#957863 (PyPy3) No.96 圏外です。

• 問題: No.96 圏外です。
• ユーザー: Mao-beta
• 提出日時: 2024-03-06 16:24:07
• 言語: PyPy3 (7.3.17)
• 結果: TLE
• 実行時間: -
• コード長: 5,361 bytes
• コンパイル時間: 246 ms
• コンパイル使用メモリ: 85,120 KB
• 実行使用メモリ: 312,380 KB
• 最終ジャッジ日時: 2026-04-16 01:25:48
• 合計ジャッジ時間: 22,811 ms
• ジャッジサーバーID （参考情報）: judge1_0 / judge2_1

ファイルパターン	結果
other	AC * 22 TLE * 1 -- * 5

ソースコード

import sys
import math
import bisect
from heapq import heapify, heappop, heappush
from collections import deque, defaultdict, Counter
from functools import lru_cache
from itertools import accumulate, combinations, permutations, product

sys.setrecursionlimit(1000000)
MOD = 10 ** 9 + 7
MOD99 = 998244353

input = lambda: sys.stdin.readline().strip()
NI = lambda: int(input())
NMI = lambda: map(int, input().split())
NLI = lambda: list(NMI())
SI = lambda: input()
SMI = lambda: input().split()
SLI = lambda: list(SMI())
EI = lambda m: [NLI() for _ in range(m)]

from collections import defaultdict


class UnionFind:
    def __init__(self, n):
        # 親要素のノード番号を格納　xが根のとき-(サイズ)を格納
        self.par = [-1 for i in range(n)]
        self.n = n
        self.roots = set(range(n))
        self.group_num = n
        self.members = defaultdict(set)

        for i in range(n):
            self.members[i].add(i)

    def find(self, x):
        # 根ならその番号を返す
        if self.par[x] < 0:
            return x
        else:
            # 親の親は親
            self.par[x] = self.find(self.par[x])
            return self.par[x]

    def is_same(self, x, y):
        # 根が同じならTrue
        return self.find(x) == self.find(y)

    def unite(self, x, y):
        x = self.find(x)
        y = self.find(y)
        if x == y: return

        # 木のサイズを比較し、小さいほうから大きいほうへつなぐ
        if self.par[x] > self.par[y]:
            x, y = y, x

        self.group_num -= 1
        self.roots.discard(y)
        assert self.group_num == len(self.roots)

        self.members[x] |= self.members[y]
        self.members[y] = set()

        self.par[x] += self.par[y]
        self.par[y] = x

    def size(self, x):
        return -self.par[self.find(x)]

    def get_members(self, x):
        root = self.find(x)
        return self.members[root]

    def get_roots(self):
        return self.roots

    def group_count(self):
        return len(self.roots)

    def all_group_members(self):
        return self.members

    def __repr__(self):
        return '\n'.join('{}: {}'.format(r, self.members[r]) for r in self.roots)


def dist2(x1, y1, x2, y2):
    return (x1-x2)**2 + (y1-y2)**2


def convex(Vs):
    """
    :param Vs(sorted by x): [[x1, y1], ... [xn, yn]]
    :return: upper, lower
    """
    def cross(x1, y1, x2, y2):
        return x1 * y2 - y1 * x2

    def is_ccw(x1, y1, x2, y2):
        return cross(x1, y1, x2, y2) > 0

    N = len(Vs)

    upper = deque()
    upper.append(Vs[0])
    upper.append(Vs[1])

    for i in range(2, N):
        V3 = Vs[i]
        x3, y3 = V3

        while len(upper) >= 2:
            V2 = upper.pop()
            V1 = upper.pop()
            x2, y2 = V2
            x1, y1 = V1

            upper.append(V1)

            if not is_ccw(x2-x1, y2-y1, x3-x2, y3-y2):
                upper.append(V2)
                upper.append(V3)
                break

        if len(upper) < 2:
            upper.append(V3)


    lower = deque()
    lower.append(Vs[-1])
    lower.append(Vs[-2])

    for i in range(N-3, -1, -1):
        V3 = Vs[i]
        x3, y3 = V3

        while len(lower) >= 2:
            V2 = lower.pop()
            V1 = lower.pop()
            x2, y2 = V2
            x1, y1 = V1

            lower.append(V1)

            if not is_ccw(x2-x1, y2-y1, x3-x2, y3-y2):
                lower.append(V2)
                lower.append(V3)
                break

        if len(lower) < 2:
            lower.append(V3)

    return upper, lower


def main():
    N = NI()
    XY = EI(N)
    XY = [[x+10000, y+10000] for x, y in XY]

    if N == 0:
        print(1)
        return
    if N == 1:
        print(2)
        return

    # B[x][y]: Xi//10 = x, Yi//10 = y となる点のリスト
    B = [[[] for _ in range(2001)] for _ in range(2001)]
    for i, (x, y) in enumerate(XY):
        B[x//10][y//10].append([x, y, i])

    # Bの8近傍+自身のみ通信可能か探索
    DX = [0, 1, 1, 1]
    DY = [1, 0, 1, -1]

    uf = UnionFind(N)

    for bx in range(2001):
        for by in range(2001):
            Bxy = B[bx][by]
            # 自身
            for x1, y1, i1 in Bxy:
                for x2, y2, i2 in Bxy:
                    if dist2(x1, y1, x2, y2) <= 100:
                        uf.unite(i1, i2)
            # 8近傍
            for dx, dy in zip(DX, DY):
                nbx = bx + dx
                nby = by + dy
                if 0 <= nbx < 2001 and 0 <= nby < 2001:
                    for x1, y1, i1 in Bxy:
                        for x2, y2, i2 in B[nbx][nby]:
                            if dist2(x1, y1, x2, y2) <= 100:
                                uf.unite(i1, i2)

    # 凸包
    members = uf.all_group_members()
    ans = 0
    for r, M in members.items():
        if len(M) <= 1:
            continue
        Vs = [XY[i] for i in M]
        Vs.sort()
        upper, lower = convex(Vs)
        lower.pop()
        lower.popleft()
        Vs = list(upper + lower)
        for i in range(len(Vs)):
            for j in range(i+1, len(Vs)):
                x1, y1 = Vs[i]
                x2, y2 = Vs[j]
                d2 = dist2(x1, y1, x2, y2)
                ans = max(ans, d2)

    print(math.sqrt(ans)+2)


if __name__ == "__main__":
    main()