【重点】【回溯】51.N皇后

题目

Python

class Solution:
    def solveNQueens(self, n: int) -> List[List[str]]:
        all_res = []
        tmp_res = [['.']*n for _ in range(n)]
        self.solve(all_res, tmp_res, 0, n)
        return all_res

    def solve(self, all_res, tmp_res, layer, n):
        if layer == n:
            all_res.append([''.join(item) for item in tmp_res])
            return 
        for i in range(n):
            if self.is_valid(tmp_res, layer, i):
                tmp_res[layer][i] = 'Q'
                self.solve(all_res, tmp_res, layer+1, n)
                tmp_res[layer][i] = '.'
    
    def is_valid(self, tmp_res, x, y):
        n = len(tmp_res)
        # 纵向判断
        for i in range(x):
            if tmp_res[i][y] == 'Q':
                return False
        # 斜向判断
        i = 1
        while x-i>= 0 and y-i >= 0:
            if tmp_res[x-i][y-i] == 'Q':
                return False
            else:
                i += 1
        i = 1
        while x-i>= 0 and y+i < n:
            if tmp_res[x-i][y+i] == 'Q':
                return False  
            else:
                i += 1
        
        return True

Java

class Solution {
    public List<List<String>> solveNQueens(int n) {
        List<List<String>> res = new ArrayList<>();
        char[][] tmp = new char[n][n];
        for (int i = 0; i < n; ++i) {
            Arrays.fill(tmp[i], '.');
        }
        dfs(tmp, 0, res);

        return res;
    }

    public void dfs(char[][] tmp, int layer, List<List<String>> res) {
        int n = tmp.length;
        if (layer == n) {
            List<String> solu = new ArrayList<>();
            for (int k = 0; k < n; ++k) {
                solu.add(String.valueOf(tmp[k]));
            }
            res.add(solu);
            return;
        }
        for (int k = 0; k < n; ++k) {
            if (isValid(tmp, layer, k)) {
                tmp[layer][k] = 'Q';
                dfs(tmp, layer + 1, res);
                tmp[layer][k] = '.';
            }
        }
    }

    boolean isValid(char[][] tmp, int x, int y) {
        int n = tmp.length;
        for (int i = 0; i < n; ++i) {
            if (tmp[i][y] == 'Q' && i < x) {
                return false;
            }
        }
        int i = 1;
        while (x - i >= 0 && y - i >= 0) { 
            if (tmp[x - i][y - i] == 'Q') {
                return false;
            }
            ++i;
        }
        i = 1;
        while (x - i >= 0 && y + i < n) {
            if (tmp[x - i][y + i] == 'Q') {
                return false;
            }
            ++i;
        }
        
        return true;
    }
}