??????O?????§?¨????(x, y)??¨????????¨
(x-x1)**2 + (y-y1)**2 = (x-x2)**2 + (y-y2)**2
x**2 -2*x1*x + x1**2 + y**2 -2*y1*y + y1**2 = ... -2*x2*x, x2**2, -2*y2*y, y2**2
?????¨????????¨ (-2*x1 + 2*x2)x + (-2y1 + 2*y2)y + (x1**2 + y1**2 - x2**2 - y2**2) = 0
x1, x3???????????????????§????
(-2*x1 + 2*x3)x + (-2y1 + 2*y3)y + (x1**2 + y1**2 - x3**2 - y3**2) = 0
"""
A = -2*x1 + 2*x2
B = -2*y1 + 2*y2
C = -2*x1 + 2*x3
D = -2*y1 + 2*y3
E = x1**2 + y1**2 - x2**2 - y2**2
F = x1**2 + y1**2 - x3**2 - y3**2
x = 1/(A*D-B*C) * (D*E - B*F)
y = 1/(A*D-B*C) * (-C*E + A*F)
# ?¨????????????¨?????? -0.0 ???????????´???????????¶?????? 0.0 ?????????
if fabs(x) < epsilon:
x = 0.0
if fabs(y) < epsilon:
y = 0.0
print('{0:.3f} {1:.3f} {2:.3f}'.format(-x, -y, r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,161
|
s464705283
|
p00010
|
u811733736
|
1481269169
|
Python
|
Python3
|
py
|
Accepted
| 30
|
7784
| 1,553
|
from math import sqrt, fabs
def calcu_cirucumcenter(x1, y1, x2, y2, x3, y3):
"""
??????O?????§?¨????(x, y)??¨????????¨
(x-x1)**2 + (y-y1)**2 = (x-x2)**2 + (y-y2)**2
x**2 -2*x1*x + x1**2 + y**2 -2*y1*y + y1**2 = ... -2*x2*x, x2**2, -2*y2*y, y2**2
?????¨????????¨ (-2*x1 + 2*x2)x + (-2y1 + 2*y2)y + (x1**2 + y1**2 - x2**2 - y2**2) = 0
x1, x3???????????????????§????
(-2*x1 + 2*x3)x + (-2y1 + 2*y3)y + (x1**2 + y1**2 - x3**2 - y3**2) = 0
??????????????¢????????\????????¢???????????£???????¨??????¨???????§£???
| a b | = |e|
| c d | |f|
"""
a = -2 * x1 + 2 * x2
b = -2 * y1 + 2 * y2
c = -2 * x1 + 2 * x3
d = -2 * y1 + 2 * y3
e = -1* (x1 ** 2 + y1 ** 2 - x2 ** 2 - y2 ** 2)
f = -1 * (x1 ** 2 + y1 ** 2 - x3 ** 2 - y3 ** 2)
x = 1 / (a * d - b * c) * (d * e - b * f)
y = 1 / (a * d - b * c) * (-c * e + a * f)
return x, y
if __name__ == '__main__':
epsilon = 1e-9
# ??????????????\???
num = int(input())
for i in range(num):
x1, y1, x2, y2, x3, y3 = [float(x) for x in input().split(' ')]
# ?????\????????????(??????)????±???????
x, y = calcu_cirucumcenter(x1, y1, x2, y2, x3, y3)
# ?¨????????????¨?????? -0.0 ???????????´???????????¶?????? 0.0 ?????????
if fabs(x) < epsilon:
x = 0.0
if fabs(y) < epsilon:
y = 0.0
# ????????????????????§????????¢?????????
r = sqrt((x - x1)**2 + (y - y1)**2)
print('{0:.3f} {1:.3f} {2:.3f}'.format(x, y, r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,162
|
s878433463
|
p00010
|
u919202930
|
1481303850
|
Python
|
Python3
|
py
|
Accepted
| 20
|
7716
| 694
|
n = int(input())
datasets = [0]*n
#datasets[k] == [x1k,y1k,x2k,y2k,x3k,y3k]
for i in range(0,n):
datasets[i] = list(map(float,input().split()))
for data in datasets:
x1p2=(data[0]+data[2])
x1m2=(data[0]-data[2])
x1p3=(data[0]+data[4])
x1m3=(data[0]-data[4])
y1p2=(data[1]+data[3])
y1m2=(data[1]-data[3])
y1p3=(data[1]+data[5])
y1m3=(data[1]-data[5])
x=(x1p2*x1m2*y1m3+y1p2*y1m2*y1m3-x1p3*x1m3*y1m2-y1p3*y1m3*y1m2)/(2*(x1m2*y1m3-x1m3*y1m2))
y=(y1p2*y1m2*x1m3+x1p2*x1m2*x1m3-y1p3*y1m3*x1m2-x1p3*x1m3*x1m2)/(2*(y1m2*x1m3-y1m3*x1m2))
r=((x-data[0])**2+(y-data[1])**2)**(1/2)
if x == 0.000:
x=0
if y == 0.000:
y=0
print("{0:.3f} {1:.3f} {2:.3f}".format(x,y,r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,163
|
s671909772
|
p00010
|
u957840591
|
1482465190
|
Python
|
Python3
|
py
|
Accepted
| 30
|
7704
| 1,871
|
class vertex(object):
def __init__(self,a):
self.x=a[0]
self.y=a[1]
class circle(object):
def __init__(self,p,r):
self.px=p.x
self.py=p.y
self.r=r
class triangle(object):
def __init__(self,a,b,c):
self.a=a
self.b=b
self.c=c
import math
self.ab=math.sqrt((self.a.x-self.b.x)**2+(self.a.y-self.b.y)**2)
self.bc=math.sqrt((self.b.x-self.c.x)**2+(self.b.y-self.c.y)**2)
self.ca=math.sqrt((self.c.x-self.a.x)**2+(self.c.y-self.a.y)**2)
c=self.ab
a=self.bc
b=self.ca
self.cosA=(b**2+c**2-a**2)/(2*b*c)
self.cosB=(a**2+c**2-b**2)/(2*a*c)
self.cosC=(b**2+a**2-c**2)/(2*b*a)
self.sinA=math.sqrt(1-self.cosA**2)
self.sinB=math.sqrt(1-self.cosB**2)
self.sinC=math.sqrt(1-self.cosC**2)
self.sin2A=2*self.sinA*self.cosA
self.sin2B=2*self.sinB*self.cosB
self.sin2C=2*self.sinC*self.cosC
def area(self):
import math
s=(self.ab+self.bc+self.ca)/2
S=math.sqrt(s*(s-self.ab)*(s-self.bc)*(s-self.ca))
return S
def circumscribed(self):
R=self.ab/(2*self.sinC)
px=(self.sin2A*self.a.x+self.sin2B*self.b.x+self.sin2C*self.c.x)/(self.sin2A+self.sin2B+self.sin2C)
py=(self.sin2A*self.a.y+self.sin2B*self.b.y+self.sin2C*self.c.y)/(self.sin2A+self.sin2B+self.sin2C)
px=round(px,3)
py=round(py,3)
R=round(R,3)
p=vertex((px,py))
return circle(p,R)
n=eval(input())
p1=[]
p2=[]
p3=[]
for i in range(n):
a,b,c,d,e,f=list(map(float,input().split()))
p1.append(vertex((a,b)))
p2.append(vertex((c,d)))
p3.append(vertex((e,f)))
for i in range(n):
Triangle=triangle(p1[i],p2[i],p3[i])
Circle=Triangle.circumscribed()
print('%.3f %.3f %.3f'%(Circle.px,Circle.py,Circle.r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,164
|
s272144446
|
p00010
|
u078042885
|
1483859447
|
Python
|
Python3
|
py
|
Accepted
| 20
|
7592
| 313
|
import math
for _ in range(int(input())):
x1,y1,x2,y2,x3,y3=map(float,input().split())
a,b,c=2*(x2-x1),2*(y2-y1),x1**2-x2**2+y1**2-y2**2
aa,bb,cc=2*(x3-x1),2*(y3-y1),x1**2-x3**2+y1**2-y3**2
x,y=(b*cc-bb*c)/(a*bb-aa*b),(c*aa-cc*a)/(a*bb-aa*b)
print('%.3f %.3f %.3f'%(x,y,math.hypot(x1-x,y1-y)))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,165
|
s722817816
|
p00010
|
u711765449
|
1483867438
|
Python
|
Python3
|
py
|
Accepted
| 20
|
7808
| 1,065
|
# -*- coding:utf-8 -*-
import sys
import math
def solve(x1,y1,x2,y2,x3,y3):
z1 = -1 * (x1**2 + y1**2)
z2 = -1 * (x2**2 + y2**2)
z3 = -1 * (x3**2 + y3**2)
a11,a12,a13 = x1,y1,1
a21,a22,a23 = x2,y2,1
a31,a32,a33 = x3,y3,1
det = a11*a22*a33 + a21*a32*a13 + a31*a12*a23 - a11*a32*a23 - a31*a22*a13 - a21*a12*a33
l = ((a22*a33 - a23*a32)*z1 + (a13*a32 - a12*a33)*z2 + (a12*a23 - a13*a22)*z3)/det
m = ((a23*a31 - a21*a33)*z1 + (a11*a33 - a13*a31)*z2 + (a13*a21 - a11*a23)*z3)/det
n = ((a21*a32 - a22*a31)*z1 + (a12*a31 - a11*a32)*z2 + (a11*a22 - a12*a21)*z3)/det
x,y,r = round(-l/2,3),round(-m/2,3),round(math.sqrt((l**2)/4+(m**2)/4-n),3)
sol = [x, y, r]
return sol
n,count = int(input()),0
array = []
for i in sys.stdin:
array.append(i)
count += 1
if count == n:
break
for i in range(len(array)):
x = array[i]
p = x.split()
res = solve(float(p[0]),float(p[1]),float(p[2]),float(p[3]),float(p[4]),float(p[5]))
print('{:.3f} {:.3f} {:.3f}'.format(res[0], res[1], res[2]))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,166
|
s948664191
|
p00010
|
u252414452
|
1486039485
|
Python
|
Python
|
py
|
Accepted
| 10
|
6500
| 534
|
import sys
import math
def to_f(e):
return float(e)
n = int(raw_input().rstrip())
for i in range(n):
line = raw_input().rstrip()
x1, y1, x2, y2, x3, y3 = map(to_f, line.split(" "))
a1 = 2*(x2-x1)
a2 = 2*(x3-x1)
b1 = 2*(y2-y1)
b2 = 2*(y3-y1)
c1 = x1**2-x2**2+y1**2-y2**2
c2 = x1**2-x3**2+y1**2-y3**2
xp = (b1*c2-b2*c1)/(a1*b2-a2*b1)
yp = (c1*a2-c2*a1)/(a1*b2-a2*b1)
r = round(math.sqrt((xp-x1)**2+(yp-y1)**2), 3)
#print(str(xp.format()+ " " + str(yp) + " " + str(r))
print "%.3f %.3f %.3f" % (xp, yp, r)
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,167
|
s792206888
|
p00010
|
u901080241
|
1488955612
|
Python
|
Python3
|
py
|
Accepted
| 30
|
7708
| 554
|
for i in range(int(input())):
x1, y1, x2, y2, x3, y3 = map(float, input().split())
c = (x1-x2)**2 + (y1-y2)**2
a = (x2-x3)**2 + (y2-y3)**2
b = (x3-x1)**2 + (y3-y1)**2
# 16s^2
s = 2*(a*b + b*c + c*a) - (a*a + b*b + c*c)
px = (a*(b+c-a)*x1 + b*(c+a-b)*x2 + c*(a+b-c)*x3) / s
py = (a*(b+c-a)*y1 + b*(c+a-b)*y2 + c*(a+b-c)*y3) / s
ar = a**0.5
br = b**0.5
cr = c**0.5
r = ar*br*cr / ((ar+br+cr)*(-ar+br+cr)*(ar-br+cr)*(ar+br-cr))**0.5
print("{:>.3f}".format(px),"{:>.3f}".format(py),"{:>.3f}".format(r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,168
|
s263333739
|
p00010
|
u459418423
|
1489557614
|
Python
|
Python3
|
py
|
Accepted
| 20
|
7772
| 683
|
#!/usr/bin/env python
# -*- coding:utf-8 -*-
import sys
n = int(sys.stdin.readline())
for i in range(n):
x1,y1,x2,y2,x3,y3 = list(map(float, sys.stdin.readline().split()))
a = ((x3-x2)**2 + (y3-y2)**2)**0.5
b = ((x1-x3)**2 + (y1-y3)**2)**0.5
c = ((x2-x1)**2 + (y2-y1)**2)**0.5
r = a*b*c / ((a+b+c) * (-a+b+c) * (a-b+c) * (a+b-c))**0.5
a2,b2,c2 = a**2,b**2,c**2
x = (a2*(b2+c2-a2)*x1 + b2*(c2+a2-b2)*x2 + c2*(a2+b2-c2)*x3) / \
(a2*(b2+c2-a2) + b2*(c2+a2-b2) + c2*(a2+b2-c2))
y = (a2*(b2+c2-a2)*y1 + b2*(c2+a2-b2)*y2 + c2*(a2+b2-c2)*y3) / \
(a2*(b2+c2-a2) + b2*(c2+a2-b2) + c2*(a2+b2-c2))
print("{:.3f} {:.3f} {:.3f}".format(x,y,r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,169
|
s666559415
|
p00010
|
u011621222
|
1490023766
|
Python
|
Python
|
py
|
Accepted
| 10
|
6408
| 334
|
from math import sqrt
n=input()
for i in range(n):
x1,y1,x2,y2,x3,y3=map(float,raw_input().split())
A1=2*(x2-x1)
B1=2*(y2-y1)
C1=x2**2+y2**2-x1**2-y1**2
A2=2*(x3-x2)
B2=2*(y3-y2)
C2=x3**2+y3**2-x2**2-y2**2
x=(C1*B2-C2*B1)/(A1*B2-A2*B1)
y=(A1*C2-A2*C1)/(A1*B2-A2*B1)
R=sqrt((x1-x)**2+(y1-y)**2)
print"%.3f %.3f %.3f"%(x,y,R)
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,170
|
s995075927
|
p00010
|
u797673668
|
1490621162
|
Python
|
Python3
|
py
|
Accepted
| 60
|
10188
| 661
|
import fractions
def calc(x1, y1, x2, y2):
return 2 * (x2 - x1), 2 * (y2 - y1), x2 ** 2 + y2 ** 2 - x1 ** 2 - y1 ** 2
n = int(input())
for _ in range(n):
x1, y1, x2, y2, x3, y3 = map(float, input().split())
cx1, cy1, z1 = calc(x1, y1, x2, y2)
cx2, cy2, z2 = calc(x1, y1, x3, y3)
gcd = fractions.gcd(cx1, cx2)
r1, r2 = cx2 // gcd, cx1 // gcd
dcy = r1 * cy1 - r2 * cy2
dz = r1 * z1 - r2 * z2
y = dz / dcy
try:
x = (z1 - cy1 * y) / cx1
except ZeroDivisionError:
x = (z2 - cy2 * y) / cx2
r = ((x - x1) ** 2 + (y - y1) ** 2) ** 0.5
print(*map(lambda x: '{:.3f}'.format(round(x, 3)), (x, y, r)))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,171
|
s154764030
|
p00010
|
u797673668
|
1490621316
|
Python
|
Python3
|
py
|
Accepted
| 60
|
10160
| 601
|
import fractions
def calc(x1, y1, x2, y2):
return 2 * (x2 - x1), 2 * (y2 - y1), x2 ** 2 + y2 ** 2 - x1 ** 2 - y1 ** 2
n = int(input())
for _ in range(n):
x1, y1, x2, y2, x3, y3 = map(float, input().split())
cx1, cy1, z1 = calc(x1, y1, x2, y2)
cx2, cy2, z2 = calc(x1, y1, x3, y3)
gcd = fractions.gcd(cx1, cx2)
r1, r2 = cx2 // gcd, cx1 // gcd
dcy = r1 * cy1 - r2 * cy2
dz = r1 * z1 - r2 * z2
y = dz / dcy
x = (z1 - cy1 * y) / cx1 if cx1 else (z2 - cy2 * y) / cx2
r = ((x - x1) ** 2 + (y - y1) ** 2) ** 0.5
print('{:.3f} {:.3f} {:.3f}'.format(x, y, r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,172
|
s262056243
|
p00010
|
u797673668
|
1490621524
|
Python
|
Python3
|
py
|
Accepted
| 20
|
7760
| 512
|
def calc(x1, y1, x2, y2):
return 2 * (x2 - x1), 2 * (y2 - y1), x2 ** 2 + y2 ** 2 - x1 ** 2 - y1 ** 2
n = int(input())
for _ in range(n):
x1, y1, x2, y2, x3, y3 = map(float, input().split())
cx1, cy1, z1 = calc(x1, y1, x2, y2)
cx2, cy2, z2 = calc(x1, y1, x3, y3)
dcy, dz = cx2 * cy1 - cx1 * cy2, cx2 * z1 - cx1 * z2
y = dz / dcy
x = (z1 - cy1 * y) / cx1 if cx1 else (z2 - cy2 * y) / cx2
r = ((x - x1) ** 2 + (y - y1) ** 2) ** 0.5
print('{:.3f} {:.3f} {:.3f}'.format(x, y, r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,173
|
s366237897
|
p00010
|
u546285759
|
1492401742
|
Python
|
Python3
|
py
|
Accepted
| 30
|
7496
| 579
|
n = int(input())
for _ in range(n):
x1, y1, x2, y2, x3, y3 = map(float, input().split())
a = pow(pow(x3-x2, 2) + pow(y3-y2, 2), 0.5)
b = pow(pow(x1-x3, 2) + pow(y1-y3, 2), 0.5)
c = pow(pow(x2-x1, 2) + pow(y2-y1, 2), 0.5)
cosA = (b**2+c**2-a**2) / (2*b*c)
sinA = 1-cosA**2
r = a / pow(sinA, 0.5) / 2
a, b, c = x1-x2, y1-y2, -(x1**2 + y1**2) + (x2**2 + y2**2)
d, e, f = x2-x3, y2-y3, -(x2**2 + y2**2) + (x3**2 + y3**2)
l = (c*e - b*f) / (e*a - b*d)
m = (c*d - a*f) / (b*d - a*e)
print("{0:.3f} {1:.3f} {2:.3f}".format(-l/2, -m/2, r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,174
|
s664393921
|
p00010
|
u462831976
|
1492655576
|
Python
|
Python3
|
py
|
Accepted
| 30
|
7772
| 553
|
# -*- coding: utf-8 -*-
import sys
import os
import math
N = int(input())
for i in range(N):
x1, y1, x2, y2, x3, y3 = map(float, input().split())
c = 2 * ((x2 - x1) * (y3 - y1) - (y2 - y1) * (x3 - x1))
x = ((y3 - y1) * (x2 ** 2 - x1 ** 2 + y2 ** 2 - y1 ** 2) + (y1 - y2) * (x3 ** 2 - x1 ** 2 + y3 ** 2 - y1 ** 2)) / c
y = ((x1 - x3) * (x2 ** 2 - x1 ** 2 + y2 ** 2 - y1 ** 2) + (x2 - x1) * (x3 ** 2 - x1 ** 2 + y3 ** 2 - y1 ** 2)) / c
r = math.sqrt((x1 - x) ** 2 + (y1 - y) ** 2)
print("{:.3f} {:.3f} {:.3f}".format(x, y, r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,175
|
s374212381
|
p00010
|
u187606290
|
1493474295
|
Python
|
Python3
|
py
|
Accepted
| 20
|
7720
| 568
|
import math
n = int(input())
for i in range(n):
x1, y1, x2, y2, x3, y3 = map(float, input().split()) # Get variables
a = 2 * (x2 - x1)
b = 2 * (y2 - y1)
c = math.pow(x2, 2) + math.pow(y2, 2) - math.pow(x1, 2) - math.pow(y1, 2)
d = 2 * (x3 - x1)
e = 2 * (y3 - y1)
f = math.pow(x3, 2) + math.pow(y3, 2) - math.pow(x1, 2) - math.pow(y1, 2)
px = (c * e - b * f) / (a * e - b * d)
py = (a * f - c * d) / (a * e - b * d)
r = math.sqrt(math.pow(x1 - px, 2) + math.pow(y1 - py, 2))
print('{:.3f}'.format(px) + ' ' + '{:.3f}'.format(py) + ' ' + '{:.3f}'.format(r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,176
|
s052458025
|
p00010
|
u519227872
|
1494010374
|
Python
|
Python3
|
py
|
Accepted
| 20
|
7632
| 764
|
from math import sqrt
n = int(input())
for i in range(n):
l = input()
x1,y1,x2,y2,x3,y3=map(float,l.split(' '))
a_2 = (x1 - x2)**2 + (y1 - y2)**2
b_2 = (x2 - x3)**2 + (y2 - y3)**2
c_2 = (x3 - x1)**2 + (y3 - y1)**2
cos_a_2 = (b_2 + c_2 - a_2)**2/(4* b_2 * c_2)
sin_a_2 = 1 - cos_a_2
r = round(sqrt(a_2/sin_a_2)/2,3)
a = (x1**2 - x3**2 + y1**2 - y3**2)*(x2 - x1)
b = (x1**2 - x2**2 + y1**2 - y2**2)*(x3 - x1)
c = (y2 - y1)*(x3 - x1)
d = (y3 - y1)*(x2 - x1)
py = round((a-b)/(c-d)/2,3)
a = (x1**2 - x3**2 + y1**2 - y3**2)*(y2 - y1)
b = (x1**2 - x2**2 + y1**2 - y2**2)*(y3 - y1)
c = (x2 - x1)*(y3 - y1)
d = (x3 - x1)*(y2 - y1)
px = round((a-b)/(c-d)/2,3)
print('%.3f %.3f %.3f' %(px, py, r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,177
|
s903524426
|
p00010
|
u519227872
|
1494011136
|
Python
|
Python3
|
py
|
Accepted
| 30
|
7672
| 772
|
from math import sqrt
n = int(input())
for i in range(n):
l = input()
x1,y1,x2,y2,x3,y3=map(float,l.split(' '))
a_2 = (x1 - x2)**2 + (y1 - y2)**2
b_2 = (x2 - x3)**2 + (y2 - y3)**2
c_2 = (x3 - x1)**2 + (y3 - y1)**2
cos_a_2 = (b_2 + c_2 - a_2)**2/(4* b_2 * c_2)
sin_a_2 = 1 - cos_a_2
r = round(sqrt(a_2/sin_a_2)/2,3)
a = (x1**2 - x3**2 + y1**2 - y3**2)*(x2 - x1)
b = (x1**2 - x2**2 + y1**2 - y2**2)*(x3 - x1)
c = (y2 - y1)*(x3 - x1)
d = (y3 - y1)*(x2 - x1)
py = round((a-b)/(c-d)/2,3) + 0
a = (x1**2 - x3**2 + y1**2 - y3**2)*(y2 - y1)
b = (x1**2 - x2**2 + y1**2 - y2**2)*(y3 - y1)
c = (x2 - x1)*(y3 - y1)
d = (x3 - x1)*(y2 - y1)
px = round((a-b)/(c-d)/2,3) + 0
print('%.3f %.3f %.3f' %(px, py, r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,178
|
s608076616
|
p00010
|
u618637847
|
1494896173
|
Python
|
Python3
|
py
|
Accepted
| 20
|
7708
| 485
|
import math
n = int(input())
for i in range(n):
x1,y1,x2,y2,x3,y3 = map(float,input().split())
a1,b1,c1 = 2*(x2-x1),2*(y2-y1), (x1**2 - x2 **2 + y1 ** 2 - y2 ** 2)
a2,b2,c2 = 2*(x3-x1), 2*(y3-y1), (x1**2 - x3 **2 + y1 ** 2 - y3 ** 2)
p1 = (b1*c2 - b2*c1)/(a1*b2 - a2*b1)
p2 = (c1*a2 - c2*a1)/(a1*b2 - a2*b1)
r = math.hypot(x1-p1, y1-p2)
temp = [p1,p2,r]
ans = map(lambda x:round(x,3),temp)
print("%03.3f %03.3f %03.3f"%(temp[0],temp[1],temp[2]))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,179
|
s778033033
|
p00010
|
u618637847
|
1494896351
|
Python
|
Python3
|
py
|
Accepted
| 20
|
7624
| 539
|
# coding: utf-8
# Here your code !
import math
num = int(input())
for i in range(num):
x1,y1,x2,y2,x3,y3 = map(float,input().split())
a1 = 2*(x2-x1)
b1 = 2*(y2-y1)
c1 = (x1*x1 - x2*x2 + y1*y1 - y2*y2)
a2 = 2*(x3-x1)
b2 = 2*(y3-y1)
c2 = (x1*x1 - x3*x3 + y1*y1 - y3*y3)
p1 = (b1*c2 - b2*c1) / (a1*b2 - a2*b1)
p2 = (c1*a2 - c2*a1) / (a1*b2 - a2*b1)
r = math.hypot(x1-p1, y1-p2)
temp = [p1,p2,r]
ans = map(lambda x:round(x,3),temp)
print("%03.3f %03.3f %03.3f"%(temp[0],temp[1],temp[2]))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,180
|
s129007203
|
p00010
|
u922489088
|
1496133651
|
Python
|
Python3
|
py
|
Accepted
| 20
|
7608
| 512
|
import sys
import math
n = int(sys.stdin.readline().rstrip())
for i in range(n):
x1,y1,x2,y2,x3,y3 = map(float, sys.stdin.readline().rstrip().split(' '))
p = ((y1-y3)*(y1**2-y2**2+x1**2-x2**2)-(y1-y2)*(y1**2-y3**2+x1**2-x3**2)) / (2*(y1-y3)*(x1-x2)-2*(y1-y2)*(x1-x3))
q = ((x1-x3)*(x1**2-x2**2+y1**2-y2**2)-(x1-x2)*(x1**2-x3**2+y1**2-y3**2)) / (2*(x1-x3)*(y1-y2)-2*(x1-x2)*(y1-y3))
r = math.sqrt((p-x1)**2 + (q-y1)**2)
print("{:0.3f} {:0.3f} {:0.3f}".format(round(p,3),round(q,3),round(r,3)))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,181
|
s167038521
|
p00010
|
u905313459
|
1496315524
|
Python
|
Python3
|
py
|
Accepted
| 20
|
7500
| 434
|
p = int(input())
for i in range(p):
x1, y1, x2, y2, x3, y3 = map(float, input().split(" "))
xa, ya, xb, yb = x2-x1, y2-y1, x3-x1, y3-y1
a = complex(xa, ya)
b = complex(xb, yb)
z0 = abs(a) ** 2 * b - abs(b) **2 * a
z0 /= a.conjugate() * b - a * b.conjugate()
z = z0 + complex(x1, y1)
zx = "{0:.3f}".format(z.real)
zy = "{0:.3f}".format(z.imag)
r = "{0:.3f}".format(abs(z0))
print(zx, zy, r)
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,182
|
s768014470
|
p00010
|
u354053070
|
1501910798
|
Python
|
Python3
|
py
|
Accepted
| 30
|
8004
| 842
|
from math import acos
from math import sin
def ang(ax, ay, ox, oy, bx, by):
oax, oay = ax - ox, ay - oy
obx, oby = bx - ox, by - oy
r1, r2 = oax ** 2 + oay ** 2, obx ** 2 + oby ** 2
return acos((oax * obx + oay * oby) / (r1 * r2) ** 0.5)
def circumcircle(x1, y1, x2, y2, x3, y3):
s2A = sin(2 * ang(x3, y3, x1, y1, x2, y2))
s2B = sin(2 * ang(x1, y1, x2, y2, x3, y3))
s2C = sin(2 * ang(x2, y2, x3, y3, x1, y1))
px = (s2A * x1 + s2B * x2 + s2C * x3) / (s2A + s2B + s2C) + 0.
py = (s2A * y1 + s2B * y2 + s2C * y3) / (s2A + s2B + s2C) + 0.
r = (((x2 - x3) ** 2 + (y2 - y3) ** 2) ** 0.5) / (2 * sin(ang(x2, y2, x1, y1, x3, y3))) + 0.
return px, py, r
n = int(input())
for i in range(n):
print("{0[0]:.3f} {0[1]:.3f} {0[2]:.3f}".format(
circumcircle(*tuple(map(float, input().split())))))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,183
|
s434711363
|
p00010
|
u957021183
|
1504763177
|
Python
|
Python3
|
py
|
Accepted
| 20
|
7844
| 996
|
# Aizu Problem 0010: Circumscribed Circle of a Triangle
#
import sys, math, os
# read input:
PYDEV = os.environ.get('PYDEV')
if PYDEV=="True":
sys.stdin = open("sample-input.txt", "rt")
def circumscribed_circle(x1, y1, x2, y2, x3, y3):
d = 2 * (x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2))
px = ( (x1**2 + y1**2) * (y2 - y3) + (x2**2 + y2**2) * (y3 - y1) + (x3**2 + y3**2) * (y1 - y2) ) / d
py = ( (x1**2 + y1**2) * (x3 - x2) + (x2**2 + y2**2) * (x1 - x3) + (x3**2 + y3**2) * (x2 - x1) ) / d
a = math.sqrt((x1 - x2)**2 + (y1 - y2)**2)
b = math.sqrt((x1 - x3)**2 + (y1 - y3)**2)
c = math.sqrt((x2 - x3)**2 + (y2 - y3)**2)
s = (a + b + c) / 2
A = math.sqrt(s * (s - a) * (s - b) * (s - c))
r = a * b * c / (4 * A)
return px, py, r
N = int(input())
for k in range(N):
x1, y1, x2, y2, x3, y3 = [float(_) for _ in input().split()]
px, py, r = circumscribed_circle(x1, y1, x2, y2, x3, y3)
print("%.3f %.3f %.3f" % (px, py, r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,184
|
s051562628
|
p00010
|
u299798926
|
1505355567
|
Python
|
Python3
|
py
|
Accepted
| 30
|
7772
| 433
|
import math
a=int(input())
for i in range(a):
x1,y1,x2,y2,x3,y3=[float(j) for j in input().split()]
A=x1**2+y1**2-x2**2-y2**2
B=x2**2+y2**2-x3**2-y3**2
x12=x1-x2
x23=x2-x3
y12=y1-y2
y23=y2-y3
x=(y23*A-y12*B)/(2*(x12*y23-x23*y12))
if (y12==0):
y=(B-2*x23*x)/(2*y23)
else:
y=(A-2*x12*x)/(2*y12)
r=math.sqrt((x1-x)**2+(y1-y)**2)
print('{:.3f} {:.3f} {:.3f}'.format(x,y,r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,185
|
s075153499
|
p00010
|
u395334793
|
1505644037
|
Python
|
Python3
|
py
|
Accepted
| 20
|
7624
| 308
|
for _ in range(int(input())):
a,d,b,e,c,f=map(float,input().split())
z=2*(b*f-c*e+c*d-a*f+a*e-b*d)
x=((e-f)*(a**2+d**2)+(f-d)*(b**2+e**2)+(d-e)*(c**2+f**2))/z
y=((c-b)*(a**2+d**2)+(a-c)*(b**2+e**2)+(b-a)*(c**2+f**2))/z
print('{0:.3f} {1:.3f} {2:.3f}'.format(x,y,((a-x)**2+(d-y)**2)**0.5))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,186
|
s779675306
|
p00010
|
u933096856
|
1505853684
|
Python
|
Python3
|
py
|
Accepted
| 40
|
7724
| 436
|
def pp(x):
if x==0:
x=0
return "{0:.3f}".format(round(x,3))
n=int(input())
for i in range(n):
x1,y1,x2,y2,x3,y3=map(float, input().split())
a=2*(x2-x1)
b=2*(y2-y1)
c=( x2**2 + y2**2 ) - ( x1**2 + y1**2 )
d=2*(x3-x1)
e=2*(y3-y1)
f=( x3**2 + y3**2 ) - ( x1**2 + y1**2 )
x=(c*e-b*f)/(a*e-b*d)
y=(a*f-c*d)/(a*e-b*d)
r=( (x-x1)**2 + (y-y1)**2 )**0.5
print(pp(x), pp(y), pp(r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,187
|
s751225048
|
p00010
|
u072398496
|
1507685881
|
Python
|
Python
|
py
|
Accepted
| 20
|
6684
| 522
|
def line(grad, x, y):
return [grad, y - grad * x]
def intersection(a, b, c, d):
return [-(b-d)/(a-c), -(b-d)/(a-c)*a+b]
n = input()
for i in range(n):
x1, y1, x2, y2, x3, y3 = map(float, raw_input().split())
a, b = line(-1 / ((y1 - y2) / (x1 - x2 + 0.000000001) + 0.000000001), (x1 + x2) / 2, (y1 + y2) / 2)
c, d = line(-1 / ((y3 - y2) / (x3 - x2 + 0.000000001) + 0.000000001), (x3 + x2) / 2, (y3 + y2) / 2)
px, py = intersection(a, b, c, d)
print "%.3f %.3f %.3f" % (px, py, ((px - x1)**2 + (py - y1)**2)**0.5)
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,188
|
s784075347
|
p00010
|
u548155360
|
1512395192
|
Python
|
Python3
|
py
|
Accepted
| 20
|
5716
| 3,058
|
# coding=utf-8
import math
if __name__ == '__main__':
n = int(input())
for i in range(n):
x1, y1, x2, y2, x3, y3 = map(float, input().split())
points_list = [[x1, y1], [x2, y2], [x3, y3]]
points_list.sort()
if points_list[0][0] == points_list[1][0]:
py = (points_list[0][1] + points_list[1][1])/2
if points_list[2][1] == points_list[0][1]:
px = (points_list[0][0] + points_list[2][0])/2
else:
a2_s = (points_list[2][1] - points_list[0][1])/(points_list[2][0] - points_list[0][0])
a2 = -1/a2_s
m13x = (points_list[0][0] + points_list[2][0])/2
m13y = (points_list[0][1] + points_list[2][1])/2
b2 = m13y - a2*m13x
px = (py - b2)/a2
elif points_list[1][0] == points_list[2][0]:
py = (points_list[1][1] + points_list[2][1])/2
if points_list[2][1] == points_list[0][1]:
px = (points_list[0][0]+points_list[2][0])/2
else:
a2_s = (points_list[2][1] - points_list[0][1])/(points_list[2][0] - points_list[0][0])
a2 = -1/a2_s
m13x = (points_list[0][0] + points_list[2][0])/2
m13y = (points_list[0][1] + points_list[2][1])/2
b2 = m13y - a2*m13x
px = (py - b2)/a2
elif points_list[0][1] == points_list[1][1]:
px = (points_list[0][0] + points_list[1][0])/2
a2_s = (points_list[2][1] - points_list[0][1]) / (points_list[2][0] - points_list[0][0])
a2 = -1 / a2_s
m13x = (points_list[0][0] + points_list[2][0]) / 2
m13y = (points_list[0][1] + points_list[2][1]) / 2
b2 = m13y - a2 * m13x
py = a2*px + b2
elif points_list[0][1] == points_list[2][1]:
px = (points_list[0][0] + points_list[2][0])/2
a1_s = (points_list[1][1] - points_list[0][1]) / (points_list[1][0] - points_list[0][0])
a1 = -1 / a1_s
m12x = (points_list[0][0] + points_list[1][0]) / 2
m12y = (points_list[0][1] + points_list[1][1]) / 2
b1 = m12y - a1 * m12x
py = a1 * px + b1
else:
a1_s = (points_list[1][1] - points_list[0][1])/(points_list[1][0] - points_list[0][0])
a1 = -1/a1_s
a2_s = (points_list[2][1] - points_list[0][1])/(points_list[2][0] - points_list[0][0])
a2 = -1/a2_s
m12x = (points_list[0][0] + points_list[1][0]) / 2
m12y = (points_list[0][1] + points_list[1][1]) / 2
m13x = (points_list[0][0] + points_list[2][0]) / 2
m13y = (points_list[0][1] + points_list[2][1]) / 2
b1 = m12y - a1 * m12x
b2 = m13y - a2 * m13x
px = (b2 - b1)/(a1 - a2)
py = a1*px + b1
r = math.sqrt(math.pow((px-points_list[0][0]), 2) + math.pow((py-points_list[0][1]), 2))
print('{0:.3f} {1:.3f} {2:.3f}'.format(px, py, r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,189
|
s872566194
|
p00010
|
u203261375
|
1513003324
|
Python
|
Python3
|
py
|
Accepted
| 30
|
5664
| 460
|
n = int(input())
for _ in range(n):
x1, y1, x2, y2, x3, y3 = map(float, input().split())
px = ((y1-y3) * (y1**2-y2**2+x1**2-x2**2) -
(y1-y2) * (y1**2-y3**2+x1**2-x3**2)) / (2*(y1-y3)*(x1-x2)-2*(y1-y2)*(x1-x3))
py = ((x1-x3) * (x1**2-x2**2+y1**2-y2**2) -
(x1-x2) * (x1**2-x3**2+y1**2-y3**2)) / (2*(x1-x3)*(y1-y2)-2*(x1-x2)*(y1-y3))
r = ((x1 - px)**2 + (y1 - py)**2)**0.5
print('{0:.3f} {1:.3f} {2:.3f}'.format(px, py, r))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,190
|
s420506779
|
p00010
|
u024715419
|
1514430596
|
Python
|
Python3
|
py
|
Accepted
| 20
|
5684
| 484
|
import math
n = int(input())
for i in range(n):
x1, y1, x2, y2, x3, y3 = map(float, input().split())
s = 0.5*((x1-x3)*(y2-y3) - (x2-x3)*(y1-y3))
a = (x2-x3)**2 + (y2-y3)**2
b = (x1-x3)**2 + (y1-y3)**2
c = (x2-x1)**2 + (y2-y1)**2
rx = (a*(b+c-a)*x1 + b*(c+a-b)*x2 + c*(a+b-c)*x3)/(16*s**2)
ry = (a*(b+c-a)*y1 + b*(c+a-b)*y2 + c*(a+b-c)*y3)/(16*s**2)
r = math.sqrt((rx-x1)**2 + (ry-y1)**2)
print( "{0:.3f} {1:.3f} {2:.3f}".format(rx+0, ry+0, r+0))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,191
|
s966441617
|
p00010
|
u764789069
|
1514696958
|
Python
|
Python
|
py
|
Accepted
| 10
|
4792
| 827
|
n = int(raw_input())
i = 0
while (i < n):
x1,y1,x2,y2,x3,y3=map(float,raw_input().split())
m1,m2=(x1+x2) / 2, (y1+y2) / 2
n1,n2=(x1+x3) / 2, (y1+y3) / 2
if y1==y2:
a = 1
b = 0
c = m1
elif x1==x2:
a = 0
b = 1
c = m2
else:
a = (x2-x1) / (y2-y1)
b = 1
c = m2+a*m1
if y1==y3:
d = 1
e = 0
f = n1
elif x1==x3:
d = 0
e = 1
f = n2
else:
d = (x3-x1) / (y3-y1)
e = 1
f = n2+d*n1
if a*d-b*c==0:
print "not exist answer"
else:
x = (float((c*e-b*f)) / (a*e-b*d))+0
y = (float((a*f-c*d)) / (a*e-b*d))+0
print ('%.3f' % round(x,3)), ('%.3f' % round(y,3)), ('%.3f' % round(((((x - x1)**2+(y-y1)**2)**0.5)),3))
i += 1
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,192
|
s891334405
|
p00010
|
u273843182
|
1514981609
|
Python
|
Python3
|
py
|
Accepted
| 20
|
5672
| 432
|
import math
N = int(input())
for i in range(N):
x1,y1,x2,y2,x3,y3 = map(float,input().split())
x =((y1-y3)*(y1*y1 -y2*y2 +x1*x1 -x2*x2) -(y1-y2)*(y1*y1 -y3*y3 +x1*x1 -x3*x3)) / (2*((y1-y3)*(x1-x2)-(y1-y2)*(x1-x3)))
y =((x1-x3)*(x1*x1 -x2*x2 +y1*y1 -y2*y2) -(x1-x2)*(x1*x1 -x3*x3 +y1*y1 -y3*y3)) / (2*((x1-x3)*(y1-y2)-(x1-x2)*(y1-y3)))
r = (x-x1)*(x-x1)+(y-y1)*(y-y1)
print("{0:.3f} {1:.3f} {2:.3f}".format(x,y,math.sqrt(r)))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,193
|
s516115277
|
p00010
|
u546285759
|
1516346062
|
Python
|
Python3
|
py
|
Accepted
| 20
|
5684
| 598
|
n = int(input())
for _ in range(n):
x1, y1, x2, y2, x3, y3 = map(float, input().split())
a = pow((x3-x2) ** 2 + (y3-y2) ** 2, 0.5)
b = pow((x3-x1) ** 2 + (y3-y1) ** 2, 0.5)
c = pow((x1-x2) ** 2 + (y1-y2) ** 2, 0.5)
cosA = (b**2 + c**2 - a**2) / (2*b*c)
sinA = pow(1 - cosA**2, 0.5)
R = a / sinA / 2
a, b, c = x1-x2, y1-y2, -(x1**2 + y1**2) + (x2**2 + y2**2)
d, e, f = x2-x3, y2-y3, -(x2**2 + y2**2) + (x3**2 + y3**2)
l = (c*e - b*f) / (e*a - b*d)
m = (c*d - a*f) / (b*d - a*e)
l, m = l*-0.5, m*-0.5
print("{:.3f} {:.3f} {:.3f}".format(l, m, R))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,194
|
s275837697
|
p00010
|
u043254318
|
1516383312
|
Python
|
Python3
|
py
|
Accepted
| 20
|
5688
| 445
|
import math
N = int(input())
for l in range(N):
x1,y1,x2,y2,x3,y3 = [float(i) for i in input().split()]
# ax + by = e
# cx + dy = f
a,b,c = x1-x2, y1-y2, (x1-x2)*(x1+x2)/2 + (y1-y2)*(y1+y2)/2
d,e,f = x1-x3, y1-y3, (x1-x3)*(x1+x3)/2 + (y1-y3)*(y1+y3)/2
X = (c*e-f*b)/(a*e-b*d)
Y = (f*a-c*d)/(a*e-b*d)
R = math.sqrt((X-x1)*(X-x1)+(Y-y1)*(Y-y1))
print(format(X, '.3f'), format(Y, '.3f'), format(R, '.3f'))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,195
|
s311357839
|
p00010
|
u150984829
|
1516782203
|
Python
|
Python3
|
py
|
Accepted
| 20
|
5684
| 285
|
for _ in[0]*int(input()):
a,b,c,d,e,f=map(float,input().split())
x=((a*a+b*b)*(d-f)+(c*c+d*d)*(f-b)+(e*e+f*f)*(b-d))/2/(a*(d-f)+c*(f-b)+e*(b-d))
y=((a*a+b*b)*(c-e)+(c*c+d*d)*(e-a)+(e*e+f*f)*(a-c))/2/(b*(c-e)+d*(e-a)+f*(a-c))
print(f"{x:.3f} {y:.3f} {((x-a)**2+(y-b)**2)**.5:.3f}")
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,196
|
s265666860
|
p00010
|
u150984829
|
1516782465
|
Python
|
Python3
|
py
|
Accepted
| 20
|
5672
| 283
|
for _ in[0]*int(input()):
a,b,c,d,e,f=map(float,input().split())
x=((a*a+b*b)*(d-f)+(c*c+d*d)*(f-b)+(e*e+f*f)*(b-d))/2/(a*(d-f)+c*(f-b)+e*(b-d))
y=((a*a+b*b)*(c-e)+(c*c+d*d)*(e-a)+(e*e+f*f)*(a-c))/2/(b*(c-e)+d*(e-a)+f*(a-c))
print('%.3f %.3f %.3f'%(x,y,((x-a)**2+(y-b)**2)**.5))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,197
|
s766615770
|
p00010
|
u150984829
|
1516782566
|
Python
|
Python3
|
py
|
Accepted
| 20
|
5668
| 266
|
for _ in[0]*int(input()):
a,b,c,d,e,f=map(float,input().split())
s,t,u=a*a+b*b,c*c+d*d,e*e+f*f
x=(s*(d-f)+t*(f-b)+u*(b-d))/2/(a*(d-f)+c*(f-b)+e*(b-d))
y=(s*(c-e)+t*(e-a)+u*(a-c))/2/(b*(c-e)+d*(e-a)+f*(a-c))
print('%.3f %.3f %.3f'%(x,y,((x-a)**2+(y-b)**2)**.5))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,198
|
s920772895
|
p00010
|
u150984829
|
1516783308
|
Python
|
Python3
|
py
|
Accepted
| 20
|
5672
| 274
|
import math
for _ in[0]*int(input()):
a,b,c,d,e,f=map(float,input().split())
s,t,u=a*a+b*b,c*c+d*d,e*e+f*f
x=(s*(d-f)+t*(f-b)+u*(b-d))/2/(a*(d-f)+c*(f-b)+e*(b-d))
y=(s*(c-e)+t*(e-a)+u*(a-c))/2/(b*(c-e)+d*(e-a)+f*(a-c))
print('%.3f %.3f %.3f'%(x,y,math.hypot(x-a,y-b)))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,199
|
s820563602
|
p00010
|
u069727578
|
1520044280
|
Python
|
Python
|
py
|
Accepted
| 10
|
4768
| 368
|
from math import sqrt
n=input()
for i in range(n):
x1,y1,x2,y2,x3,y3=map(float,raw_input().split())
A1=2*(x2-x1)
B1=2*(y2-y1)
C1=x2**2+y2**2-x1**2-y1**2
A2=2*(x3-x2)
B2=2*(y3-y2)
C2=x3**2+y3**2-x2**2-y2**2
x=(C1*B2-C2*B1)/(A1*B2-A2*B1)
y=(A1*C2-A2*C1)/(A1*B2-A2*B1)
R=sqrt((x1-x)**2+(y1-y)**2)
print"%.3f %.3f %.3f"%(x,y,R)
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,200
|
s029881406
|
p00010
|
u166871988
|
1523704484
|
Python
|
Python3
|
py
|
Accepted
| 20
|
5688
| 425
|
import math
n=int(input())
for i in range(n):
x1,y1,x2,y2,x3,y3=[float(i) for i in input().split()]
A=math.hypot(x2-x3,y2-y3)**2
B=math.hypot(x1-x3,y1-y3)**2
C=math.hypot(x1-x2,y1-y2)**2
t1=A*(B+C-A)
t2=B*(A+C-B)
t3=C*(A+B-C)
px=(t1*x1+t2*x2+t3*x3)/(t1+t2+t3)
py=(t1*y1+t2*y2+t3*y3)/(t1+t2+t3)
r=math.hypot(px-x1,py-y1)
print("%.3f %.3f %.3f"%(round(px,3),round(py,3),round(r,3)))
|
p00010
|
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<H1>Circumscribed Circle of A Triangle.</H1>
<p>
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.
</p>
<H2>Input</H2>
<p>
Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:<br/>
<br/>
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$<br/>
<br/>
in a line. All the input are real numbers.
</p>
<H2>Output</H2>
<p>
For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.
</p>
<h2>Constraints</h2>
<ul>
<li>$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$</li>
<li>$ n \leq 20$</li>
</ul>
<H2>Sample Input</H2>
<pre>
1
0.0 0.0 2.0 0.0 2.0 2.0
</pre>
<H2>Output for the Sample Input</H2>
<pre>
1.000 1.000 1.414
</pre>
|
1
0.0 0.0 2.0 0.0 2.0 2.0
|
1.000 1.000 1.414
| 5,201
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.