Problem: There are N holes in a two-dimensional plane. The coordinates of the i-th hole are (x_i,y_i).  Let R=10^{10^{10^{10}}}. Ringo performs the following operation:    * Randomly choose a point from the interior of a circle of radius R centered at the origin, and put Snuke there. Snuke will move to the hole with the smallest Euclidean distance from the point, and fall into that hole. If there are multiple such holes, the hole with the smallest index will be chosen.  For every i (1 \leq i \leq N), find the probability that Snuke falls into the i-th hole.  Here, the operation of randomly choosing a point from the interior of a circle of radius R is defined as follows:    * Pick two real numbers x and y independently according to uniform distribution on [-R,R].   * If x^2+y^2\leq R^2, the point (x,y) is chosen. Otherwise, repeat picking the real numbers x,y until the condition is met.

Submission attempts (in order):
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools

sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]

def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)


def main():
    n = I()
    a = [LI() for _ in range(n)]
    count = 100000
    k = math.pi * 2 / count
    l = 10**10
    s = 1 / count
    r = [0] * n
    for i in range(count):
        t = k * i
        x = int(math.sin(t) * l)
        y = int(math.cos(t) * l)

        mi = 0
        mm = inf ** 2
        for j in range(n):
            tm = pow(x-a[j][0], 2) + pow(y-a[j][1], 2)
            if mm > tm:
                mm = tm
                mi = j
        r[mi] += s

    return '\n'.join(map(str,r))


print(main())


import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools

sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]

def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)


def ccw(a, b, c):
    ax = b[0] - a[0]
    ay = b[1] - a[1]
    bx = c[0] - a[0]
    by = c[1] - a[1]
    t = ax*by - ay*bx;
    if t > 0:
        return 1
    if t < 0:
        return -1
    if ax*bx + ay*by < 0:
        return 2
    if ax*ax + ay*ay < bx*bx + by*by:
        return -2
    return 0

def convex_hull(ps):
    n = len(ps)
    k = 0
    ps.sort()
    ch = [[-1,-1] for _ in range(n*2)]
    for i in range(n):
        while k >= 2 and ccw(ch[k-2], ch[k-1], ps[i]) <= 0:
            k -= 1
        ch[k] = ps[i]
        k += 1
    t = k + 1
    for i in range(n-2,-1,-1):
        while k >= t and ccw(ch[k-2], ch[k-1], ps[i]) <= 0:
            k -= 1
        ch[k] = ps[i]
        k += 1
    ch = ch[:k-1]
    return ch

def radian(a, b):
    return math.atan2(b[1]-a[1], b[0]-a[0])

def main():
    n = I()
    a = [LI() + [_] for _ in range(n)]
    t = convex_hull(a)
    l = len(t)
    r = [0] * n
    if l == 2:
        r[t[0][2]] = 0.5
        r[t[1][2]] = 0.5
    else:
        for i in range(l):
            r1 = radian(t[i], t[i-1])
            r2 = radian(t[i], t[(i+1) % l])
            k = r2 - r1
            while k < 0:
                k += math.pi * 2
            e = (k-math.pi) / math.pi / 2
            r[t[i][2]] = e

    return '\n'.join(map(str,r))


print(main())


Verdicts: Wrong Answer

Accepted