結果

問題 No.1998 Manhattan Restaurant
ユーザー gew1fw
提出日時 2025-06-12 16:34:29
言語 PyPy3
(7.3.15)
結果
TLE  
実行時間 -
コード長 2,870 bytes
コンパイル時間 137 ms
コンパイル使用メモリ 82,192 KB
実行使用メモリ 237,260 KB
最終ジャッジ日時 2025-06-12 16:34:39
合計ジャッジ時間 5,318 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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ファイルパターン 結果
sample AC * 4
other AC * 11 TLE * 1 -- * 19
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

def main():
    input = sys.stdin.read().split()
    idx = 0
    N = int(input[idx])
    idx += 1
    points = []
    a_list = []
    b_list = []
    for _ in range(N):
        x = int(input[idx])
        y = int(input[idx + 1])
        idx += 2
        a = x + y
        b = x - y
        points.append((a, b))
        a_list.append(a)
        b_list.append(b)
    
    a_min = min(a_list)
    a_max = max(a_list)
    b_min = min(b_list)
    b_max = max(b_list)
    
    low = 0
    high = 1 << 60
    answer = 0
    
    while low <= high:
        mid = (low + high) // 2
        if (a_max - a_min) <= 2 * mid and (b_max - b_min) <= 2 * mid:
            answer = mid
            high = mid - 1
            continue
        
        possible = False
        for key in [lambda p: p[0], lambda p: p[1], lambda p: (p[0] + p[1]), lambda p: (p[0] - p[1])]:
            sorted_points = sorted(points, key=key)
            n = len(sorted_points)
            
            prefix_a_min = [float('inf')] * (n + 1)
            prefix_a_max = [-float('inf')] * (n + 1)
            prefix_b_min = [float('inf')] * (n + 1)
            prefix_b_max = [-float('inf')] * (n + 1)
            
            for i in range(n):
                prefix_a_min[i+1] = min(prefix_a_min[i], sorted_points[i][0])
                prefix_a_max[i+1] = max(prefix_a_max[i], sorted_points[i][0])
                prefix_b_min[i+1] = min(prefix_b_min[i], sorted_points[i][1])
                prefix_b_max[i+1] = max(prefix_b_max[i], sorted_points[i][1])
            
            suffix_a_min = [float('inf')] * (n + 1)
            suffix_a_max = [-float('inf')] * (n + 1)
            suffix_b_min = [float('inf')] * (n + 1)
            suffix_b_max = [-float('inf')] * (n + 1)
            
            for i in range(n-1, -1, -1):
                suffix_a_min[i] = min(suffix_a_min[i+1], sorted_points[i][0])
                suffix_a_max[i] = max(suffix_a_max[i+1], sorted_points[i][0])
                suffix_b_min[i] = min(suffix_b_min[i+1], sorted_points[i][1])
                suffix_b_max[i] = max(suffix_b_max[i+1], sorted_points[i][1])
            
            for i in range(n + 1):
                left_a_range = prefix_a_max[i] - prefix_a_min[i]
                left_b_range = prefix_b_max[i] - prefix_b_min[i]
                right_a_range = suffix_a_max[i] - suffix_a_min[i]
                right_b_range = suffix_b_max[i] - suffix_b_min[i]
                
                if left_a_range <= 2 * mid and left_b_range <= 2 * mid and right_a_range <= 2 * mid and right_b_range <= 2 * mid:
                    possible = True
                    break
            if possible:
                break
        
        if possible:
            answer = mid
            high = mid - 1
        else:
            low = mid + 1
    
    print(answer)

if __name__ == '__main__':
    main()
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