結果

問題 No.655 E869120 and Good Triangles
ユーザー lam6er
提出日時 2025-03-20 19:02:53
言語 PyPy3
(7.3.15)
結果
TLE  
実行時間 -
コード長 3,806 bytes
コンパイル時間 242 ms
コンパイル使用メモリ 82,544 KB
実行使用メモリ 280,156 KB
最終ジャッジ日時 2025-03-20 19:03:13
合計ジャッジ時間 4,842 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample -- * 3
other AC * 10 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
from collections import deque

def main():
    N, K, P = map(int, sys.stdin.readline().split())
    blacks = [tuple(map(int, sys.stdin.readline().split())) for _ in range(K)]
    
    # Initialize distance matrix with infinity
    INF = float('inf')
    dist = [ [INF] * (x + 1) for x in range(N + 1) ]
    q = deque()
    
    for x, y in blacks:
        dist[x][y] = 0
        q.append((x, y))
    
    # Multi-source BFS
    while q:
        x, y = q.popleft()
        # Directions: up-left, up-right, left, right, down-left, down-right
        directions = [ (-1, -1), (-1, 0), (0, -1), (0, 1), (1, 0), (1, 1) ]
        for dx, dy in directions:
            nx = x + dx
            ny = y + dy
            if 1 <= nx <= N and 1 <= ny <= nx:
                if dist[nx][ny] > dist[x][y] + 1:
                    dist[nx][ny] = dist[x][y] + 1
                    q.append((nx, ny))
    
    # Compute row_prefix
    row_prefix = [ [0] * (N + 2) for _ in range(N + 2) ]
    for x in range(1, N + 1):
        for y in range(1, x + 1):
            row_prefix[x][y] = row_prefix[x][y - 1] + dist[x][y]
        # Fill rest with row_prefix[x][x]
        for y in range(x + 1, N + 2):
            row_prefix[x][y] = row_prefix[x][x]
    
    # Compute column_prefix for columns 0 to N (max y is N since row N has y up to N)
    max_col = N
    column_prefix = [ [0] * (N + 2) for _ in range(max_col + 2) ]
    for y in range(0, max_col + 1):
        current_sum = 0
        column_prefix[y][0] = 0
        for x in range(1, N + 1):
            if y == 0:
                val = 0
            else:
                if y > x:
                    val = 0
                else:
                    val = row_prefix[x][y]
            current_sum += val
            column_prefix[y][x] = current_sum
    
    # Compute diagonal_prefix for c from 0 to -N+1
    diagonal_prefix = {}
    start_x_for_c = {}
    max_c = 0
    min_c = - (N - 1)
    for c in range(min_c, 1):
        start_x = max(1, 1 - c)
        arr = [0] * (N + 2)
        sum_c = 0
        current_sum = 0
        prev = 0
        for x in range(1, N + 1):
            y = x + c
            if x < start_x or y < 1 or y > x:
                arr[x] = current_sum
                prev = current_sum
                continue
            current_sum += row_prefix[x][y]
            arr[x] = current_sum
            prev = current_sum
        diagonal_prefix[c] = arr
        start_x_for_c[c] = start_x
    
    total = 0
    for i in range(1, N + 1):
        max_s = N - i + 1
        if max_s < 1:
            continue
        for j in range(1, i + 1):
            c = j - i
            if c < min_c:
                continue
            # Binary search for minimal s where sum >= P
            low = 1
            high = max_s
            s0 = high + 1
            while low <= high:
                mid = (low + high) // 2
                s = mid
                start_x = start_x_for_c.get(c, 1)
                valid_low = max(i, start_x)
                valid_high = min(i + s - 1, N)
                sum_d = 0
                if valid_low <= valid_high:
                    sum_d = diagonal_prefix[c][valid_high] - (diagonal_prefix[c][valid_low - 1] if valid_low > 1 else 0)
                
                # Compute sum_col
                if j == 1:
                    sum_col = 0
                else:
                    sum_col = column_prefix[j - 1][i + s - 1] - column_prefix[j - 1][i - 1]
                
                total_sum = sum_d - sum_col
                if total_sum >= P:
                    s0 = mid
                    high = mid - 1
                else:
                    low = mid + 1
            if s0 <= max_s:
                total += max_s - s0 + 1
    print(total)

if __name__ == "__main__":
    main()
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