結果

問題 No.96 圏外です。
コンテスト
ユーザー lam6er
提出日時 2025-04-16 01:14:08
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 727 ms / 5,000 ms
コード長 3,752 bytes
コンパイル時間 325 ms
コンパイル使用メモリ 82,120 KB
実行使用メモリ 136,044 KB
最終ジャッジ日時 2025-04-16 01:15:43
合計ジャッジ時間 9,787 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
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ファイルパターン 結果
other AC * 28
権限があれば一括ダウンロードができます

ソースコード

diff # 

import sys
import math
from collections import defaultdict

class UnionFind:
    def __init__(self, size):
        self.parent = list(range(size))
        self.rank = [0] * size

    def find(self, x):
        if self.parent[x] != x:
            self.parent[x] = self.find(self.parent[x])
        return self.parent[x]

    def union(self, x, y):
        x_root = self.find(x)
        y_root = self.find(y)
        if x_root == y_root:
            return
        if self.rank[x_root] < self.rank[y_root]:
            self.parent[x_root] = y_root
        else:
            self.parent[y_root] = x_root
            if self.rank[x_root] == self.rank[y_root]:
                self.rank[x_root] += 1

def distance_sq(p1, p2):
    dx = p1[0] - p2[0]
    dy = p1[1] - p2[1]
    return dx * dx + dy * dy

def convex_hull(points):
    points = sorted(points)
    if len(points) <= 1:
        return points
    lower = []
    for p in points:
        while len(lower) >= 2 and ( (lower[-1][0] - lower[-2][0]) * (p[1] - lower[-2][1]) - (lower[-1][1] - lower[-2][1]) * (p[0] - lower[-2][0]) ) <= 0:
            lower.pop()
        lower.append(p)
    upper = []
    for p in reversed(points):
        while len(upper) >= 2 and ( (upper[-1][0] - upper[-2][0]) * (p[1] - upper[-2][1]) - (upper[-1][1] - upper[-2][1]) * (p[0] - upper[-2][0]) ) <= 0:
            upper.pop()
        upper.append(p)
    return lower[:-1] + upper[:-1]

def rotating_calipers(hull):
    n = len(hull)
    if n == 1:
        return 0.0
    if n == 2:
        return math.hypot(hull[0][0] - hull[1][0], hull[0][1] - hull[1][1])
    max_dist_sq = 0.0
    j = 1
    for i in range(n):
        next_i = (i + 1) % n
        dx1 = hull[next_i][0] - hull[i][0]
        dy1 = hull[next_i][1] - hull[i][1]
        while True:
            next_j = (j + 1) % n
            dx2 = hull[next_j][0] - hull[j][0]
            dy2 = hull[next_j][1] - hull[j][1]
            cross = dx1 * dy2 - dy1 * dx2
            if cross > 0:
                j = next_j
                dx1 = hull[next_i][0] - hull[i][0]
                dy1 = hull[next_i][1] - hull[i][1]
            else:
                break
        current_dist_sq = (hull[i][0] - hull[j][0])**2 + (hull[i][1] - hull[j][1])**2
        if current_dist_sq > max_dist_sq:
            max_dist_sq = current_dist_sq
    return math.sqrt(max_dist_sq)

def main():
    input = sys.stdin.read().split()
    ptr = 0
    N = int(input[ptr])
    ptr += 1
    if N == 0:
        print("1.000000000")
        return
    points = []
    grid = defaultdict(list)
    for i in range(N):
        x = int(input[ptr])
        y = int(input[ptr + 1])
        ptr += 2
        points.append((x, y))
        cell_x = x // 10
        cell_y = y // 10
        grid[(cell_x, cell_y)].append(i)
    uf = UnionFind(N)
    for i in range(N):
        x, y = points[i]
        cell_x = x // 10
        cell_y = y // 10
        for dx in (-1, 0, 1):
            for dy in (-1, 0, 1):
                key = (cell_x + dx, cell_y + dy)
                if key not in grid:
                    continue
                for j in grid[key]:
                    if j == i:
                        continue
                    if distance_sq(points[i], points[j]) <= 100:
                        uf.union(i, j)
    groups = defaultdict(list)
    for i in range(N):
        root = uf.find(i)
        groups[root].append(points[i])
    D_max = 0.0
    for group in groups.values():
        if len(group) == 0:
            continue
        hull = convex_hull(group)
        if not hull:
            continue
        d = rotating_calipers(hull)
        if d > D_max:
            D_max = d
    ans = max(1.0, D_max + 2.0)
    print("{0:.9f}".format(ans))

if __name__ == '__main__':
    main()
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