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 math 
c = math.cos(math.radians(60))
s = math.sin(math.radians(60))

def koch(d,p1,p2):
    if d == 0:
        return 
    sx = (2 * p1[0] + p2[0]) / 3
    sy = (2 * p1[1] + p2[1]) / 3

    tx = (p1[0] + p2[0] * 2) / 3
    ty = (p1[1] + p2[1] * 2) / 3

    dx = tx - sx
    dy = ty - sy

    ux = dx * c - dy * s + sx
    uy = dx * s + dy * c + sy

    koch(d-1,p1,(sx,sy))
    print("{0:.8f} {1:.8f}".format(sx,sy))

    koch(d-1,(sx,sy),(ux,uy))
    print("{0:.8f} {1:.8f}".format(ux,uy))

    koch(d-1,(ux,uy),(tx,ty))
    print("{0:.8f} {1:.8f}".format(tx,ty))

    koch(d-1,(tx,ty),p2)

n = int(input())
print("{0:.8f} {1:.8f}".format(0,0))
koch(n,(0,0),(100,0))
print("{0:.8f} {1:.8f}".format(100,0))

Submission status: Accepted

Solution code:
from math import sin, cos, pi


class Point:

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

    def __str__(self):
        return f"{self.x:.8f} {self.y:.8f}"


def kock(n, p1: Point, p2: Point):
    if n == 0:
        return
    s = Point(
        x=(2*p1.x + p2.x)/3,
        y=(2*p1.y + p2.y)/3
    )
    t = Point(
        x=(p1.x + 2*p2.x)/3,
        y=(p1.y + 2*p2.y)/3
    )
    u = Point(
        x=(t.x - s.x) * cos(pi / 3) - (t.y - s.y) * sin(pi / 3) + s.x,
        y=(t.x - s.x) * sin(pi / 3) + (t.y - s.y) * cos(pi / 3) + s.y
    )
    kock(n - 1, p1, s)
    print(s)
    kock(n - 1, s, u)
    print(u)
    kock(n - 1, u, t)
    print(t)
    kock(n - 1, t, p2)


def main():
    n = int(input())
    p1 = Point(0.0, 0.0)
    p2 = Point(100.0, 0.0)
    print(p1)
    kock(n, p1, p2)
    print(p2)

main()

Submission status: Accepted

Solution code:
from collections import deque
if __name__ == "__main__":
    new_lines = deque([[[0.0, 0.0], [100.0, 0.0]]])
    n = int(input())
    sin60 = 3**0.5/2.0
    cos60 = 1.0/2.0
    for _ in range(n):
        lines = new_lines
        new_lines = deque()
        while lines:
            t1, t2 = lines.popleft()
            n1 = [(2.0*t1[0]+t2[0])/3.0, (2.0*t1[1]+t2[1])/3.0]
            n3 = [(t1[0]+2.0*t2[0])/3.0, (t1[1]+2.0*t2[1])/3.0]
            x, y = [n3[0]-n1[0], n3[1]-n1[1]]
            x60, y60 = [cos60*x - sin60*y ,sin60*x + cos60*y]
            n2 = [n1[0]+x60, n1[1]+y60]
            new_lines.append([t1, n1])
            new_lines.append([n1, n2])
            new_lines.append([n2, n3])
            new_lines.append([n3, t2])
    coordinates = list(zip(*new_lines))[0] + ([100.0, 0.0],)
    for coordinate in coordinates:
        print(*coordinate)

Submission status: Accepted

Solution code:
import math
def koch(n, p1, p2):
    if n == 0:
        return
    sx = (2*p1[0]+p2[0])/3
    sy = (2*p1[1]+p2[1])/3
    s = (sx, sy)
    tx = (p1[0]+2*p2[0])/3
    ty = (p1[1]+2*p2[1])/3
    t = (tx, ty)
    ux = (tx-sx)*math.cos(math.pi/3) - (ty-sy)*math.sin(math.pi/3) + sx
    uy = (tx-sx)*math.sin(math.pi/3) + (ty-sy)*math.cos(math.pi/3) + sy
    u = (ux, uy)
    koch(n-1, p1, s)
    print(s[0], s[1])
    koch(n-1, s, u)
    print(u[0], u[1])
    koch(n-1, u, t)
    print(t[0], t[1])
    koch(n-1, t, p2)
n = int(input())
p1 = (0, 0)
p2 = (100, 0)
print(0, 0)
koch(n, p1, p2)
print(100, 0)

Submission status: Accepted

Solution code:
import math

def koch(start, end, n, r):
    if n > 0:
        #途中の頂点をa, b, cとする
        a = [(start[0]*2 + end[0]*1) / 3, (start[1]*2 + end[1]*1) / 3]
        c = [(start[0]*1 + end[0]*2) / 3, (start[1]*1 + end[1]*2) / 3]

        x = c[0] - a[0]
        y = c[1] - a[1]

        b = [x * math.cos(math.pi/3) - y * math.sin(math.pi/3) + a[0], x * math.sin(math.pi/3) + y * math.cos(math.pi/3) + a[1]]

        koch(start, a, n-1, r)
        koch(a, b, n-1, r)
        koch(b, c, n-1, r)
        koch(c, end, n-1, r)

    else:
        r.append(start)

n = int(input())

r = []

koch([0, 0], [100, 0], n, r)
r.append([100, 0])

for rr in r:
    print(str(rr[0]) + ' ' + str(rr[1]))

Submission status: Accepted

Solution code:
import math
def rot60(s, t):
    v = t - s
    a = 1/2 + complex(0,(math.sqrt(3)/2))
    return v * a + s

def pr(p):
    x = p.real
    y = p.imag
    print('%.10f %.10f'%(x, y))

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

    s = (p2 - p1) * (1/3) + p1
    t = (p2 - p1) * (2/3) + p1
    u = rot60(s, t)
    dfs(p1, s, n - 1)
    pr(s)
    dfs(s, u, n - 1)
    pr(u)
    dfs(u, t, n - 1)
    pr(t)
    dfs(t, p2, n -1)
    
n = int(input())
s = (0 + 0j)
t = (100 + 0j)
pr(s)
dfs(s, t, n) 
pr(t)

Submission status: Accepted

Solution code:
"""
コッホ曲線を構成する
numpyは使えないっぽい
"""
import math

class Point: 
    #こうすると見やすくなるっぽいけどそうするんだったらPoint(,)の形で全部書いていくと良い
    def __init__(self, x, y):
        self.x = x
        self.y = y


def outPut(point):
    print("%.8f %.8f"%(point.x, point.y))

def calc(depth, left, right):
    dif_x = right.x-left.x
    dif_y = right.y-left.y

    nleft_x = left.x+dif_x/3
    nleft_y = left.y+dif_y/3

    nright_x = right.x-dif_x/3
    nright_y = right.y-dif_y/3

    #dif/3を回転させる
    top_x = (dif_x*math.cos(math.pi/3)-dif_y*math.sin(math.pi/3))/3+nleft_x
    top_y = (dif_x*math.sin(math.pi/3)+dif_y*math.cos(math.pi/3))/3+nleft_y

    new_left = Point(nleft_x, nleft_y)
    new_right = Point(nright_x, nright_y)
    tmp_top = Point(top_x, top_y)

    if depth > 1:
        calc(depth-1, left, new_left)
        calc(depth-1, new_left, tmp_top)
        calc(depth-1, tmp_top, new_right)
        calc(depth-1, new_right, right)
    else: #depth==1が停止条件
        outPut(left)
        outPut(new_left)
        outPut(tmp_top)
        outPut(new_right) #rightは抜いてある

n = int(input())
start = Point(0, 0)
end = Point(100, 0)

if n == 0:
    outPut(start)
    outPut(end)
else:
    calc(n, start, end)
    outPut(end)

Submission status: Accepted

Solution code:
import math

n = int(input())

def koch(c, px, py, qx, qy):
  if c > 0:
    sx = (2*px+qx)/3
    sy = (2*py+qy)/3
    tx = (px+2*qx)/3
    ty = (py+2*qy)/3
    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
    koch(c-1, px, py, sx, sy)
    S = [sx, sy]
    print(" ".join(map(str, S)))
    koch(c-1, sx, sy, ux, uy)
    U = [ux, uy]
    print(" ".join(map(str, U)))    
    koch(c-1, ux, uy, tx, ty)
    T = [tx, ty]
    print(" ".join(map(str, T)))
    koch(c-1, tx, ty, qx, qy)

print("0 0")
koch(n, 0, 0, 100, 0)
print("100 0")

Submission status: Accepted

Solution code:
import math

def koch(d, a, b):
    if d== 0:
        return
    s=[0,0]
    t=[0,0]
    u=[0,0]
    
    s[0] = (2.0*a[0]+1.0*b[0])/3.0
    s[1] = (2.0*a[1]+1.0*b[1])/3.0
    t[0] = (1.0*a[0]+2.0*b[0])/3.0
    t[1] = (1.0*a[1]+2.0*b[1])/3.0
    u[0] = (t[0] - s[0])*math.cos(math.radians(60))-(t[1] - s[1])*math.sin(math.radians(60)) + s[0]
    u[1] = (t[0] - s[0])*math.sin(math.radians(60))+(t[1] - s[1])*math.cos(math.radians(60)) + s[1]
    
    koch(d-1,a,s)
    print("{:.8f}".format(s[0]), "{:.8f}".format(s[1]))  
    koch(d-1,s,u)
    print("{:.8f}".format(u[0]), "{:.8f}".format(u[1]))  
    koch(d-1,u,t)      
    print("{:.8f}".format(t[0]), "{:.8f}".format(t[1]))  
    koch(d-1, t, b)

n = int(input())

p1=[0,0]
p2=[100,0]

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

Submission status: Accepted

Solution code:
import math

def rot60(s, t):
    v = t - s
    a = 1/2 + complex(0, (math.sqrt(3)/2))
    return v * a + s

def pr(p):
    x = p.real
    y = p.imag
    print('%.10f %.10f'%(x,y))

def dfs(p1, p2, n):
    if n == 0:
        return
    s = (p2-p1)*(1/3) + p1
    t = (p2-p1)*(2/3) + p1
    u = rot60(s, t)
    dfs(p1, s, n-1)
    pr(s)
    dfs(s, u, n-1)
    pr(u)
    dfs(u, t, n-1)
    pr(t)
    dfs(t, p2, n-1)

n = int(input())
s = (0 + 0j)
t = (100 + 0j)
pr(s)
dfs(s, t, n)
pr(t)

Submission status: Accepted

Solution code:
import math

def make_3_points(p1, p2):
    """p1, p2 を分割する３点を作成する。
    
    p1, p2 を両端の点とする線分を３等分する２点 s, t を
    頂点とする正三角形の頂点 (s, u, t) のタプルを返す。
    """
    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)

    theta = math.radians(60)

    x = t[0] - s[0]
    y = t[1] - s[1]

    u = (math.cos(theta) * x - math.sin(theta) * y, math.sin(theta) * x + math.cos(theta) * y)
    u = (u[0] + s[0], u[1] + s[1])

    return (s, u, t)

def make_koch(n, pl):
    if n == 0:
        return pl
    next_pl = [pl[0]]
    for i in range(1, len(pl)):
        s, u, t = make_3_points(next_pl[-1], pl[i])
        next_pl += [s, u, t, pl[i]]
    
    pl = None
    return make_koch(n - 1, next_pl)

n = int(input())
rl = make_koch(n, [(0, 0), (100, 0)])
for p1, p2 in rl:
    print(p1, p2)

Submission status: Accepted

Solution code:
# ALDS1_5_C
import math

n = int(input())
def koch(d, p1, p2):
    if d == 0:
        return
    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 = [(t[0] - s[0]) * 0.5 - (t[1] - s[1]) * 0.866025403 + s[0],
        (t[0] - s[0]) * 0.866025403 + (t[1] - s[1]) * 0.5 + s[1]]

    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)

print(0.0, 0.0)
koch(n, [0, 0], [100, 0])
print(100.0, 0.0)

Submission status: Accepted

Solution code:
import math


class vec2d(object):
    def __init__(self, x, y) -> None:
        self.x = float(x)
        self.y = float(y)

    def rot(self, theta: float):
        newx = self.x * math.cos(theta) - self.y * math.sin(theta)
        newy = self.x * math.sin(theta) + self.y * math.cos(theta)
        return vec2d(newx, newy)

    def __str__(self):
        return ' '.join(map(str, [self.x, self.y]))

    def __format__(self, format_spec):
        return ' '.join(map(lambda x: format(x, format_spec), [self.x, self.y]))

    def __add__(self, other):
        return vec2d(self.x + other.x, self.y + other.y)

    def __sub__(self, other):
        return vec2d(self.x - other.x, self.y - other.y)

    def __mul__(self, k):
        return vec2d(self.x * k, self.y * k)

    def __truediv__(self, k):
        return self.__mul__(1 / k)

    def prod(self, other):
        return self.x * other.x + self.y * other.y


def cochcurve(p1, p2, n):
    if n > 0:
        pd = (p2 - p1) / 3
        ps = p1 + pd
        pu = ps + pd.rot(math.pi / 3)
        pt = ps + pd
        cochcurve(p1, ps, n-1)
        print(f'{ps:>12.6f}')
        cochcurve(ps, pu, n-1)
        print(f'{pu:>12.6f}')
        cochcurve(pu, pt, n-1)
        print(f'{pt:>12.6f}')
        cochcurve(pt, p2, n-1)


n = int(input())
S = vec2d(0, 0)
T = vec2d(100, 0)
print(f'{S:>12.6f}')
cochcurve(S, T, n)
print(f'{T:>12.6f}')

Submission status: Accepted

Solution code:
import math

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

def koch(d, p1, p2):
    

    if d == 0:
        return
    
    t = Point((p1.x + 2 * p2.x )/3,(p1.y + 2 * p2.y )/3 )
    s = Point((p2.x + 2 * p1.x )/3,(p2.y + 2 * p1.y )/3 )
    
    u = Point((t.x-s.x) * (math.cos(math.pi / 3)) - (t.y-s.y) * (math.sin(math.pi / 3)) + s.x, (t.x-s.x) * (math.sin(math.pi / 3)) + (t.y-s.y) * (math.cos(math.pi / 3)) + s.y)
    #print(s.x, s.y , t.x, t.y, u.x, u.y)
    

    
    koch(d - 1, p1, s)
    print(s.x, s.y)
    koch(d - 1, s, u)
    print(u.x, u.y)
    koch(d - 1, u, t)
    print(t.x, t.y)
    koch(d - 1, t, p2)


n = int(input())
    
p1 = Point(0, 0)
p2 = Point(100, 0)

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

Submission status: Accepted

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

Submission status: Accepted

Solution code:
import math

def koch(start,end,n):
  if n==0:
    return
  else:
    point1=[0,0]
    point2=[0,0]
    point3=[0,0]
    
    point1[0]=(end[0]-start[0])/3 +start[0]
    point1[1]=(end[1]-start[1])/3 +start[1]
    
    point3[0]=(end[0]-start[0])*2/3+start[0]
    point3[1]=(end[1]-start[1])*2/3+start[1]
    
    rad60 = math.radians(60)
    point2[0]=(point3[0]-point1[0])* math.cos(rad60) -(point3[1]-point1[1])*math.sin(rad60) +point1[0]
    point2[1]=(point3[0]-point1[0])* math.sin(rad60) +(point3[1]-point1[1])*math.cos(rad60) +point1[1]
    
    koch(start,point1,n-1)
    print(*point1)
    koch(point1,point2,n-1)
    print(*point2)
    koch(point2,point3,n-1)
    print(*point3)
    koch(point3,end,n-1)

n=int(input())

start=[0,0]
end=[100,0]

print(*start)

if n>0:
  koch(start,end,n)
  

print(*end)

Submission status: Accepted

Solution code:
from math import*
a=(0,0)
b=(100,0)

def koch(n,ax,ay,bx,by):
    if n==0:
        return 0
    th=pi/3
    sx=(2*ax+bx)/3
    sy=(2*ay+by)/3
    tx=(ax+2*bx)/3
    ty=(ay+2*by)/3
    ux=(tx-sx)*cos(th)-(ty-sy)*sin(th)+sx
    uy=(tx-sx)*sin(th)+(ty-sy)*cos(th)+sy
    
    koch(n-1,ax,ay,sx,sy)
    print(sx,sy)
    koch(n-1,sx,sy,ux,uy)
    print(ux,uy)
    koch(n-1,ux,uy,tx,ty)
    print(tx,ty)
    koch(n-1,tx,ty,bx,by)


n=int(input())
print(*a)
koch(n,*a,*b)
print(*b)

Submission status: Accepted

Solution code:
from math import *
import sys

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def div3(a,b):
    c1=(2*a+b)/3
    c2=(a+2*b)/3
    return [c1,c2]

def main():
    n=int(input())
    xy=[[0,0],[100,0]]
    #aa=list(map(int, input().split()))
    for _ in range(n):
        nxy=[[0,0]]
        for [x0,y0],[x4,y4] in zip(xy,xy[1:]):
            x1,x3=div3(x0,x4)
            y1,y3=div3(y0,y4)
            a=((x3-x1)**2+(y3-y1)**2)**0.5
            rad=atan2(y3-y1,x3-x1)
            x2=x1+a*cos(rad+pi/3)
            y2=y1+a*sin(rad+pi/3)
            nxy+=[[x1,y1],[x2,y2],[x3,y3],[x4,y4]]
        xy=nxy
    for x,y in xy:
        print(x,y)

main()

Submission status: Accepted

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

start = (0,0)
end = (100,0)

def koch(n,p1,p2):
    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 )

    ux = (t[0] - s[0])/2 - (t[1] - s[1])*math.sqrt(3)/2 + s[0]
    uy = (t[0] - s[0])*math.sqrt(3)/2 + (t[1] - s[1])/2 + s[1]
    u = (ux, uy)
    koch(n-1,p1, s)
    ppp(s)
    koch(n-1, s, u)
    ppp(u)
    koch(n-1, u, t)
    ppp(t)
    koch(n-1, t,p2)

def ppp(t):
    print("{:.08f} {:.08f}".format(t[0],t[1]))

ppp(start)
koch(n,start,end)
ppp(end)

Submission status: Accepted

Solution code:

import math


class Point:
    def __init__(self, x=None, y=None):
        self.x = x
        self.y = y

    def print(self):
        print(round(self.x, 8), round(self.y, 8))


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

    s = Point()
    u = Point()
    t = Point()

    theta = math.radians(60.0)

    s.x = p1.x * 2.0/3.0 + p2.x * 1.0/3.0
    s.y = p1.y * 2.0/3.0 + p2.y * 1.0/3.0

    t.x = p1.x * 1.0/3.0 + p2.x * 2.0/3.0
    t.y = p1.y * 1.0/3.0 + p2.y * 2.0/3.0

    u.x = (t.x - s.x) * math.cos(theta) - (t.y - s.y) * math.sin(theta) + s.x
    u.y = (t.x - s.x) * math.sin(theta) + (t.y - s.y) * math.cos(theta) + s.y

    koch(d-1, p1, s)
    s.print()
    koch(d-1, s, u)
    u.print()
    koch(d-1, u, t)
    t.print()
    koch(d-1, t, p2)


N = int(input())

p1 = Point(0, 0)
p2 = Point(100, 0)

p1.print()
koch(N, p1, p2)
p2.print()

Submission status: Accepted

Solution code:
from math import cos,sin,radians

n=int(input())

def koch(n):
    if n==0:
        return [[0,0],[100,0]]
    points=koch(n-1)
    new_points=[]
    for i in range(len(points)-1):
        a_x=points[i][0]
        a_y=points[i][1]
        b_x=points[i+1][0]
        b_y=points[i+1][1]
        c_x,c_y=a_x*2/3+b_x/3,a_y*2/3+b_y/3
        d_x,d_y=a_x/3+b_x*2/3,a_y/3+b_y*2/3
        e_x=(d_x-c_x)*cos(radians(60))-(d_y-c_y)*sin(radians(60))+c_x
        e_y=(d_x-c_x)*sin(radians(60))+(d_y-c_y)*cos(radians(60))+c_y
        if [a_x,a_y] not in new_points:
            new_points.append([a_x,a_y])
        new_points.append([c_x,c_y])
        new_points.append([e_x,e_y])
        new_points.append([d_x,d_y])
        if [b_x,b_y] not in new_points:
            new_points.append([b_x,b_y])
    return new_points

for i in koch(n):
    print(*i)

Submission status: Accepted

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

n=int(input())
p1=[0,0]
p2=[100,0]
print(*p1)
kock(n,p1,p2)
print(*p2)

Submission status: Accepted

Solution code:
import math
class KochCurve(object):
	x = 0.0
	y = 0.0
	def koch(self, n, a, b):
		if n == 0:
			return 
		s = KochCurve()
		t = KochCurve()
		u = KochCurve()
		th = math.pi * 60.0 / 180.0
		s.x = (2.0 * a.x + 1.0 * b.x) / 3.0
		s.y = (2.0 * a.y + 1.0 * b.y) / 3.0
		t.x = (1.0 * a.x + 2.0 * b.x) / 3.0
		t.y = (1.0 * a.y + 2.0 * b.y) / 3.0
		u.x = (t.x - s.x) * math.cos(th) - (t.y - s.y) * math.sin(th) + s.x
		u.y = (t.x - s.x) * math.sin(th) + (t.y - s.y) * math.cos(th) + s.y	
		KochCurve().koch(n - 1, a, s)
		msg = "%.8f %.8f" % (s.x, s.y)
		print(msg)
		KochCurve().koch(n - 1, s, u)
		msg = "%.8f %.8f" % (u.x, u.y)
		print(msg)
		KochCurve().koch(n - 1, u, t)
		msg = "%.8f %.8f" % (t.x, t.y)
		print(msg)
		KochCurve().koch(n - 1, t, b)
a = KochCurve()
b = KochCurve()
n = int(input())
a.x = 0
a.y = 0
b.x = 100
b.y = 0
msg = "%.8f %.8f" % (a.x, a.y)
print(msg)
KochCurve().koch(n, a, b)
msg = "%.8f %.8f" % (b.x, b.y)
print(msg)

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-
import math

class KochCurve(object):
	# public変数
	x = 0.0
	y = 0.0

	# private変数
	#__xy = 0.0

	# 解法
	def koch(self, n, a, b):
		if n == 0:
			return 

		s = KochCurve()
		t = KochCurve()
		u = KochCurve()
		th = math.pi * 60.0 / 180.0

		s.x = (2.0 * a.x + 1.0 * b.x) / 3.0
		s.y = (2.0 * a.y + 1.0 * b.y) / 3.0
		t.x = (1.0 * a.x + 2.0 * b.x) / 3.0
		t.y = (1.0 * a.y + 2.0 * b.y) / 3.0
		u.x = (t.x - s.x) * math.cos(th) - (t.y - s.y) * math.sin(th) + s.x
		u.y = (t.x - s.x) * math.sin(th) + (t.y - s.y) * math.cos(th) + s.y
		
		KochCurve().koch(n - 1, a, s)
		msg = "%.8f %.8f" % (s.x, s.y)
		print(msg)
		KochCurve().koch(n - 1, s, u)
		msg = "%.8f %.8f" % (u.x, u.y)
		print(msg)
		KochCurve().koch(n - 1, u, t)
		msg = "%.8f %.8f" % (t.x, t.y)
		print(msg)
		KochCurve().koch(n - 1, t, b)


if __name__ == '__main__':
	a = KochCurve()
	b = KochCurve()

	n = int(input())

	a.x = 0
	a.y = 0
	b.x = 100
	b.y = 0

	msg = "%.8f %.8f" % (a.x, a.y)
	print(msg)
	KochCurve().koch(n, a, b)
	msg = "%.8f %.8f" % (b.x, b.y)
	print(msg)

Submission status: Accepted

Solution code:
def koch(n, left, right):
	vector = [(right[0] - left[0])/3, (right[1] - left[1])/3]
	vector_up = [-vector[1]*(3**0.5)/2, vector[0]*(3**0.5)/2]
	point1 = [left[0] + vector[0], left[1] + vector[1]]
	point2 = [left[0] + 2*vector[0], left[1] + 2*vector[1]]
	middle = [left[0] + vector[0]*3/2 + vector_up[0],
			  left[1] + vector[1]*3/2 + vector_up[1]]

	if n == 0:
		return [right]

	if n == 1:
		return [point1, middle, point2, right]

	return koch(n-1, left, point1) + koch(n-1, point1, middle)\
			+ koch(n-1, middle, point2) + koch(n-1, point2, right)

if __name__ == "__main__":
	for point in [[0,0]] + koch(int(input()), [0,0], [100,0]):
		print(*point)

Submission status: Accepted

Solution code:
import math

pi=math.pi

def Koch(n,p0,p1):
        if n==0:
           return False

        s=[0 for i in range(2)]
        t=[0 for i in range(2)]
        u=[0 for i in range(2)]
        
        s =[(2*p0[0]+1*p1[0])/3.0,(2*p0[1]+1*p1[1])/3.0]
        t =[(1*p0[0]+2*p1[0])/3.0,(1*p0[1]+2*p1[1])/3.0]
        u =[(t[0]-s[0]) * math.cos (pi / 3) - (t[1]-s[1])* math.sin (pi / 3)+s[0],(t[0]-s[0]) * math.sin (pi / 3) + (t[1]-s[1])* math.cos (pi / 3)+s[1]]
        Koch(n-1,p0,s)
        print("{0:.8f} {1:.8f}".format(s[0],s[1]))
        Koch(n-1,s,u)
        print("{0:.8f} {1:.8f}".format(u[0],u[1]))
        Koch(n-1,u,t)
        print("{0:.8f} {1:.8f}".format(t[0],t[1]))
        Koch(n-1,t,p1)

p0=[0, 0]
p1=[100,0]
n=int(input())

print("{0:.8f} {1:.8f}".format(p0[0],p0[1]))
Koch(n,p0,p1)
print("{0:.8f} {1:.8f}".format(p1[0],p1[1]))

Submission status: Accepted

Solution code:
import math

def rot60(s,t):
    v=t-s
    a=1/2+complex(0,(math.sqrt(3)/2))
    return v*a+s

def puts(p):
    x=p.real
    y=p.imag
    print('{real} {imaginary}'.format(real=x,imaginary=y))

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

    s=(p2-p1)*(1/3)+p1
    t=(p2-p1)*(2/3)+p1
    u=rot60(s,t)
    koch(p1,s,n-1)
    puts(s)
    koch(s,u,n-1)
    puts(u)
    koch(u,t,n-1)
    puts(t)
    koch(t,p2,n-1)
    
n=int(input())
s=complex(0,0)
t=complex(100,0)
puts(s)
koch(s,t,n) 
puts(t)

Submission status: Accepted

Solution code:
import math

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

    sx = 2/3*p1[0]+1/3*p2[0]
    sy = 2/3*p1[1]+1/3*p2[1]
    s = (sx,sy)

    tx = 1/3*p1[0]+2/3*p2[0]
    ty = 1/3*p1[1]+2/3*p2[1]
    t = (tx,ty)

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

    k(n-1,p1,s)
    print(*s)
    k(n-1,s,u)
    print(*u)
    k(n-1,u,t)
    print(*t)
    k(n-1,t,p2)

n=int(input())
p1=(0,0)
p2=(100,0)

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

Submission status: Accepted

Solution code:
import math

def koch(n,p1x,p1y,p2x,p2y):
    if n == 0:
        return
    
    sx = (2*p1x+1*p2x)/3
    sy = (2*p1y+1*p2y)/3
    tx = (1*p1x+2*p2x)/3
    ty = (1*p1y+2*p2y)/3
    theta = math.pi/3  #180[deg] == math.pi[rad]
    ux = math.cos(theta)*(tx-sx) - math.sin(theta)*(ty-sy)+sx
    uy = math.sin(theta)*(tx-sx) + math.cos(theta)*(ty-sy)+sy

    koch(n-1, p1x, p1y, sx, sy)
    print("{:.8f} {:.8f}".format(sx, sy))
    koch(n-1, sx, sy, ux, uy)
    print("{:.8f} {:.8f}".format(ux, uy))
    koch(n-1, ux, uy, tx, ty)
    print("{:.8f} {:.8f}".format(tx, ty))
    koch(n-1, tx, ty, p2x, p2y)

n = int(input())
p1x,p1y = 0.0,0.0
p2x,p2y = 100.0,0.0
print("{:.8f} {:.8f}".format(p1x, p1y))
koch(n, p1x, p1y, p2x, p2y)
print("{:.8f} {:.8f}".format(p2x, p2y))

Submission status: Accepted

Solution code:
from math import cos, sin, pi


def make_koch_curve(N, n1, n2):
    s = ((2 * n1[0] + n2[0]) / 3, (2 * n1[1] + n2[1]) / 3)
    t = ((n1[0] + 2 * n2[0]) / 3, (n1[1] + 2 * n2[1]) / 3)
    u = ((t[0] - s[0])*cos(pi/3) - (t[1] - s[1])*sin(pi/3) + s[0],
         (t[0] - s[0])*sin(pi/3) + (t[1] - s[1])*cos(pi/3) + s[1])
    if N == 0:
        return
    make_koch_curve(N-1, n1, s)
    print(*s)
    make_koch_curve(N-1, s, u)
    print(*u)
    make_koch_curve(N-1, u, t)
    print(*t)
    make_koch_curve(N-1, t, n2)


def main():
    N = int(input())
    n1 = (0., 0.)
    n2 = (100., 0.)
    print(*n1)
    make_koch_curve(N, n1, n2)
    print(*n2)


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import math
#import matplotlib.pyplot as plt

def kock(n,p1,p2):
    #global x
    #global y
    if n==0:
        return
    s=[0,0]
    t=[0,0]
    u=[0,0]
    
    s[0]=(float((2*p1[0]+p2[0])/3))
    s[1]=(float((2*p1[1]+p2[1])/3))
    t[0]=(float((p1[0]+2*p2[0])/3))
    t[1]=(float((p1[1]+2*p2[1])/3))

    u[0]=((t[0]-s[0])*math.cos(math.radians(60))-(t[1]-s[1])*math.sin(math.radians(60))+s[0])
    u[1]=((t[0]-s[0])*math.sin(math.radians(60))+(t[1]-s[1])*math.cos(math.radians(60))+s[1])
    


    kock(n-1,p1,s)
    print(*s)
   # x.append(s[0])
    #y.append(s[1])
    kock(n-1,s,u)
    print(*u)
    #x.append(u[0])
    #y.append(u[1])
    kock(n-1,u,t)
    print(*t)
    #x.append(t[0])
    #y.append(t[1])
    kock(n-1,t,p2)



n=int(input())
p1=[0.0,0.0]
p2=[100.0,0.0]
#x=[]
#y=[]
print(*p1)
#x.append(p1[0])
#y.append(p1[1])
kock(n,p1,p2)
print(*p2)

Submission status: Accepted

Solution code:
import math
class Point(object):
     def __init__(self, x,y):
          self.x = x*1.0
          self.y = y*1.0
def Koch(n,p1,p2):
    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)
    u=Point((t.x-s.x)*math.cos(math.radians(60))-(t.y-s.y)*math.sin(math.radians(60))+s.x,(t.x-s.x)*math.sin(math.radians(60))+(t.y-s.y)*math.cos(math.radians(60))+s.y)
    if n==0:
        return
    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)
n=input()
p1=Point(0,0)
p2=Point(100,0)
print p1.x,p1.y
Koch(n,p1,p2)
print p2.x,p2.y

Submission status: Accepted

Solution code:
import math

n = int(input())

def koch(n,a,b): #a,b:tuple
    if n==0:
        return
    th = math.pi*60/180
    s = ((2*a[0]+b[0])/3,(2*a[1]+b[1])/3)
    t = ((a[0]+2*b[0])/3,(a[1]+2*b[1])/3)
    u = ((t[0]-s[0])*math.cos(th)-(t[1]-s[1])*math.sin(th)+s[0],(t[0]-s[0])*math.sin(th)+(t[1]-s[1])*math.cos(th)+s[1])

    koch(n-1,a,s)
    print(s[0],s[1])
    koch(n-1,s,u)
    print(u[0],u[1])
    koch(n-1,u,t)
    print(t[0],t[1])
    koch(n-1,t,b)

a = (0,0)
b = (100,0)
print(a[0],a[1])
koch(n,a,b)
print(b[0],b[1])

Submission status: Accepted

Solution code:
import math

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

    sx = (2*p1[0] + p2[0]) / 3
    sy = (2*p1[1] + p2[1]) / 3
    s = [sx,sy]
    tx = (p1[0] + 2*p2[0]) / 3
    ty = (p1[1] + 2*p2[1]) / 3
    t = [tx,ty]
    ux = (t[0] - s[0]) * 0.5 - (t[1] - s[1]) * math.sin(math.radians(60)) + s[0]
    uy = (t[0] - s[0]) * math.sin(math.radians(60)) + (t[1] - s[1]) * 0.5 + s[1]
    u = [ux,uy]
    
    koch(n-1, p1, s)
    print(s[0], " ", s[1]) 
    koch(n-1, s, u)
    print(u[0], " ", u[1]) 
    koch(n-1, u, t)
    print(t[0], " ", t[1]) 
    koch(n-1, t, p2)

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

print(p1[0], " ", p1[1])
koch(n, p1, p2)
print(p2[0], " ", p2[1])

Submission status: Accepted

Solution code:
"""ICGNYN 17D8103016H 土屋　怜"""
import random
import math

def hura (a):
    ind=1
    for i in range(len(a)-1):
        c= [(a[i*4+1][0]-a[i*4][0])/3+a[i*4][0], (a[i*4+1][1]-a[i*4][1])/3+a[i*4][1]]
        d=[(a[i*4+1][0]-a[i*4][0])*2/3+a[i*4][0], (a[i*4+1][1]-a[i*4][1])*2/3+a[i*4][1]]
        cos=math.cos(math.pi/3)
        sin=math.sin(math.pi/3)
        f = [d[0]-c[0],d[1]-c[1]]
        b= [f[0]*cos-sin*f[1]+c[0],sin*f[0]+cos*f[1]+c[1]]
        a.insert(ind,c)
        a.insert(ind+1,b)
        a.insert(ind+2,d)
        ind=ind+4
        

N = int(input())
x=[[0,0],[100,0]]
for i in range(N):
    hura(x)
for i in range(len(x)):
  print(x[i][0],end="")
  print(" ",end="")
  print(x[i][1])

Submission status: Accepted

Solution code:
import math

def CalcCoordinate(xa, ya, xb, yb):
    arg = math.atan2(yb-ya, xb-xa) #角度
    d = math.sqrt((xb-xa)*(xb-xa) + (yb-ya)*(yb-ya)) #AとBの距離
    xc = d/2 #ピタゴラスの定理より
    #S = math.sqrt(3)*d*d/2
    #正三角形にヘロンの公式を適用(3辺の長さが同じなので3*d)
    yc = math.sqrt(3)*d/2

    #if(yb <= ya):
    ux = xc*math.cos(arg) - yc*math.sin(arg) + xa
    uy = xc*math.sin(arg) + yc*math.cos(arg) + ya
    return ux, uy
    """
    else:
        ux = xc*math.cos(arg) + yc*math.sin(arg) + xa
        uy = xc*math.sin(arg) - yc*math.cos(arg) + ya
        return ux, uy
"""

def MakeTriangle(x1, y1, x2, y2, n):
    if(n != 0):
        sx = (2*x1 + x2) / 3
        sy = (2*y1 + y2) / 3
        tx = (x1 + 2*x2) / 3
        ty = (y1 + 2*y2) / 3
        ux, uy = CalcCoordinate(sx, sy, tx, ty)
        MakeTriangle(x1, y1, sx, sy, n-1)
        print(sx, sy)
        MakeTriangle(sx, sy, ux, uy, n-1)
        print(ux, uy)
        MakeTriangle(ux, uy, tx, ty, n-1)
        print(tx, ty)
        MakeTriangle(tx, ty, x2, y2, n-1)
    else:
        return
        
  

x1 = 0
y1 = 0
x2 = 100
y2 = 0

n = int(input())

print(x1, y1)
MakeTriangle(x1, y1, x2, y2, n)
print(x2, y2)

Submission status: Accepted

Solution code:
import math


def koch(count, p1, p2):
    if count == 0:
        return
    s = [0, 0]
    t = [0, 0]
    u = [0, 0]
    s[0] = (2 * p1[0] + p2[0]) / 3
    s[1] = (2 * p1[1] + p2[1]) / 3
    t[0] = (2 * p2[0] + p1[0]) / 3
    t[1] = (2 * p2[1] + p1[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(count - 1, p1, s)
    print(s[0], s[1])

    koch(count - 1, s, u)
    print(u[0], u[1])

    koch(count - 1, u, t)
    print(t[0], t[1])

    koch(count - 1, t, p2)


if __name__ == '__main__':
    n = int(input())
    p1 = [0.0, 0.0]
    p2 = [100.0, 0.0]
    print(p1[0], p1[1])
    koch(n, p1, p2)
    print(p2[0], p2[1])

Submission status: Accepted

Solution code:
import math
def koch(left, right, n):
    if n < 1: print(" ".join(map(str, left))); return
    
    s, t, u = [0] * 2, [0] * 2, [0] * 2
    s[0] = (2 * left[0] + right[0]) / 3.0
    s[1] = (2 * left[1] + right[1]) / 3.0
    
    t[0] = (left[0] + 2 * right[0]) / 3.0
    t[1] = (left[1] + 2 * right[1]) / 3.0
    
    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(left, s, n-1)
    koch(s, u, n-1)
    koch(u, t, n-1)
    koch(t, right, n-1)
    
n = int(input())
left = [0, 0]
right = [100, 0]

koch(left, right, n)
print(right[0], right[1])