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为了解决这个问题，我们需要在给定的网格地图上部署尽可能多的炮兵部队，同时确保任何两支炮兵部队之间不能互相攻击。攻击范围是每个炮兵部队横向和纵向各两格，包括其所在的位置。

方法思路

解决代码

import sys
from sys import stdin
def main():
    n, m = map(int, stdin.readline().split())
    grid = []
    for _ in range(n):
        line = stdin.readline().strip()
        grid.append(line)
    
    # 预处理attak_matrix
    attak_matrix = [[False for _ in range(m)] for _ in range(m)]
    for x in range(m):
        for y in range(m):
            if (x == y + 1 and x != y) or (y == x + 1 and y != x):
                attak_matrix[x][y] = True
            elif (x == y - 1 and x != y) or (y == x - 1 and y != x):
                attak_matrix[x][y] = True
    
    # 预处理allowed_masks
    allowed_masks = [set() for _ in range(1 << m)]
    for current_mask in range(1 << m):
        current_attack = 0
        for x in range(m):
            if (current_mask >> x) & 1:
                current_attack |= (1 << x)
        for prev_mask in range(1 << m):
            prev_attack = 0
            for y in range(m):
                if (prev_mask >> y) & 1:
                    prev_attack |= (1 << y)
            conflict = False
            for x in range(m):
                if (current_mask >> x) & 1:
                    for y in range(m):
                        if (prev_mask >> y) & 1 and attak_matrix[x][y]:
                            conflict = True
                            break
                    if conflict:
                        break
            if not conflict:
                allowed_masks[current_mask].add(prev_mask)
    
    # 初始化动态规划
    dp = [ [-1 for _ in range(1 << m)] for _ in range(n+1)]
    dp[0][0] = 0
    
    for i in range(1, n+1):
        for current_mask in range(1 << m):
            # 检查当前mask是否有炮兵在H的位置
            valid = True
            for x in range(m):
                if (current_mask >> x) & 1 and grid[i-1][x] == 'H':
                    valid = False
                    break
            if not valid:
                continue
            current_count = bin(current_mask).count('1')
            max_prev = 0
            for prev_mask in allowed_masks[current_mask]:
                if dp[i-1][prev_mask] != -1:
                    if dp[i-1][prev_mask] + current_count > max_prev:
                        max_prev = dp[i-1][prev_mask] + current_count
            if max_prev > 0:
                dp[i][current_mask] = max_prev
            else:
                dp[i][current_mask] = current_count if current_count > 0 else 0
    
    max_result = 0
    for mask in range(1 << m):
        if dp[n][mask] > max_result:
            max_result = dp[n][mask]
    print(max_result)
if __name__ == "__main__":
    main()

代码解释

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