結果

問題 No.96 圏外です。
ユーザー lam6er
提出日時 2025-04-16 01:12:50
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 720 ms / 5,000 ms
コード長 3,875 bytes
コンパイル時間 505 ms
コンパイル使用メモリ 82,572 KB
実行使用メモリ 133,688 KB
最終ジャッジ日時 2025-04-16 01:14:22
合計ジャッジ時間 9,914 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge4
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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 convex_hull(points):
    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 cross(o, a, b):
    return (a[0] - o[0]) * (b[1] - o[1]) - (a[1] - o[1]) * (b[0] - o[0])

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
            dx = hull[next_i][0] - hull[i][0]
            dy = hull[next_i][1] - hull[i][1]
            dxj = hull[next_j][0] - hull[j][0]
            dyj = hull[next_j][1] - hull[j][1]
            cross_product = dx * dyj - dxj * dy
            if cross_product > 0:
                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
        current_dist_next = math.hypot(hull[i][0] - hull[next_j][0], hull[i][1] - hull[next_j][1])
        if current_dist_next > max_dist:
            max_dist = current_dist_next
    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 i in range(N):
        x, y = points[i]
        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):
                neighbor_cell = (cell_x + dx, cell_y + dy)
                if neighbor_cell in grid:
                    for j in grid[neighbor_cell]:
                        if j > i:
                            xj, yj = points[j]
                            dx_ = x - xj
                            dy_ = y - yj
                            dist_sq = dx_ ** 2 + dy_ ** 2
                            if dist_sq <= 100:
                                uf.union(i, j)
    roots = defaultdict(list)
    for i in range(N):
        root = uf.find(i)
        roots[root].append(points[i])
    max_candidate = 0.0
    for group in roots.values():
        if len(group) == 0:
            continue
        hull = convex_hull(group)
        if len(hull) <= 1:
            diam = 0.0
        else:
            diam = rotating_calipers(hull)
        candidate = diam + 2.0
        if candidate > max_candidate:
            max_candidate = candidate
    print("{0:.9f}".format(max_candidate))

if __name__ == '__main__':
    main()
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