結果

問題 No.96 圏外です。
ユーザー lam6er
提出日時 2025-04-16 01:12:24
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 773 ms / 5,000 ms
コード長 3,548 bytes
コンパイル時間 499 ms
コンパイル使用メモリ 82,248 KB
実行使用メモリ 140,632 KB
最終ジャッジ日時 2025-04-16 01:14:19
合計ジャッジ時間 10,341 ms
ジャッジサーバーID
（参考情報） 		judge2 / 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 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(points):
    n = len(points)
    if n == 1:
        return 0.0
    if n == 2:
        return math.hypot(points[0][0] - points[1][0], points[0][1] - points[1][1])
    max_dist = 0.0
    k = 1
    for i in range(n):
        ni = (i + 1) % n
        while True:
            nk = (k + 1) % n
            val = cross(points[i], points[ni], points[nk]) - cross(points[i], points[ni], points[k])
            if val > 1e-9:
                k = nk
            else:
                break
        current_dist = math.hypot(points[i][0] - points[k][0], points[i][1] - points[k][1])
        if current_dist > max_dist:
            max_dist = current_dist
    return max_dist

def main():
    import sys
    input = sys.stdin.read().split()
    idx = 0
    N = int(input[idx])
    idx += 1
    if N == 0:
        print(1.0)
        return
    points = []
    for _ in range(N):
        x = float(input[idx])
        y = float(input[idx + 1])
        points.append((x, y))
        idx += 2

    uf = UnionFind(N)
    grid = defaultdict(list)
    for i in range(N):
        x, y = points[i]
        gx = int(math.floor(x / 10.0))
        gy = int(math.floor(y / 10.0))
        grid[(gx, gy)].append(i)

    dx = [-1, 0, 1]
    dy = [-1, 0, 1]
    for i in range(N):
        x1, y1 = points[i]
        gx = int(math.floor(x1 / 10.0))
        gy = int(math.floor(y1 / 10.0))
        for dgx in dx:
            for dgy in dy:
                ngx = gx + dgx
                ngy = gy + dgy
                if (ngx, ngy) in grid:
                    for j in grid[(ngx, ngy)]:
                        if j == i:
                            continue
                        x2, y2 = points[j]
                        dist_sq = (x1 - x2)**2 + (y1 - y2)**2
                        if dist_sq <= 100.0 + 1e-9:
                            uf.union(i, 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():
        if len(group) == 0:
            continue
        ch = convex_hull(group)
        d = rotating_calipers(ch)
        candidate = d + 2.0
        if candidate > max_candidate:
            max_candidate = candidate

    result = max(max_candidate, 1.0)
    print("{0:.9f}".format(result))

if __name__ == "__main__":
    main()
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