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 sys
from math import sin, cos, radians
input = sys.stdin.readline
deg = radians(60)

def Koch(n, p1_x, p1_y, p2_x, p2_y):
    if n != 0:
        s_x = (2 * p1_x + p2_x) / 3
        s_y = (2 * p1_y + p2_y) / 3
        t_x = (p1_x + 2 * p2_x) / 3
        t_y = (p1_y + 2 * p2_y) / 3
        u_x = (t_x - s_x) * cos(deg) - (t_y - s_y) * sin(deg) + s_x
        u_y = (t_x - s_x) * sin(deg) + (t_y - s_y) * cos(deg) + s_y
        Koch(n - 1, p1_x, p1_y, s_x, s_y)
        print('{:.8f} {:.8f}'.format(s_x, s_y))
        Koch(n - 1, s_x, s_y, u_x, u_y)
        print('{:.8f} {:.8f}'.format(u_x, u_y))
        Koch(n - 1, u_x, u_y, t_x, t_y)
        print('{:.8f} {:.8f}'.format(t_x, t_y))
        Koch(n - 1, t_x, t_y, p2_x, p2_y)
    else:
        return

n = int(input())
p1_x, p1_y = 0, 0
p2_x, p2_y = 100, 0
print('{:.8f} {:.8f}'.format(p1_x, p1_y))
Koch(n, p1_x, p1_y, p2_x, p2_y)
print('{:.8f} {:.8f}'.format(p2_x, p2_y))

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:
N = int(input())
from math import sin, cos, pi
th = pi/3
def koch(d, p1, p2):
    if d == 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]) * cos(th) - (t[1] - s[1]) * sin(th) + s[0]
    u[1] = (t[0] - s[0]) * sin(th) + (t[1] - s[1]) * cos(th) + 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)

p_start = [0.0, 0.0]
p_end = [100.0, 0.0]
print(*p_start)
koch(N, p_start, p_end)
print(*p_end)

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, 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) #無限フローでERRORのでnを使う
    
    #plot(x1, y1)
    #plot(sx, sy)
    #plot(ux, uy)
    #plot(tx, ty)
    #plot(x2, y2)

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

Submission status: Accepted

Solution code:
import math
cos = math.cos(math.radians(60))
sin = math.sin(math.radians(60))

def koch(count, p1x, p1y, p2x, p2y):
    global cos
    global sin
    if count == 0:
        return
    sx, sy = (2*p1x + p2x)/3, (2*p1y + p2y)/3
    tx, ty = (p1x + 2*p2x)/3, (p1y + 2*p2y)/3
    ux, uy = cos*(sx + tx) - sin*(ty - sy), sin*(tx - sx) + cos*(sy + ty)

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

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

Submission status: Accepted

Solution code:
import math

def Koch(Px, Py, Qx, Qy, n) :
    if n == 0 :
        return
    else :
        Ax = (2 * Px + Qx) / 3
        Ay = (2 * Py + Qy) / 3
        Bx = (Px + 2 * Qx) / 3
        By = (Py + 2 * Qy) / 3
        Cx = Ax + (Bx - Ax) * math.cos(math.pi/3) - (By - Ay) * math.sin(math.pi/3) 
        Cy = Ay + (Bx - Ax) * math.sin(math.pi/3) + (By - Ay) * math.cos(math.pi/3)
        
        Koch(Px, Py, Ax, Ay, n-1)
        print(Ax, Ay)
        Koch(Ax, Ay, Cx, Cy, n-1)
        print(Cx, Cy)
        Koch(Cx, Cy, Bx, By, n-1)
        print(Bx, By)
        Koch(Bx, By, Qx, Qy, n-1)

n = int(input())
print(0, 0.00000000)
Koch(0.00000000, 0.00000000, 100.00000000, 0.00000000, n)
print(100.00000000, 0.00000000)

Submission status: Accepted

Solution code:
#(41)ゴッホ曲線

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
pi = math.pi

th = pi * 60.0 / 180.0
cos = math.cos(th)
sin = math.sin(th)

class Point():
    def __init__(self):
        self.x = 0.0
        self.y = 0.0
        
def koch(n, p1, p2):
    if n == 0:
        return None
    
    s = Point()
    t = Point()
    u = Point()
    
    s.x = (2.0 * p1.x + 1.0 * p2.x) / 3.0
    s.y = (2.0 * p1.y + 1.0 * p2.y) / 3.0
    t.x = (1.0 * p1.x + 2.0 * p2.x) / 3.0
    t.y = (1.0 * p1.y + 2.0 * p2.y) / 3.0
    u.x = (t.x - s.x) * cos - (t.y - s.y) * sin + s.x
    u.y = (t.x - s.x) * sin + (t.y - s.y) * cos + s.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)
    
def main():
       
    p1 = Point()
    p2 = Point()
    
    n = int(input())
    
    p2.x = 100
    
    print(p1.x, p1.y)
    koch(n, p1, p2)
    print(p2.x, p2.y)
    
    return 0
    
if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import cmath

def koch(n, p1, p2):
  if not n:
    return None
  s = (2*p1 + p2) / 3
  t = (p1 + 2*p2) / 3
  u = s + cmath.rect(1, cmath.pi/3) * (t - s)
  koch(n-1, p1, s)
  print(s.real, s.imag)
  koch(n-1, s, u)
  print(u.real, u.imag)
  koch(n-1, u, t)
  print(t.real, t.imag)
  koch(n-1, t, p2)

p1, p2 = 0j, 100+0j
print(p1.real, p1.imag)    
koch(int(input()), p1, p2)
print(p2.real, p2.imag)

Submission status: Accepted

Solution code:
  
import math

class Pos:
  def init(x, y):
    self.x = x
    self.y = y

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

  s, t = Pos(), Pos()
  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

  cos60 = math.cos(math.radians(60))
  sin60 = math.sin(math.radians(60))

  u = Pos()
  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

  kock(n-1, p1, s)
  print("{:.5f} {:.5f}".format(s.x, s.y))
  kock(n-1, s, u)
  print("{:.5f} {:.5f}".format(u.x, u.y))
  kock(n-1, u, t)
  print("{:.5f} {:.5f}".format(t.x, t.y))
  kock(n-1, t, p2)

n = int(input())

p1, p2 = Pos(), Pos()
p1.x, p1.y = 0.0, 0.0
p2.x, p2.y = 100.0, 0.0

print("{:.5f} {:.5f}".format(p1.x, p1.y))
kock(n, p1, p2)
print("{:.5f} {:.5f}".format(p2.x, p2.y))

Submission status: Accepted

Solution code:
import math

c60 = math.cos(math.radians(60))
s60 = math.sin(math.radians(60))

def koch(d, p1, p2):
    """ Print the coordinates of the vertices of Koch Curve.
    d is the depth of recursion.
    p1, p2 are coordinates of end point of the initial state.
    """
    if d == 0:
        return

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

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

    dx = tx - sx
    dy = ty - sy

    ux = dx * c60 - dy * s60 + sx
    uy = dx * s60 + dy * c60 + 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())

ax = 0
ay = 0

bx = 100
by = 0

print("{0:.8f} {1:.8f}".format(ax, ay))
koch(n, (ax, ay), (bx, by))
print("{0:.8f} {1:.8f}".format(bx, by))

Submission status: Accepted

Solution code:
import math

def Koch(Px, Py, Qx, Qy, n) :
    if n == 0 :
        return
    else :
        Ax = (2 * Px + Qx) / 3
        Ay = (2 * Py + Qy) / 3
        Bx = (Px + 2 * Qx) / 3
        By = (Py + 2 * Qy) / 3
        Cx = Ax + (Bx - Ax) * math.cos(math.pi/3) - (By - Ay) * math.sin(math.pi/3) 
        Cy = Ay + (Bx - Ax) * math.sin(math.pi/3) + (By - Ay) * math.cos(math.pi/3)
        
        Koch(Px, Py, Ax, Ay, n-1)
        print(Ax, Ay)
        Koch(Ax, Ay, Cx, Cy, n-1)
        print(Cx, Cy)
        Koch(Cx, Cy, Bx, By, n-1)
        print(Bx, By)
        Koch(Bx, By, Qx, Qy, n-1)

n = int(input())
print(0, 0.00000000)
Koch(0.00000000, 0.00000000, 100.00000000, 0.00000000, n)
print(100.00000000, 0.00000000)

Submission status: Accepted

Solution code:
import math

pi = math.pi

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

def koch(n, p1, p2):
    if n == 0:
        return
    s = [(2*p1[0]+p2[0])/3.0,(2*p1[1]+p2[1])/3.0]
    t = [(1*p1[0]+2*p2[0])/3.0,(p1[1]+2*p2[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, p1, s)
    print(*s)
    koch(n - 1, s, u)
    print(*u)
    koch(n - 1, u, t)
    print(*t)
    koch(n - 1, t, p2)

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

Submission status: Accepted

Solution code:
import math


def koch(n, p1_x, p1_y, p2_x, p2_y):
    if n == 0:
        print(f"{p1_x:.8f} {p1_y:.8f}")
        return

    # p1, p2からs, t, uを計算

    # 与えられた線分(p1, p2) を3等分点s、tを求める
    s_x = (2 * p1_x + 1 * p2_x) / 3
    s_y = (2 * p1_y + 1 * p2_y) / 3

    t_x = (p1_x + 2 * p2_x) / 3
    t_y = (p1_y + 2 * p2_y) / 3

    # 線分を3等分する2点 s,t を頂点とする正三角形 (s,u,t) を作成する
    u_x = (
        (t_x - s_x) * math.cos(math.pi / 3) - (t_y - s_y) * math.sin(math.pi / 3) + s_x
    )
    u_y = (
        (t_x - s_x) * math.sin(math.pi / 3) + (t_y - s_y) * math.cos(math.pi / 3) + s_y
    )

    # 線分 (p1,s)、線分 (s,u)、線分 (u,t)、線分 (t,p2)に対して再帰的に同じ操作を繰り返す
    koch(n - 1, p1_x, p1_y, s_x, s_y)
    koch(n - 1, s_x, s_y, u_x, u_y)
    koch(n - 1, u_x, u_y, t_x, t_y)
    koch(n - 1, t_x, t_y, p2_x, p2_y)


n = int(input())
koch(n, 0, 0, 100, 0)
print("100.00000000 0.00000000")

Submission status: Accepted

Solution code:
import math
def kock(n,p1,p2):
    a=math.radians(60)
    if n==0:
        return 0
    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])*math.cos(a)-(t[1]-s[1])*math.sin(a))+s[0],(t[0]-s[0])*math.sin(a)+(t[1]-s[1])*math.cos(a)+s[1]]
    kock(n-1,p1,s)
    print(" ".join(map(str,s)))
    kock(n-1,s,u)
    print(" ".join(map(str,u)))
    kock(n-1,u,t)
    print(" ".join(map(str,t)))
    kock(n-1,t,p2)
n=int(input())
start=[float(0),float(0)]
end=[float(100),float(0)]
print(" ".join(map(str,start)))
kock(n,start,end)
print(" ".join(map(str,end)))

Submission status: Accepted

Solution code:
import math
cos60 = math.cos(math.pi*60/180)
sin60 = math.sin(math.pi*60/180)
#add_triangle
# input: start(x, y) end(x, y)
def add_triangle(start, end):
    x1 = (2*start[0] + end[0]) / 3
    x3 = (start[0] + 2*end[0]) / 3
    y1 = (2*start[1] + end[1]) / 3
    y3 = (start[1] + 2*end[1]) / 3
    x2 = x1 + (x3-x1)*cos60 - (y3-y1)*sin60
    y2 = y1 + (x3-x1)*sin60 + (y3-y1)*cos60
    return [(x1,y1), (x2,y2), (x3,y3)]

#koch_recursion
#input list [(x1,y1),(x2,y2),(x3,y3)...]
def koch_recursion(list1):
    output = []
    for i in range(len(list1)-1):
        output.append(list1[i])
        output += add_triangle(list1[i], list1[i+1])
    output.append(list1[len(list1)-1])
    return output

#Koch  call koch_recursion(0, 100)
def Koch(start, end, n):
    output = [start, end]
    for i in range(n):
        output = koch_recursion(output)
    for x, y in output:
        print("{:.8f} {:.8f}".format(x, y))

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

Submission status: Accepted

Solution code:

def s(p,q):
    a=p[0]
    b=p[1]
    c=q[0]
    d=q[1]
    return [(2*a+c)/3,(2*b+d)/3]
def t(p,q):
    a=p[0]
    b=p[1]
    c=q[0]
    d=q[1]    
    return [(a+2*c)/3,(b+2*d)/3]
def u(p,q):
    a=p[0]
    b=p[1]
    c=q[0]
    d=q[1]
    return [(a+c)/2+(3**(1/2))*(b-d)/6,(b+d)/2+(3**(1/2))*(c-a)/6]

def koch(p1,p2,n):
    if n==0:
        return [p1]
    else:
        return koch(p1,s(p1,p2),n-1)+koch(s(p1,p2),u(p1,p2),n-1)+koch(u(p1,p2),t(p1,p2),n-1)+koch(t(p1,p2),p2,n-1)

n=int(input())
a=[0,0]
b=[100,0]
for i in koch(a,b,n):
    print(str(i[0])+" "+str(i[1]))

print(str(b[0])+" "+str(b[1]))

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:
from math import sin, cos, pi

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

    s = [None, None]
    u = [None, None]
    t = [None, None]
    
    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])*cos(1/3*pi) - (t[1] - s[1])*sin(1/3*pi) + s[0]
    u[1] = (t[0] - s[0])*sin(1/3*pi) + (t[1] - s[1])*cos(1/3*pi) + s[1]

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

num = int(input())
print(0.0, 0.0)
koch_curve(num, [0.0, 0.0], [100.0, 0.0])
print(100.0, 0.0)

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 koch(n,p1,p2):

    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)

    theta = math.radians(60)
    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)

    if n>0:
        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)
    else: return

n = int(input())
a = [0.00000000,0.00000000]
b = [100.00000000,0.00000000]
print(*map(float,a))
koch(n,a,b)
print(*map(float,b))

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 + 1 * x2)/3
    sy = (2 * y1 + 1 * y2)/3
    tx = (1 * x1 + 2 * x2)/3
    ty = (1 * 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 sys, os, math, bisect, itertools, collections, heapq, queue

# from scipy.sparse.csgraph import csgraph_from_dense, floyd_warshall
# from decimal import Decimal
# from collections import defaultdict, deque

sys.setrecursionlimit(10000000)

ii = lambda: int(sys.stdin.buffer.readline().rstrip())
il = lambda: list(map(int, sys.stdin.buffer.readline().split()))
fl = lambda: list(map(float, sys.stdin.buffer.readline().split()))
iln = lambda n: [int(sys.stdin.buffer.readline().rstrip()) for _ in range(n)]

iss = lambda: sys.stdin.buffer.readline().decode().rstrip()
sl = lambda: list(map(str, sys.stdin.buffer.readline().decode().split()))
isn = lambda n: [sys.stdin.buffer.readline().decode().rstrip() for _ in range(n)]

lcm = lambda x, y: (x * y) // math.gcd(x, y)

MOD = 10 ** 9 + 7
MAX = float('inf')


def koch(N, ax, ay, bx, by):
    if N == 0: return

    # 度をラジアンに変換
    radians = math.radians(60)
    # 線分を3等分する、
    # 座標sと座標tの位置を求める
    sx = (2 * ax + bx) / 3
    sy = (2 * ay + by) / 3
    tx = (ax + 2 * bx) / 3
    ty = (ay + 2 * by) / 3

    # 座標sと座標tから正三角形となる座標uを求める
    ux = (tx - sx) * math.cos(radians) - (ty - sy) * math.sin(radians) + sx
    uy = (tx - sx) * math.sin(radians) + (ty - sy) * math.cos(radians) + sy

    # 座標aと座標sのコッホ曲線を求める
    koch(N - 1, ax, ay, sx, sy)
    print('{:.08f} {:.08f}'.format(sx, sy))  # 座標s

    # 座標sと座標uのコッホ曲線を求める
    koch(N - 1, sx, sy, ux, uy)
    print('{:.08f} {:.08f}'.format(ux, uy))  # 座標u

    # 座標uと座標tのコッホ曲線を求める
    koch(N - 1, ux, uy, tx, ty)
    print('{:.08f} {:.08f}'.format(tx, ty))  # 座標t

    # 座標tと座標bのコッホ曲線を求める
    koch(N - 1, tx, ty, bx, by)


def main():
    if os.getenv("LOCAL"):
        sys.stdin = open("input.txt", "r")

    N = ii()
    print('{:.08f} {:.08f}'.format(0, 0))  # 座標a
    koch(N, 0, 0, 100, 0)
    print('{:.08f} {:.08f}'.format(100, 0))  # 座標b


if __name__ == '__main__':
    main()

Submission status: Accepted

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

    s_x = p1[0] * 2/3 + p2[0] * 1/3
    s_y = p1[1] * 2/3 + p2[1] * 1/3

    t_x = p1[0] * 1/3 + p2[0] * 2/3
    t_y = p1[1] * 1/3 + p2[1] * 2/3

    u_x = (t_x - s_x) * 1/2 - (t_y - s_y) * 3 ** 0.5 / 2 + s_x
    u_y = (t_x - s_x) * 3 ** 0.5 / 2 + (t_y - s_y) / 2 + s_y

    s, t, u = (s_x, s_y), (t_x, t_y), (u_x, u_y)
    
    koch(n - 1, p1, s)
    print(' '.join(str(i) for i in s))
    koch(n - 1, s, u)
    print(' '.join(str(i) for i in u))
    koch(n - 1, u, t)
    print(' '.join(str(i) for i in t))
    koch(n - 1, t, p2)
    
    
S, G = (0, 0), (100, 0)
print(' '.join(str(i) for i in S))
koch(int(input()), S, G)
print(' '.join(str(i) for i in G))

Submission status: Accepted

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

A = []
def koch(d, p1, p2):
    rot = math.radians(60)
    if d == 0:
        return 0
    else:
        s = ((2.0 * p1[0] + p2[0]) / 3.0, (2.0 * p1[1] + p2[1]) / 3.0)
        t = ((2.0 * p2[0] + p1[0]) / 3.0, (2.0 * p2[1] + p1[1]) / 3.0)
        ux = (t[0] - s[0]) * math.cos(rot) - (t[1] - s[1]) * math.sin(rot) + s[0]
        uy = (t[0] - s[0]) * math.sin(rot) + (t[1] - s[1]) * math.cos(rot) + s[1]
        u = (ux, uy)
        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)

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:
from math import sqrt
q3 = sqrt(3)
fmt = "%.8f %.8f"
def koch(x0, y0, x1, y1, c):
    if c == n:
        return (fmt % (x0, y0),)
    xp = (x0*2 + x1) / 3
    yp = (y0*2 + y1) / 3

    xq = (x0 + x1*2) / 3
    yq = (y0 + y1*2) / 3

    dx = (x1 - x0) / 6
    dy = (y1 - y0) / 6

    xr = xp + (dx - dy * q3)
    yr = yp + (dx * q3 + dy)

    return koch(x0, y0, xp, yp, c+1) + koch(xp, yp, xr, yr, c+1) + koch(xr, yr, xq, yq, c+1) + koch(xq, yq, x1, y1, c+1)
n = int(input())
print(*koch(0, 0, 100, 0, 0)+(fmt % (100, 0),), sep='\n')

Submission status: Accepted

Solution code:
n = int(input())
r3 = 3 ** 0.5
A = (0.0, 0.0)
B = (100.0, 0.0)

def koch(n, A, B):
    if n == 0:
        return

    C1 = ((2 * A[0] + B[0]) / 3, (2 * A[1] + B[1]) / 3)
    C3 = ((A[0] + 2 * B[0]) / 3, (A[1] + 2 * B[1]) / 3)
    X, Y = C3[0] - C1[0], C3[1] - C1[1]
    C2 = (C1[0] + (X - Y * r3) / 2, C1[1] + (X * r3 + Y) / 2)

    koch(n - 1, A, C1)
    print("{:.5f} {:.5f}".format(C1[0], C1[1]))
    koch(n - 1, C1, C2)
    print("{:.5f} {:.5f}".format(C2[0], C2[1]))
    koch(n - 1, C2, C3)
    print("{:.5f} {:.5f}".format(C3[0], C3[1]))
    koch(n - 1, C3, B)

print("{:.5f} {:.5f}".format(A[0], A[1]))
koch(n, A, B)
print("{:.5f} {:.5f}".format(B[0], B[1]))

Submission status: Accepted

Solution code:
from math import cos, sin, pi


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

    def show(self):
        print(f"{self.x:.8f} {self.y:.8f}")


def calc_s(p1, p2) -> Point:
    x = p1.x * 2 / 3 + p2.x / 3
    y = p1.y * 2 / 3 + p2.y / 3
    s = Point(x, y)
    return s


def calc_t(p1, p2) -> Point:
    x = p1.x / 3 + p2.x * 2 / 3
    y = p1.y / 3 + p2.y * 2 / 3
    t = Point(x, y)
    return t


def calc_u(s, t) -> Point:
    theta = pi / 3
    x = s.x + (t.x - s.x) * cos(theta) - (t.y - s.y) * sin(theta)
    y = s.y + (t.x - s.x) * sin(theta) + (t.y - s.y) * cos(theta)
    u = Point(x, y)
    return u


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

    s = calc_s(p1, p2)
    t = calc_t(p1, p2)
    u = calc_u(s, t)

    koch(n - 1, p1, s)
    s.show()

    koch(n - 1, s, u)
    u.show()

    koch(n - 1, u, t)
    t.show()

    koch(n - 1, t, p2)


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

    p1.show()
    koch(n, p1, p2)
    p2.show()


if __name__ == "__main__":
    main()

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)*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(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 KC(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]
    u=[(t[0]-s[0])*math.cos(math.pi/3)-(t[1]-s[1])*math.sin(math.pi/3)+s[0],(t[0]-s[0])*math.sin(math.pi/3)+(t[1]-s[1])*math.cos(math.pi/3)+s[1]]
    KC(n-1,p1,s)
    print(str(format(s[0],'.8f'))+" "+str(format(s[1],'.8f')))
    KC(n-1,s,u)
    print(str(format(u[0],'.8f'))+" "+str(format(u[1],'.8f')))
    KC(n-1,u,t)
    print(str(format(t[0],'.8f'))+" "+str(format(t[1],'.8f')))
    KC(n-1,t,p2)
    
  
if __name__=="__main__":
    n=int(input())
    p1=[0,0]
    p2=[100,0]
    print(str(format(p1[0],'.8f'))+" "+str(format(p1[1],'.8f')))
    KC(n,p1,p2)
    print(str(format(p2[0],'.8f'))+" "+str(format(p2[1],'.7f')))

Submission status: Accepted

Solution code:
import math

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


def roll(div1,div2):
    tmp_start = Point(div2.x-div1.x,div2.y-div1.y)
    tmp_end = Point(tmp_start.x*math.cos(math.pi/3) -tmp_start.y*math.sin(math.pi/3),
                    tmp_start.x*math.sin(math.pi/3) + tmp_start.y*math.cos(math.pi/3))
    ret = Point(tmp_end.x + div1.x,tmp_end.y + div1.y)
    return ret;


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


def calc(left,right,count):
    div1 = Point((2*left.x + right.x)/3,(2*left.y + right.y)/3)
    div2 = Point((2*right.x + left.x)/3,(2*right.y + left.y)/3)
    peek = roll(div1,div2)

    if count > 1:
        calc(left,div1,count-1)
        calc(div1,peek,count-1)
        calc(peek,div2,count-1)
        calc(div2,right,count-1)
    else:
        outPut(left);
        outPut(div1);
        outPut(peek);
        outPut(div2);


N = int(input())
left = Point(0,0)
right = Point(100,0)

if N == 0:
    outPut(left)
    outPut(right)
else:
    calc(left,right,N)
    outPut(right)

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=(ty-sy)*(1/2)+(tx-sx)*(math.sqrt(3)/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)

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)

Submission status: Accepted

Solution code:
import math
def plot(x,y):
    print(f'{x:.8f} {y:.8f}')

def Koch(n,x1,y1,x2,y2): #3点を求めるプログラム
    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) #分割された座標から求める、n-1で無限ループにならないようにする
    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 matrix_mul(mx1, mx2):
    n = len(mx1)
    m = len(mx1[0])
    _m = len(mx2)
    l = len(mx2[0])
    if m != _m:
        print("[!] Invalid Matrix Size.")
        return - 1

    ans = [[None] * l for _ in range(n)]

    for i in range(n):
        for j in range(l):
            _e = 0
            for k in range(m):
                _e += mx1[i][k] * mx2[k][j]
            ans[i][j] = _e

    return ans


def roll(p1, p2, r: int):
    """r must be radian"""
    _tmp = [[p2[0] - p1[0]], [p2[1] - p1[1]]]
    rad = math.pi*r/180
    matrix = [[math.cos(rad), -math.sin(rad)], [math.sin(rad), math.cos(rad)]]
    _tmp = matrix_mul(matrix, _tmp)
    return [p1[0]+_tmp[0][0], p1[1]+_tmp[1][0]]


def print_point(p):
    print("%.8f %.8f" % (p[0], p[1]))


def koch_curve(p1, p2, d: int):
    """p1: start point, p2: end point, d: depth of recursive"""
    if d == 0:
        print_point(p2)
    else:
        s = [p1[0] + (p2[0] - p1[0])/3, p1[1] + (p2[1] - p1[1])/3]
        t = [p1[0] + (p2[0] - p1[0])*2/3, p1[1] + (p2[1] - p1[1])*2/3]
        u = roll(s, t, 60)
        koch_curve(p1, s, d - 1)
        koch_curve(s, u, d - 1)
        koch_curve(u, t, d - 1)
        koch_curve(t, p2, d - 1)


n = int(input())
p1, p2 = [0.0, 0.0], [100.0, 0.0]
print_point(p1)
koch_curve(p1, p2, n)

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)+sy+(ty-sy)*(1/2)
    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)