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为了解决这个问题，我们需要在网格地图上部署炮兵，使得任何两支炮兵之间不能互相攻击。攻击范围是横向左右各两格，纵向上下各两格。我们需要找到最多可以部署的炮兵数量。

方法思路

解决代码

import sys
def main():
    N, M = map(int, sys.stdin.readline().split())
    grid = []
    for _ in range(N):
        line = sys.stdin.readline().strip()
        grid.append(line)
    
    # 状态的大小是 2^M
    max_state = 1 << M
    dp = [[0] * max_state for _ in range(N)]
    
    for row in range(N):
        for state_prev in range(max_state):
            current_count = dp[row][state_prev]
            if current_count == 0 and row == 0:
                continue
            for col in range(M):
                # 检查前一行的 col-1, col, col+1 是否被占用
                conflict = False
                if col - 1 >= 0:
                    if (state_prev >> (col - 1)) & 1:
                        conflict = True
                if not conflict and (state_prev >> col) & 1:
                    conflict = True
                if not conflict and col < M - 1:
                    if (state_prev >> (col + 1)) & 1:
                        conflict = True
                if conflict:
                    continue
                # 可以放置炮兵，计算新的状态
                new_state = state_prev
                if (new_state >> col) & 1:
                    continue  # 已经放置了炮兵
                new_state |= (1 << col)
                new_count = current_count + 1
                if new_count > dp[row + 1][new_state]:
                    dp[row + 1][new_state] = new_count
            # 处理不放置炮兵的情况
            for col in range(M):
                new_state = state_prev
                if (new_state >> col) & 1:
                    continue
                new_count = current_count
                if new_count > dp[row + 1][new_state]:
                    dp[row + 1][new_state] = new_count
    
    max_k = 0
    for state in range(max_state):
        if dp[N][state] > max_k:
            max_k = dp[N][state]
    print(max_k)
if __name__ == '__main__':
    main()

代码解释

通过这种方法，我们可以高效地解决问题，确保在防止误伤的前提下，部署最多的炮兵。

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