Problem:


Koch Curve

Write a program which reads an integer n and draws a Koch curve based on recursive calles of depth n.

The Koch curve is well known as a kind of fractals.

You can draw a Koch curve in the following algorithm:

Divide a given segment (p1, p2) into three equal segments.

Replace the middle segment by the two sides of an equilateral triangle (s, u, t) of the same length as the segment.

Repeat this procedure recursively for new segments (p1, s), (s, u), (u, t), (t, p2).

You should start (0, 0), (100, 0) as the first segment.

Input

An integer n is given.

Output

Print each point (x, y) of the Koch curve. Print a point in a line. You should start the point(0, 0), which is the endpoint of the first segment and end with the point (100, 0), the other endpoint so that you can draw the Koch curve as an unbroken line. Each solution should be given as a decimal with an arbitrary number of fractional digits, and with an absolute error of at most 10-4.

Constraints

 0 ≤ n ≤ 6

Sample Input 1

1

Sample Output 1

0.00000000 0.00000000
33.33333333 0.00000000
50.00000000 28.86751346
66.66666667 0.00000000
100.00000000 0.00000000

Sample Input 2

2

Sample Output 2

0.00000000 0.00000000
11.11111111 0.00000000
16.66666667 9.62250449
22.22222222 0.00000000
33.33333333 0.00000000
38.88888889 9.62250449
33.33333333 19.24500897
44.44444444 19.24500897
50.00000000 28.86751346
55.55555556 19.24500897
66.66666667 19.24500897
61.11111111 9.62250449
66.66666667 0.00000000
77.77777778 0.00000000
83.33333333 9.62250449
88.88888889 0.00000000
100.00000000 0.00000000

Notes



Sample input:
1


Sample output:
0.00000000 0.00000000
33.33333333 0.00000000
50.00000000 28.86751346
66.66666667 0.00000000
100.00000000 0.00000000

Submission status: Accepted

Solution code:
import cmath
def f():
 global d
 p=[]
 for i in range(len(d)-1):
  a,b=d[i],d[i+1]
  r=(b-a)/3
  p+=[a,a+r,a+r+r*cmath.rect(1,cmath.pi/3),b-r]
 d=p+[d[-1]]
d=[0j,100+0j]
for _ in[0]*int(input()):f()
for e in d:print(e.real,e.imag)

Submission status: Accepted

Solution code:
import cmath
def f():
 global d
 p=[]
 for i in range(len(d)-1):
  a,b=d[i],d[i+1]
  r=(b-a)/3
  p+=[a,a+r,a+r+r*(1+3**.5*1j)/2,b-r]
 d=p+[d[-1]]
d=[0j,100+0j]
for _ in[0]*int(input()):f()
for e in d:print(e.real,e.imag)

Submission status: Accepted

Solution code:
def f():
 global d
 p=[]
 for i in range(len(d)-1):
  a,b=d[i],d[i+1]
  r=(b-a)/3
  p+=[a,a+r,a+r+r*(.5+3**.5*.5j),b-r]
 d=p+[d[-1]]
d=[0j,100+0j]
for _ in[0]*int(input()):f()
for e in d:print(e.real,e.imag)

Submission status: Accepted

Solution code:
def f():
 global d
 p=[]
 for i in range(len(d)-1):
  a,b=d[i],d[i+1]
  r=(b-a)/3
  p+=[a,a+r,(a+b+r*1j*3**.5)/2,b-r]
 d=p+[d[-1]]
d=[0j,100+0j]
for _ in[0]*int(input()):f()
for e in d:print(e.real,e.imag)

Submission status: Accepted

Solution code:
def f():
 global d
 p=[d[0]]
 for i in range(len(d)-1):
  a,b=d[i],d[i+1]
  r=(b-a)/3
  p+=[a+r,a+r+r*(1+3**.5*1j)/2,b-r,b]
 d=p
d=[0j,100+0j]
for _ in[0]*int(input()):f()
for e in d:print(e.real,e.imag)

Submission status: Accepted

Solution code:
d=[0j,100+0j]
for _ in[0]*int(input()):
 p=[d[0]]
 for i in range(len(d)-1):
  a,b=d[i],d[i+1]
  r=(b-a)/3
  p+=[a+r,a+r+r*(1+3**.5*1j)/2,b-r,b]
 d=p
for e in d:print(e.real,e.imag)

Submission status: Accepted

Solution code:
#!/usr/bin/python3
# -*- coding: utf-8 -*-

import sys
import math

DEG60 = math.pi/3

def repl_edge(n, edges):
    # print('n=',n, 'edges=', len(edges))
    if n == 0:
        return edges
    new_list = list()
    for edge in edges:  # single tupple
        p1 = edge[0]
        p2 = edge[1]
        p_angle = edge[2]
        s = ((p1[0]*2+p2[0])/3, (p1[1]*2+p2[1])/3)
        t = ((p1[0]+p2[0]*2)/3, (p1[1]+p2[1]*2)/3)
        r = abs((t[0]-s[0])**2 + (t[1]-s[1])**2) ** 0.5
        angle = p_angle + DEG60
        u = (s[0] + math.cos(angle)*r, s[1] + math.sin(angle)*r)
        # print('r=', r, 'u=', u, 'angle=', angle)
        new_list += [(p1, s, p_angle), (s, u, p_angle+DEG60), \
                    (u, t, p_angle-DEG60), (t, p2, p_angle)]

    new_list = repl_edge(n-1, new_list)
    return new_list


n = int(sys.stdin.readline())
p1 = (0.0, 0.0)
p2 = (100.0, 0.0)
edges = [(p1, p2, 0.0)]

edges = repl_edge(n, edges)
for edge in edges:
    print(round(edge[0][0],6), round(edge[0][1],6))
print(round(edges[-1][1][0],6), round(edges[-1][1][1],6))

Submission status: Accepted

Solution code:
import math
angle = math.pi / 3 # 60度

def koch(p1, p2, n):
    if n == 0:
        return

    s = ((p1[0] * 2 + p2[0]) / 3, (p1[1] * 2 + p2[1]) / 3)
    t = ((p1[0] + p2[0] * 2) / 3, (p1[1] + p2[1] * 2) / 3)
    u = ((t[0] - s[0]) * math.cos(angle) - (t[1] - s[1]) * math.sin(angle) + s[0], \
        (t[0] - s[0]) * math.sin(angle) + (t[1] - s[1]) * math.cos(angle) + s[1])

    koch(p1, s, n-1)
    print("{0:.8f} {1:.8f}".format(s[0], s[1]))
    koch(s, u, n-1)
    print("{0:.8f} {1:.8f}".format(u[0], u[1]))
    koch(u, t, n-1)
    print("{0:.8f} {1:.8f}".format(t[0], t[1]))
    koch(t, p2, n-1)

n = int(input())
print("{0:.8f} {1:.8f}".format(0.0, 0.0))
koch((0.0, 0.0), (100.0, 0.0), n)
print("{0:.8f} {1:.8f}".format(100.0, 0.0))

Submission status: Accepted

Solution code:
import math


def koch(p1, p2, count):
    """Find points in koch curve after count times operations.

    >>> ps = koch((0, 0), (100, 0), 1)
    >>> cs = ["({:.4f}, {:.4f})".format(*p) for p in ps]
    >>> print("\\n".join(cs))
    (0.0000, 0.0000)
    (33.3333, 0.0000)
    (50.0000, 28.8675)
    (66.6667, 0.0000)
    (100.0000, 0.0000)
    """

    if count == 0:
        return []

    (x1, y1) = p1
    (x2, y2) = p2

    r, t = cartesian_to_polar(x2-x1, y2-y1)

    x3, y3 = polar_to_cartesian(r/3, t)
    p3 = (x3+x1, y3+y1)

    x4, y4 = polar_to_cartesian(r / (2*math.cos(math.pi/6)), t + math.pi/6)
    p4 = (x4+x1, y4+y1)

    x5, y5 = polar_to_cartesian(2*r/3, t)
    p5 = (x5+x1, y5+y1)

    return (koch(p1, p3, count-1)
            + [p3] + koch(p3, p4, count-1)
            + [p4] + koch(p4, p5, count-1)
            + [p5] + koch(p5, p2, count-1))


def polar_to_cartesian(x, y):
    return (x * math.cos(y), x * math.sin(y))


def cartesian_to_polar(x, y):
    return (math.sqrt(x**2 + y**2), math.atan2(y, x))


def run():
    n = int(input())
    p1 = (0.0, 0.0)
    p2 = (100.0, 0.0)
    ps = [p1] + koch(p1, p2, n) + [p2]

    # plot(ps)
    print("\n".join(["{:.5f} {:.5f}".format(*p) for p in ps]))


def plot(ps):
    import pylab
    xs = [x for x, y in ps]
    ys = [y for x, y in ps]

    pylab.plot(xs, ys)
    pylab.xlim(0, 100)
    pylab.ylim(0, 100)
    pylab.show()


if __name__ == '__main__':
    run()

Submission status: Accepted

Solution code:
import math
def koch(d, p1, p2):
    if d == 0:
        return
    
    v = [p2[0] - p1[0], p2[1] - p1[1]]
    s = [p1[0] + v[0] / 3, p1[1] + v[1] / 3]
    t = [p1[0] + 2 * v[0] / 3, p1[1] + 2 * v[1] / 3]
    u = [p1[0] + v[0] / 2 - v[1] * math.sqrt(3) / 6, p1[1] + v[1] / 2 + v[0] * math.sqrt(3) / 6]

    koch(d - 1, p1, s)
    print(" ".join(map(str, s)))
    koch(d - 1, s, u)
    print(" ".join(map(str, u)))
    koch(d - 1, u, t)
    print(" ".join(map(str, t)))
    koch(d - 1, t, p2)

n = int(input())
print("0 0")
koch(n, [0, 0], [100, 0])
print("100 0")

Submission status: Accepted

Solution code:
import math

def rotate(x, y, theta):
    return (round(x*math.cos(theta) -1*y*math.sin(theta), 5), round(x*math.sin(theta) + y*math.cos(theta), 5))

def koch(p1, p2, n):
    s = (round((2*p1[0] + p2[0])/3, 5), round((2*p1[1] + p2[1])/3, 5))
    t = (round((p1[0] + 2*p2[0])/3, 5), round((p1[1] + 2*p2[1])/3, 5))
    rotated = rotate(t[0]-s[0], t[1]-s[1], math.pi/3)
    u = (s[0] + rotated[0], s[1] + rotated[1])

    if n == 0:
        print(round(p1[0], 5), round(p1[1], 5))
    elif n == -1:
        return None

    koch(p1, s, n-1)
    koch(s, u, n-1)
    koch(u, t, n-1)
    koch(t, p2, n-1)

n = int(input())
koch((0.0, 0.0), (100, 0.0), n)
print(100, 0.0)

Submission status: Accepted

Solution code:
import math

n = int(input())


def koch(d, p1, p2):
    """

    :param int d:
    :param list p1:
    :param list p2:
    :return:
    """
    if d == 0:
        return

    s, t, u = [0, 0], [0, 0], [0, 0]
    s[0] = (2*p1[0]+p2[0]) / 3
    s[1] = (2*p1[1]+p2[1]) / 3
    t[0] = (p1[0] + 2 * p2[0]) / 3
    t[1] = (p1[1]+2*p2[1]) / 3
    u[0] = (t[0]-s[0]) * math.cos(math.pi/3) - (t[1]-s[1]) * math.sin(math.pi/3) + s[0]
    u[1] = (t[0]-s[0]) * math.sin(math.pi/3) + (t[1]-s[1]) * math.cos(math.pi/3) + s[1]

    koch(d-1, p1, s)
    print(s[0], s[1])
    koch(d-1, s, u)
    print(u[0], u[1])
    koch(d-1, u, t)
    print(t[0], t[1])
    koch(d-1, t, p2)


def main():
    print(0.00000000, 0.00000000)
    koch(n, [0, 0], [100, 0])
    print(100.00000000, 0.00000000)


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import math

def pr8(a):
	print("{:.10}".format(a[0]),end=" ")
	print("{:.10}".format(a[1]))

def koch(n,p1,p2):
	if n==0:
		return
	s=[0 for i in range(2)]
	t=[0 for i in range(2)]
	u=[0 for i in range(2)]
	
	s[0]=(2*p1[0]+1*p2[0])/3
	s[1]=(2*p1[1]+1*p2[1])/3
	t[0]=(1*p1[0]+2*p2[0])/3
	t[1]=(1*p1[1]+2*p2[1])/3
	
	rad=math.radians(60)
	
	u[0]=(t[0]-s[0])*math.cos(rad)-(t[1]-s[1])*math.sin(rad)+s[0]
	u[1]=(t[0]-s[0])*math.sin(rad)+(t[1]-s[1])*math.cos(rad)+s[1]
	
	koch(n-1,p1,s)
	#pr8(s)
	print(*s)	
	koch(n-1,s,u)
	#pr8(u)
	print(*u)
	koch(n-1,u,t)
	#pr8(t)
	print(*t)
	koch(n-1,t,p2)
	
n=int(input())
p1=[0,0]
p2=[100,0]

print(*p1)
koch(n,p1,p2)
print(*p2)

Submission status: Accepted

Solution code:
#16D8103010K
#ALDS_5_C

import math

def koch(n,p1,p2):
	if n==0:
		return
	s=[0 for i in range(2)]
	t=[0 for i in range(2)]
	u=[0 for i in range(2)]
	
	s[0]=(2*p1[0]+1*p2[0])/3
	s[1]=(2*p1[1]+1*p2[1])/3
	t[0]=(1*p1[0]+2*p2[0])/3
	t[1]=(1*p1[1]+2*p2[1])/3
	
	rad=math.radians(60)
	
	u[0]=(t[0]-s[0])*math.cos(rad)-(t[1]-s[1])*math.sin(rad)+s[0]
	u[1]=(t[0]-s[0])*math.sin(rad)+(t[1]-s[1])*math.cos(rad)+s[1]
	
	koch(n-1,p1,s)
	#pr8(s)
	print(*s)	
	koch(n-1,s,u)
	#pr8(u)
	print(*u)
	koch(n-1,u,t)
	#pr8(t)
	print(*t)
	koch(n-1,t,p2)
	
n=int(input())
p1=[0,0]
p2=[100,0]

print(*p1)
koch(n,p1,p2)
print(*p2)

Submission status: Accepted

Solution code:
import math

def koch(n,p1,p2):
	if n==0:
		return
	s=[0 for i in range(2)]
	t=[0 for i in range(2)]
	u=[0 for i in range(2)]
	
	s[0]=(2*p1[0]+1*p2[0])/3
	s[1]=(2*p1[1]+1*p2[1])/3
	t[0]=(1*p1[0]+2*p2[0])/3
	t[1]=(1*p1[1]+2*p2[1])/3
	
	rad=math.radians(60)
	
	u[0]=(t[0]-s[0])*math.cos(rad)-(t[1]-s[1])*math.sin(rad)+s[0]
	u[1]=(t[0]-s[0])*math.sin(rad)+(t[1]-s[1])*math.cos(rad)+s[1]
	
	koch(n-1,p1,s)
	print(*s)	
	
	koch(n-1,s,u)
	print(*u)
	
	koch(n-1,u,t)
	print(*t)
	
	koch(n-1,t,p2)
	
n=int(input())
p1=[0,0]
p2=[100,0]

print(*p1)
koch(n,p1,p2)
print(*p2)

Submission status: Accepted

Solution code:
import math
class Dot:
    x=0.0
    y=0.0
    def __init__(self,x,y):
        self.x=x
        self.y=y
    def __lt__(self,other):
        return self.x < other.x
    def print(self):
        x=self.x
        y=self.y
        print("{:.8f} {:.8f}".format(x,y))       
def kock(n,a,b,dots):
    if n == 0:
        return
    s=Dot((2*a.x+b.x)/3,(2*a.y+b.y)/3)
    t=Dot((a.x+2*b.x)/3,(a.y+2*b.y)/3)
    rad=math.radians(60)
    x=(t.x-s.x)*math.cos(rad)-(t.y-s.y)*math.sin(rad)+s.x
    y=(t.x-s.x)*math.sin(rad)+(t.y-s.y)*math.cos(rad)+s.y
    u=Dot(x,y)

    kock(n-1,a,s,dots)
    s.print()
    dots.append(s)
    kock(n-1,s,u,dots)
    u.print()
    dots.append(u)
    kock(n-1,u,t,dots)
    t.print()
    dots.append(t)
    kock(n-1,t,b,dots)

if __name__ == "__main__":
    n=int(input())
    dots=[]
    dot1=Dot(0,0)
    dot2=Dot(100,0)
    dots.append(dot1)
    dots.append(dot2)
    dot1.print()
    kock(n,dot1,dot2,dots)
    dot2.print()

Submission status: Accepted

Solution code:
from collections import namedtuple
import math
Co = namedtuple('Co', 'x y')

def f(i, n, l, r):
    if i >= n:
        return
    il = Co(x=(1/3 * r.x + (1 - 1/3) * l.x), y=(1/3 * r.y + (1 - 1/3) * l.y))
    ir = Co(x=(2/3 * r.x + (1 - 2/3) * l.x), y=(2/3 * r.y + (1 - 2/3) * l.y))

    trix = 1/2 * (ir.x + il.x - math.sqrt(3) * ir.y + math.sqrt(3) * il.y)
    triy = 1/2 * (math.sqrt(3) * ir.x - math.sqrt(3) * il.x + ir.y + il.y)
    trico = Co(trix, triy)

    f(i+1, n, l, il)
    print(il.x, il.y)
    f(i+1, n, il, trico)
    print(trico.x, trico.y)
    f(i+1, n, trico, ir)
    print(ir.x, ir.y)
    f(i+1, n, ir, r)

if __name__ == '__main__':
    n = int(input())
    print(0, 0)
    f(0, n, Co(0,0), Co(100,0))
    print(100, 0)

Submission status: Accepted

Solution code:
from collections import namedtuple
import math
Co = namedtuple('Co', 'x y')

def f(i, n, l, r):
    if i >= n:
        print(l.x, l.y)
        return
    il = Co(x=(1/3 * r.x + (1 - 1/3) * l.x), y=(1/3 * r.y + (1 - 1/3) * l.y))
    ir = Co(x=(2/3 * r.x + (1 - 2/3) * l.x), y=(2/3 * r.y + (1 - 2/3) * l.y))

    trix = 1/2 * (ir.x + il.x - math.sqrt(3) * ir.y + math.sqrt(3) * il.y)
    triy = 1/2 * (math.sqrt(3) * ir.x - math.sqrt(3) * il.x + ir.y + il.y)
    trico = Co(trix, triy)

    f(i+1, n, l, il)
    #print(il.x, il.y)
    f(i+1, n, il, trico)
    #print(trico.x, trico.y)
    f(i+1, n, trico, ir)
    #print(ir.x, ir.y)
    f(i+1, n, ir, r)

if __name__ == '__main__':
    n = int(input())
    #print(0, 0)
    f(0, n, Co(0,0), Co(100,0))
    print(100, 0)

Submission status: Accepted

Solution code:
import math
def koch(d, p1, p2):
    if d == 0:
        return
    x=p2[0]-p1[0]
    y=p2[1]-p1[1]
    s = [(p1[0]*2+p2[0]*1)/3.0,(p1[1]*2+p2[1]*1)/3.0]
    t = [(p1[0]*1+p2[0]*2)/3.0,(p1[1]*1+p2[1]*2)/3.0]
    u = [p1[0]+x/2-y*math.sqrt(3)/6,p1[1]+y/2+x*math.sqrt(3)/6]
    koch(d - 1, p1, s)
    print(*s)
    koch(d - 1, s, u)
    print(*u)
    koch(d - 1, u, t)
    print(*t)
    koch(d - 1, t, p2)
 
n = int(input())
p1=[0,0]
p2=[100,0]
print(*p1)
koch(n,p1,p2)
print(*p2)

Submission status: Accepted

Solution code:
import math
n = int(input())
edge_s = (0.0, 0.0)
edge_e = (100.0, 0.0)

def print_tuple(tup):
    print("%.8f %.8f"%(tup[0],tup[1]))

def koch(start, end, n):
    if(n == 0):
        return
    s = ((2*start[0] + end[0]) / 3, (2*start[1] + end[1])/3)
    t = ((start[0] + 2*end[0]) / 3, (start[1] + 2*end[1])/3)
    u = (s[0] +  (t[0]-s[0])*math.cos(math.pi/3)-(t[1]-s[1])*math.sin(math.pi/3), s[1] + (t[0]-s[0]) * math.sin(math.pi/3) + (t[1]-s[1]) * math.cos(math.pi/3))
    n -= 1
    koch(start, s, n)
    print_tuple(s)
    koch(s, u, n)
    print_tuple(u)
    koch(u, t, n)
    print_tuple(t)
    koch(t, end, n)
print_tuple(edge_s)
koch(edge_s, edge_e, n)
print_tuple(edge_e)

Submission status: Accepted

Solution code:
import math

class dot():
    def __init__(self, x, y):
        self.x = x
        self.y = y


def koch(n, p1, p2):
    if n != 0:
        r = 60.0*math.pi/180.0

        x = (2.0*p1.x+1.0*p2.x)/3.0
        y = (2.0*p1.y+1.0*p2.y)/3.0
        s = dot(x, y)

        x = (1.0*p1.x+2.0*p2.x)/3.0
        y = (1.0*p1.y+2.0*p2.y)/3.0
        t = dot(x, y)

        x = (t.x-s.x)*math.cos(r) - (t.y-s.y)*math.sin(r) + s.x
        y = (t.x-s.x)*math.sin(r) + (t.y-s.y)*math.cos(r) + s.y
        u = dot(x, y)

        koch(n-1, p1, s)
        print(s.x, ' ', s.y)
        koch(n-1, s, u)
        print(u.x, ' ', u.y)
        koch(n-1, u, t)
        print(t.x, ' ', t.y)
        koch(n-1, t, p2)


p1 = dot(0.0, 0.0)
p2 = dot(100.0, 0.0)
n = int(input())

print(p1.x, ' ', p1.y)
koch(n, p1, p2)
print(p2.x, ' ', p2.y)

Submission status: Accepted

Solution code:
import math

n = int(input())

sin60 = (math.sqrt)(3)/2
cos60 = 1/2


def koch(n, p1_x, p2_x, p1_y, p2_y):
    if n == 0:
        return

    s_x = (2*p1_x + 1*p2_x) / 3
    s_y = (2*p1_y + 1*p2_y) / 3
    t_x = (1*p1_x + 2*p2_x) / 3
    t_y = (1*p1_y + 2*p2_y) / 3
    u_x = (t_x - s_x)*cos60 - (t_y - s_y)*sin60 + s_x
    u_y = (t_x - s_x)*sin60 + (t_y - s_y)*cos60 + s_y

    koch(n-1, p1_x, s_x, p1_y, s_y)
    print(s_x, s_y)
    koch(n-1, s_x, u_x, s_y, u_y)
    print(u_x, u_y)
    koch(n-1, u_x, t_x, u_y, t_y)
    print(t_x, t_y)
    koch(n-1, t_x, p2_x, t_y, p2_y)


print(0.00000000, 0.00000000)
koch(n, 0, 100, 0, 0)
print(100.00000000, 0.00000000)

Submission status: Accepted

Solution code:
import math

def kock(n,p1x,p1y,p2x,p2y):
    if(n==0):
        return

    sx = (2*p1x+p2x)/3.0
    sy = (2*p1y+p2y)/3.0
    tx = (p1x+2*p2x)/3.0
    ty = (p1y+2*p2y)/3.0

    ux = (tx-sx)*math.cos(math.radians(60)) - (ty-sy)*math.sin(math.radians(60)) + sx
    uy = (tx-sx)*math.sin(math.radians(60)) + (ty-sy)*math.cos(math.radians(60)) + sy

    kock(n-1,p1x,p1y,sx,sy)
    print(sx,sy)
    kock(n-1,sx,sy,ux,uy)
    print(ux,uy)
    kock(n-1,ux,uy,tx,ty)
    print(tx,ty)
    kock(n-1,tx,ty,p2x,p2y)


n = int(input())
print(0,0)
kock(n,0,0,100,0)
print(100,0)

Submission status: Accepted

Solution code:
import math
def f(n, p1, p2):
    if n == 0: return
    s = []
    t = []
    u = []
    s.append((2*p1[0] + p2[0])/3)
    s.append((2*p1[1] + p2[1])/3)
    t.append((p1[0] + 2*p2[0])/3)
    t.append((p1[1] + 2*p2[1])/3)
    u.append((t[0]-s[0])*math.cos(math.radians(60))
             - (t[1]-s[1])*math.sin(math.radians(60)) + s[0])
    u.append((t[0]-s[0])*math.sin(math.radians(60))
             + (t[1]-s[1])*math.cos(math.radians(60)) + s[1])
    f(n-1, p1, s)
    print(s[0],s[1])
    f(n-1, s, u)
    print(u[0],u[1])
    f(n-1, u, t)
    print(t[0],t[1])
    f(n-1, t, p2)


n = int(input())
p1 = [0,0]
p2 = [100,0]
print(p1[0],p1[1])
f(n, p1, p2)
print(p2[0],p2[1])

Submission status: Accepted

Solution code:
import math
def koch(a, p1, p2):
    if a == 0:
        return
     
    v = [p2[0] - p1[0], p2[1] - p1[1]]
    s = [p1[0] + v[0] / 3, p1[1] + v[1] / 3]
    t = [p1[0] + 2 * v[0] / 3, p1[1] + 2 * v[1] / 3]
    u = [p1[0] + v[0] / 2 - v[1] * math.sqrt(3) / 6, p1[1] + v[1] / 2 + v[0] * math.sqrt(3) / 6]
 
    koch(a-1,p1,s)
    print(" ".join(map(str, s)))
    koch(a-1,s,u)
    print(" ".join(map(str, u)))
    koch(a-1,u,t)
    print(" ".join(map(str, t)))
    koch(a-1,t,p2)
 
n = int(input())
print("0 0")
koch(n, [0, 0], [100, 0])
print("100 0")

Submission status: Accepted

Solution code:
import math

n = int(input())
p1 = (0, 0)
p2 = (100, 0)
points = []

def koch(n, p, q):
    if n == 0:
        return

    x1, y1 = p
    x2, y2 = q
    sx = (2 * x1 + 1 * x2) / 3
    sy = (2 * y1 + 1 * y2) / 3
    s = (sx, sy)
    tx = (1 * x1 + 2 * x2) / 3
    ty = (1 * y1 + 2 * y2) / 3
    t = (tx, ty)
    theta = math.pi / 3
    ux = (tx - sx) * math.cos(theta) - (ty - sy) * math.sin(theta) + sx
    uy = (tx - sx) * math.sin(theta) + (ty - sy) * math.cos(theta) + sy
    u = (ux, uy)

    koch(n - 1, p, s)
    print(*s)
    koch(n - 1, s, u)
    print(*u)
    koch(n - 1, u, t)
    print(*t)
    koch(n - 1, t, q)


print(*p1)
koch(n, p1, p2)
print(*p2)

Submission status: Accepted

Solution code:
import math
 
n=int(input())
 

a=math.sin(math.radians(60))
b=math.cos(math.radians(60))

 
def f(n,x1,x2,y1,y2):
    if n==0:
        return
 
    sx=(2*x1 + 1*x2) / 3
    sy=(2*y1 + 1*y2) / 3
    tx=(1*x1 + 2*x2) / 3
    ty=(1*y1 + 2*y2) / 3
    ux=(tx-sx)*b - (ty-sy)*a + sx
    uy=(tx-sx)*a + (ty-sy)*b + sy
 
    f(n-1,x1,sx,y1,sy)
    print(sx, sy)
    f(n-1,sx,ux,sy,uy)
    print(ux, uy)
    f(n-1,ux,tx,uy,ty)
    print(tx, ty)
    f(n-1,tx,x2,ty,y2)
 
 
print(0.00000000, 0.00000000)
f(n,0,100,0,0)
print(100.00000000, 0.00000000)

Submission status: Accepted

Solution code:
import math
 
n = int(input())
 
 
 
def koch(n,x_0,y_0,x_1,y_1):
    if n == 0:
        return   
    x_m1 = x_0 + (x_1- x_0)/3
    y_m1 = y_0 + (y_1 -y_0)/3
    x_m2 = x_0 + (x_1- x_0)* 2/3
    y_m2 = y_0 + (y_1 -y_0) *2/3
    x_m =  (x_m2 - x_m1) * math.cos(math.pi/3) - (y_m2 - y_m1) * math.sin(math.pi/3) + x_m1
    y_m =  (x_m2 - x_m1) * math.sin(math.pi/3) + (y_m2 - y_m1) * math.cos(math.pi/3) + y_m1
 
    koch(n-1,x_0,y_0,x_m1,y_m1)
    print(x_m1,y_m1)
    koch(n-1,x_m1,y_m1,x_m,y_m)
    print(x_m,y_m)
    koch(n-1,x_m,y_m,x_m2,y_m2)
    print(x_m2,y_m2)
    koch(n-1,x_m2,y_m2,x_1,y_1)
     
print(0,0)
koch(n,0,0,100,0)
print(100,0)

Submission status: Accepted

Solution code:
import math
  
n = int(input())
  
  
  
def koch(n,x_0,y_0,x_1,y_1):
    if n == 0:
        return  
    x_m1 = x_0 + (x_1- x_0)/3
    y_m1 = y_0 + (y_1 -y_0)/3
    x_m2 = x_0 + (x_1- x_0)* 2/3
    y_m2 = y_0 + (y_1 -y_0) *2/3
    x_m =  (x_m2 - x_m1) * math.cos(math.pi/3) - (y_m2 - y_m1) * math.sin(math.pi/3) + x_m1
    y_m =  (x_m2 - x_m1) * math.sin(math.pi/3) + (y_m2 - y_m1) * math.cos(math.pi/3) + y_m1
  
    koch(n-1,x_0,y_0,x_m1,y_m1)
    print(x_m1,y_m1)
    koch(n-1,x_m1,y_m1,x_m,y_m)
    print(x_m,y_m)
    koch(n-1,x_m,y_m,x_m2,y_m2)
    print(x_m2,y_m2)
    koch(n-1,x_m2,y_m2,x_1,y_1)
      
print(0,0)
koch(n,0,0,100,0)
print(100,0)

Submission status: Accepted

Solution code:
import math


def make_stu(p1, p2):
    s = [(2 * p1[0] + p2[0]) / 3, (2 * p1[1] + p2[1]) / 3]
    t = [(p1[0] + 2 * p2[0]) / 3, (p1[1] + 2 * p2[1]) / 3]
    u = [s[0] + (t[0] - s[0]) / 2 - math.sqrt(3) * (t[1] - s[1]) / 2,
         s[1] + (t[1] - s[1]) / 2 + math.sqrt(3) * (t[0] - s[0]) / 2]
    return s, t, u


def koch_curve(n, p1, p2):
    if n >= 1:
        s, t, u = make_stu(p1, p2)
        if n == 1:
            print(s[0], s[1])
            print(u[0], u[1])
            print(t[0], t[1])
        else:
            koch_curve(n - 1, p1, s)
            print(s[0], s[1])
            koch_curve(n - 1, s, u)
            print(u[0], u[1])
            koch_curve(n - 1, u, t)
            print(t[0], t[1])
            koch_curve(n - 1, t, p2)

n = int(input())

print(0.0, 0.0)
koch_curve(n, [0.0, 0.0], [100.0, 0.0])
print(100.0, 0.0)

Submission status: Accepted

Solution code:
n = int(input())

def three_points(p1,p2):
    q1 = ((2*p1[0]+p2[0])/3, (2*p1[1]+p2[1])/3)
    q2 = ((p1[0]+2*p2[0])/3, (p1[1]+2*p2[1])/3)
    dx,dy = p2[0]-p1[0], p2[1]-p1[1]
    q3 = (p1[0]+dx/2-3**0.5/6*dy, p1[1]+dy/2+3**0.5/6*dx)
    return [q1,q3,q2]

m = [(0,0),(100,0)]
for i in range(n):
    tmpm = []
    for j in range(len(m)-1):
        tmpm += [m[j]] + three_points(m[j],m[j+1])
    tmpm += [m[-1]]
    m = tmpm

for x in m:
    print(x[0], x[1])

Submission status: Accepted

Solution code:
import math
def stdinput():
    from sys import stdin
    return stdin.readline().strip()

def main():
    n = int(stdinput())
    nodes = [[0., 0.], [100., 0.]]

    for _ in range(n):
        next_nodes = []
        for s_node, e_node in zip(nodes[:], nodes[1:]):
            next_nodes.append(s_node)
            next_nodes += koch(s_node, e_node)
        next_nodes.append(nodes[-1])
        nodes = next_nodes

    for node in nodes:
        print(*map(lambda a: f'{round(a,8):.8f}', node))

def koch(start, end):
    nodes = []

    dx = (end[0] - start[0]) / 3
    dy = (end[1] - start[1]) / 3
    
    s = [start[0] + dx, start[1] + dy]
    t = [start[0] + 2 * dx, start[1] + 2 * dy]

    nodes.append(s)
    nodes.append(determine_koch(s, t))
    nodes.append(t)
    
    return nodes

def determine_koch(s, t):
    dx = (t[0] - s[0]) * math.sqrt(3) / 2
    dy = (t[1] - s[1]) * math.sqrt(3) / 2

    u0 = [s[0] - dy, s[1] + dx]
    u1 = [t[0] - dy, t[1] + dx]

    return [
        (u0[0] + u1[0]) / 2,
        (u0[1] + u1[1]) / 2
    ]

if __name__ == '__main__':
    main()
    # import cProfile
    # cProfile.run('main()')

Submission status: Accepted

Solution code:
from math import sqrt
def koch(d, p1, p2):
    if d == 0:
        return
     
    v = [p2[0] - p1[0], p2[1] - p1[1]]
    s = [p1[0] + v[0] / 3, p1[1] + v[1] / 3]
    t = [p1[0] + 2 * v[0] / 3, p1[1] + 2 * v[1] / 3]
    u = [p1[0] + v[0] / 2 - v[1] *sqrt(3) / 6, p1[1] + v[1] / 2 + v[0] *sqrt(3) / 6]
 
    koch(d - 1, p1, s)
    print(" ".join(map(str, s)))
    koch(d - 1, s, u)
    print(" ".join(map(str, u)))
    koch(d - 1, u, t)
    print(" ".join(map(str, t)))
    koch(d - 1, t, p2)
 
n = int(input())
print("0 0")
koch(n, [0, 0], [100, 0])
print("100 0")

Submission status: Accepted

Solution code:
import math, cmath

def koch(p1, p2, n):
    if n == 0:
        return [p1, p2]
    
    rad60 = math.pi/3
    v1 = (p2 - p1)/3
    v2 = cmath.rect(abs(v1), cmath.phase(v1)+rad60)
    q1 = p1 + v1
    q2 = q1 + v2
    q3 = q1 + v1
    if n == 1:
        return [p1,q1,q2,q3,p2]
    else:
        x1 = koch(p1,q1,n-1)[1:-1]
        x2 = koch(q1,q2,n-1)[1:-1]
        x3 = koch(q2,q3,n-1)[1:-1]
        x4 = koch(q3,p2,n-1)[1:-1]
        x = [p1]+x1+[q1]+x2+[q2]+x3+[q3]+x4+[p2]
    return x

n = int(raw_input())
p1 = complex(0,0)
p2 = complex(100,0)

for e in koch(p1,p2,n):
    print e.real,e.imag

Submission status: Accepted

Solution code:
import math, cmath

def koch(p1, p2, n):
    if n == 0:
        return [p1, p2]
    
    rad60 = math.pi/3
    v1 = (p2 - p1)/3
    v2 = cmath.rect(abs(v1), cmath.phase(v1)+rad60)
    q1 = p1 + v1
    q2 = q1 + v2
    q3 = q1 + v1
    if n == 1:
        return [p1,q1,q2,q3,p2]
    else:
        x1 = koch(p1,q1,n-1)[:-1]
        x2 = koch(q1,q2,n-1)[:-1]
        x3 = koch(q2,q3,n-1)[:-1]
        x4 = koch(q3,p2,n-1)
        x = x1 + x2 + x3 + x4
    return x

n = int(raw_input())
p1 = complex(0,0)
p2 = complex(100,0)

for e in koch(p1,p2,n):
    print e.real,e.imag

Submission status: Accepted

Solution code:
#!/usr/bin/env python
from __future__ import division, print_function
from sys import stdin
from math import pi, sin, cos

COS_PI_3 = cos(pi / 3.0)
SIN_PI_3 = sin(pi / 3.0)


def koch_curve(s, e, n):
    if not n:
        return (s, e)
    x = (e[0]-s[0]) / 3.0
    y = (e[1]-s[1]) / 3.0
    p1 = (s[0] + x, s[1] + y)
    p2 = (x*COS_PI_3 - y*SIN_PI_3 + p1[0], x*SIN_PI_3 + y*COS_PI_3 + p1[1])
    p3 = (e[0] - x, e[1] - y)
    return (koch_curve(s, p1, n-1) + koch_curve(p1, p2, n-1)[1:] +
            koch_curve(p2, p3, n-1)[1:] + koch_curve(p3, e, n-1)[1:])


n = int(stdin.readline())
for x, y in koch_curve((0, 0), (100, 0), n):
    print('{:.8f} {:.8f}'.format(x, y))

Submission status: Accepted

Solution code:
from math import sqrt
from collections import namedtuple

Point = namedtuple('Point', 'x y')

def rot60(p):
    return Point(C60 * p.x - S60 * p.y, S60 * p.x + C60 * p.y)

def koch(n, p1, p2):
    if n == 0: return
    s = Point((2*p1.x + p2.x)/3, (2*p1.y + p2.y)/3)
    t = Point((p1.x + 2*p2.x)/3, (p1.y + 2*p2.y)/3)
    q = rot60(Point((p2.x - p1.x)/3, (p2.y - p1.y)/3))
    u = Point(s.x + q.x, s.y + q.y)

    koch(n - 1, p1, s)
    print(f.format(s.x, s.y))

    koch(n - 1, s, u)
    print(f.format(u.x, u.y))

    koch(n - 1, u, t)
    print(f.format(t.x, t.y))

    koch(n - 1, t, p2)


C60 = 1 / 2
S60 = sqrt(3) / 2
f = '{:8f} {:8f}'

n = int(input())
print(f.format(0, 0))
koch(n, Point(0, 0), Point(100, 0))
print(f.format(100, 0))

Submission status: Accepted

Solution code:
import math

class Point():
    def __init__(self, x, y):
        self.x = x
        self.y = y


def koch(n, a, b):
    if n == 0:
        return
    th = math.radians(60)
    s = Point((2*a.x+b.x)/3, (2*a.y+b.y)/3)
    t = Point((a.x+2*b.x)/3, (a.y+2*b.y)/3)
    u = Point((t.x-s.x)* math.cos(th) - (t.y-s.y)*math.sin(th)+s.x,
                (t.x-s.x)* math.sin(th) + (t.y-s.y)*math.cos(th)+s.y)

    koch(n-1, a, s)
    print(s.x, s.y)
    koch(n-1, s, u)
    print(u.x, u.y)
    koch(n-1, u, t)
    print(t.x, t.y)
    koch(n-1, t, b)

if __name__ == '__main__':
    import sys
    input = sys.stdin.readline

    n = int(input())

    a = Point(0, 0)
    b = Point(100, 0)

    print(a.x, a.y)
    koch(n, a, b)
    print(b.x, b.y)

Submission status: Accepted

Solution code:
import math

def triangle(co1, co2):
    ans = []
    x1 = co1[0]
    y1 = co1[1]
    x2 = co2[0]
    y2 = co2[1]
    part1 = [(2 * x1 + x2) /3, (2 * y1 + y2) / 3]
    part2 = [(x1 + 2 * x2) /3, (y1 + 2 * y2) / 3]
    #part2をpart1中心に60度回転
    edge = [(part2[0] - part1[0])/2 - (part2[1] - part1[1])/ 2 * math.sqrt(3) + part1[0], (part2[0] - part1[0])/2 * math.sqrt(3) + (part2[1] - part1[1])/ 2 + part1[1]]
    ans.extend([part1, edge, part2, co2])
    return ans
def rec(A, n):
    if n == 0:
        return
    
    rec(A, n-1)
    for i in range(4 ** (n-1)):
        A[n].extend(triangle(A[n-1][i], A[n-1][i+1]))

n = int(input())
koch = [[[0.0, 0.0]] for i in range(n + 1)]
koch[0].append([100.0, 0.0])
rec(koch, n)
for i in range(4 ** n + 1):
    print(*koch[n][i])

Submission status: Accepted

Solution code:
import math

def plot(x,y):
    print(f'{x:.8f} {y:.8f}')
    
def Koch(n, x1,y1,x2,y2):
    if n == 0: 
        plot(x1,y1)        
        return
    sx = (2 * x1 + x2) / 3
    sy = (2 * y1 + y2) / 3
    tx = (x1 + 2 * x2) / 3
    ty = (y1 + 2 * y2) / 3
    ux = (tx-sx)*(1/2)-(ty-sy)*(math.sqrt(3)/2)+sx
    uy = (tx-sx)*(math.sqrt(3)/2)+(ty-sy)*(1/2)+sy
    Koch(n-1, x1, y1, sx, sy)
    Koch(n-1, sx, sy, ux, uy)
    Koch(n-1, ux, uy, tx, ty)
    Koch(n-1, tx, ty, x2, y2)

n = int(input())
Koch(n, 0, 0, 100, 0)
plot(100,0)

Submission status: Accepted

Solution code:
import math

def plot(x,y):
    print(f"{x:.8f} {y:.8f}")

def koch(n,x1,y1,x2,y2):
    if n==0:
        plot(x1,y1)
        return
    ax=(2*x1+x2)/3
    ay=(2*y1+y2)/3
    bx=(x1+2*x2)/3
    by=(y1+2*y2)/3
    cx=(bx-ax)*(1/2)-(by-ay)*(math.sqrt(3)/2)+ax
    cy=(bx-ax)*(math.sqrt(3)/2)+(by-ay)*(1/2)+ay
    koch(n-1,x1,y1,ax,ay)
    koch(n-1,ax,ay,cx,cy)
    koch(n-1,cx,cy,bx,by)
    koch(n-1,bx,by,x2,y2)
    
n=int(input())
koch(n,0,0,100,0)
plot(100,0)

Submission status: Accepted

Solution code:
import math
def plot(x,y):
	print(f'{x:.8f} {y:.8f}')
def koch(n,x1,y1,x2,y2):
	if n==0:
		plot(x1,y1)
		return
	sx=(2*x1+x2)/3
	sy=(2*y1+y2)/3
	tx=(x1+2*x2)/3
	ty=(y1+2*y2)/3
	ux=(tx-sx)*(1/2)-(ty-sy)*(math.sqrt(3)/2)+sx
	uy=(tx-sx)*(math.sqrt(3)/2)+(ty-sy)*(1/2)+sy
	koch(n-1,x1,y1,sx,sy)
	koch(n-1,sx,sy,ux,uy)
	koch(n-1,ux,uy,tx,ty)
	koch(n-1,tx,ty,x2,y2)
n=int(input())
koch(n,0,0,100,0)
plot(100,0)

Submission status: Accepted

Solution code:
import math as m
def plot(x,y):
    print(f'{x:.8f} {y:.8f}')
def koch(n,x1,y1,x2,y2):
    if n==0:
        plot(x1,y1)
        return
    sx=(2*x1+x2)/3
    sy=(2*y1+y2)/3
    tx=(x1+2*x2)/3
    ty=(y1+2*y2)/3
    ux=(tx-sx)*m.cos(m.radians(60))-(ty-sy)*m.sin(m.radians(60))+sx
    uy=(tx-sx)*m.sin(m.radians(60))+(ty-sy)*m.cos(m.radians(60))+sy
    koch(n-1,x1,y1,sx,sy)
    koch(n-1,sx,sy,ux,uy)
    koch(n-1,ux,uy,tx,ty)
    koch(n-1,tx,ty,x2,y2)
n=int(input())
koch(n,0,0,100,0)
plot(100,0)

Submission status: Accepted

Solution code:
import math

def plot(x,y):
    print(f'{x:.8f} {y:.8f}')
    
def koch(n,x1,y1,x2,y2):
    if n==0:
        plot(x1,y1)
        return
    sx=(2*x1+x2)/3
    sy=(2*y1+y2)/3
    tx=(x1+2*x2)/3
    ty=(y1+2*y2)/3
    ux=(tx-sx)*(1/2)-(ty-sy)*(math.sqrt(3)/2)+sx
    uy=(tx-sx)*(math.sqrt(3)/2)+(ty-sy)*(1/2)+sy
    koch(n-1,x1,y1,sx,sy)
    koch(n-1,sx,sy,ux,uy)
    koch(n-1,ux,uy,tx,ty)
    koch(n-1,tx,ty,x2,y2)

n=int(input())
koch(n,0,0,100,0)
plot(100,0)

Submission status: Accepted

Solution code:
import math

def plot(x,y):
    print(f"{x:.8f} {y:.8f}")
def koch(n,x1,y1,x2,y2):
    if n==0:
        plot(x1,y1)
        return
    sx=(2*x1+x2)/3
    sy=(2*y1+y2)/3
    tx=(x1+2*x2)/3
    ty=(y1+2*y2)/3
    ux=(tx-sx)*(1/2)-(ty-sy)*(math.sqrt(3)/2)+sx
    uy=(tx-sx)*(math.sqrt(3)/2)+(ty-sy)*(1/2)+sy
    koch(n-1,x1,y1,sx,sy)
    koch(n-1,sx,sy,ux,uy)
    koch(n-1,ux,uy,tx,ty)
    koch(n-1,tx,ty,x2,y2)
n=int(input())
koch(n,0,0,100,0)
plot(100,0)