面试经典150题 P52 N皇后 II

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时间轴

时间轴

2025-11-30

init

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题目：

P52 N皇后 II

https://leetcode.cn/problems/n-queens-ii/description/?envType=study-plan-v2&envId=top-interview-150

经典回溯问题，考虑每一行只能且必须放一个皇后，然后每次回溯考虑下一行放哪里。注意标记能被攻击的区域时要-1 而不是赋值为-1。这是避免两个皇后可以同时攻击一个区域。

#include <vector>
using std::vector;

class Solution {
    private:
	int cnt;
	void backtrace(vector<vector<int> > &board, int row, int n)
	{
		if (row == n) {
			this->cnt++;
			return;
		}
		int i, j, k;
		for (j = 0; j < n; j++) { // column
			if (board[row][j] == 0) {
				for (i = row + 1; i < n; i++) { //set column of other row
					board[i][j] -= 1;
				}
				i = row + 1;
				k = j + 1;
				while (i < n && k < n) {
					board[i][k] -= 1;
					i++;
					k++;
				}
				i = row + 1;
				k = j - 1;
				while (i < n && k >= 0) {
					board[i][k] -= 1;
					i++;
					k--;
				}

				board[row][j] = 1;

				backtrace(board, row + 1, n);

				i = row + 1;
				k = j + 1;
				while (i < n && k < n) {
					board[i][k] += 1;
					i++;
					k++;
				}
				i = row + 1;
				k = j - 1;
				while (i < n && k >= 0) {
					board[i][k] += 1;
					i++;
					k--;
				}
				for (i = row + 1; i < n; i++) { //set column of other row
					board[i][j] += 1;
				}
				board[row][j] = 0;
			}
		}
	}

    public:
	int totalNQueens(int n)
	{
		this->cnt = 0;

		vector<vector<int> > board = vector(n, vector<int>(n, 0));
		backtrace(board, 0, n);
		return cnt;
	}
};

int main()
{
	Solution S;
	S.totalNQueens(4);
}