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 01:14:03
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 782 ms / 5,000 ms
コード長 3,894 bytes
コンパイル時間 203 ms
コンパイル使用メモリ 81,636 KB
実行使用メモリ 146,820 KB
最終ジャッジ日時 2025-04-16 01:15:25
合計ジャッジ時間 9,657 ms
ジャッジサーバーID
（参考情報） 		judge5 / 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 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 cross(o, a, b):
    return (a[0] - o[0]) * (b[1] - o[1]) - (a[1] - o[1]) * (b[0] - o[0])

def convex_hull(points):
    if not points:
        return []
    points = sorted(points)
    lower = []
    for p in points:
        while len(lower) >= 2 and cross(lower[-2], lower[-1], p) <= 0:
            lower.pop()
        lower.append(p)
    upper = []
    for p in reversed(points):
        while len(upper) >= 2 and cross(upper[-2], upper[-1], p) <= 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 = 0.0
    j = 1
    for i in range(n):
        next_i = (i + 1) % n
        while True:
            next_j = (j + 1) % n
            a = (hull[next_i][0] - hull[i][0], hull[next_i][1] - hull[i][1])
            b = (hull[next_j][0] - hull[j][0], hull[next_j][1] - hull[j][1])
            cross_prod = a[0] * b[1] - a[1] * b[0]
            if cross_prod > 1e-8:
                j = next_j
            else:
                break
        current_dist = math.hypot(hull[i][0] - hull[j][0], hull[i][1] - hull[j][1])
        if current_dist > max_dist:
            max_dist = current_dist
    return max_dist

def main():
    import sys
    input = sys.stdin.read().split()
    ptr = 0
    n = int(input[ptr])
    ptr += 1
    if n == 0:
        print("1.000000000")
        return
    points = []
    for _ in range(n):
        x = int(input[ptr])
        y = int(input[ptr+1])
        ptr +=2
        points.append((x, y))
    
    grid = defaultdict(list)
    for idx, (x, y) in enumerate(points):
        gx = x // 10
        gy = y // 10
        grid[(gx, gy)].append((x, y, idx))
    
    uf = UnionFind(n)
    
    for idx in range(n):
        x, y = points[idx]
        gx = x // 10
        gy = y // 10
        for dx in (-1, 0, 1):
            for dy in (-1, 0, 1):
                key = (gx + dx, gy + dy)
                if key not in grid:
                    continue
                for (nx, ny, j) in grid[key]:
                    if j <= idx:
                        continue
                    dx_val = x - nx
                    dy_val = y - ny
                    dist_sq = dx_val * dx_val + dy_val * dy_val
                    if dist_sq <= 100:
                        uf.union(idx, j)
    
    groups = defaultdict(list)
    for i in range(n):
        root = uf.find(i)
        groups[root].append(points[i])
    
    max_candidate = 0.0
    for group in groups.values():
        m = len(group)
        if m == 0:
            continue
        if m == 1:
            d = 0.0
        elif m == 2:
            d = math.hypot(group[0][0] - group[1][0], group[0][1] - group[1][1])
        else:
            hull = convex_hull(group)
            if not hull:
                d = 0.0
            else:
                d = rotating_calipers(hull)
        current_max = d + 2.0
        if current_max > max_candidate:
            max_candidate = current_max
    
    answer = max(max_candidate, 1.0)
    print("{0:.9f}".format(answer))

if __name__ == "__main__":
    main()
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