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314 lines
8.2 KiB
Markdown
314 lines
8.2 KiB
Markdown
<p align="center">
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<a href="https://programmercarl.com/other/xunlianying.html" target="_blank">
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<img src="../pics/训练营.png" width="1000"/>
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</a>
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<p align="center"><strong><a href="https://mp.weixin.qq.com/s/tqCxrMEU-ajQumL1i8im9A">参与本项目</a>，贡献其他语言版本的代码，拥抱开源，让更多学习算法的小伙伴们收益！</strong></p>
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# 52. N皇后II
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题目链接：[https://leetcode.cn/problems/n-queens-ii/](https://leetcode.cn/problems/n-queens-ii/)
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n 皇后问题研究的是如何将 n 个皇后放置在 n×n 的棋盘上，并且使皇后彼此之间不能相互攻击。
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上图为 8 皇后问题的一种解法。
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给定一个整数 n，返回 n 皇后不同的解决方案的数量。
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示例:
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输入: 4
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输出: 2
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解释: 4 皇后问题存在如下两个不同的解法。
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解法 1
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[
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[".Q..",
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"...Q",
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"Q...",
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"..Q."],
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解法 2
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["..Q.",
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"Q...",
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"...Q",
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".Q.."]
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]
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# 思路
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详看：[51.N皇后](https://mp.weixin.qq.com/s/lU_QwCMj6g60nh8m98GAWg) ，基本没有区别
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# C++代码
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```CPP
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class Solution {
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private:
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int count = 0;
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void backtracking(int n, int row, vector<string>& chessboard) {
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if (row == n) {
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count++;
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return;
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}
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for (int col = 0; col < n; col++) {
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if (isValid(row, col, chessboard, n)) {
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chessboard[row][col] = 'Q'; // 放置皇后
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backtracking(n, row + 1, chessboard);
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chessboard[row][col] = '.'; // 回溯
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}
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}
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}
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bool isValid(int row, int col, vector<string>& chessboard, int n) {
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int count = 0;
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// 检查列
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for (int i = 0; i < row; i++) { // 这是一个剪枝
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if (chessboard[i][col] == 'Q') {
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return false;
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}
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}
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// 检查 45度角是否有皇后
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for (int i = row - 1, j = col - 1; i >=0 && j >= 0; i--, j--) {
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if (chessboard[i][j] == 'Q') {
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return false;
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}
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}
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// 检查 135度角是否有皇后
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for(int i = row - 1, j = col + 1; i >= 0 && j < n; i--, j++) {
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if (chessboard[i][j] == 'Q') {
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return false;
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}
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}
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return true;
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}
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public:
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int totalNQueens(int n) {
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std::vector<std::string> chessboard(n, std::string(n, '.'));
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backtracking(n, 0, chessboard);
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return count;
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}
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};
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```
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# 其他语言补充
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JavaScript
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```javascript
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var totalNQueens = function(n) {
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let count = 0;
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const backtracking = (n, row, chessboard) => {
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if(row === n){
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count++;
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return;
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}
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for(let col = 0; col < n; col++){
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if(isValid(row, col, chessboard, n)) { // 验证合法就可以放
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chessboard[row][col] = 'Q'; // 放置皇后
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backtracking(n, row + 1, chessboard);
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chessboard[row][col] = '.'; // 回溯
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}
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}
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}
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const isValid = (row, col, chessboard, n) => {
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// 检查列
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for(let i = 0; i < row; i++){ // 这是一个剪枝
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if(chessboard[i][col] === 'Q'){
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return false;
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}
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}
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// 检查 45度角是否有皇后
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for(let i = row - 1, j = col - 1; i >= 0 && j >= 0; i--, j--){
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if(chessboard[i][j] === 'Q'){
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return false;
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}
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}
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// 检查 135度角是否有皇后
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for(let i = row - 1, j = col + 1; i >= 0 && j < n; i--, j++){
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if(chessboard[i][j] === 'Q'){
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return false;
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}
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}
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return true;
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}
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const chessboard = new Array(n).fill([]).map(() => new Array(n).fill('.'));
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backtracking(n, 0, chessboard);
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return count;
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};
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```
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TypeScript：
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```typescript
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// 0-该格为空，1-该格有皇后
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type GridStatus = 0 | 1;
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function totalNQueens(n: number): number {
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let resCount: number = 0;
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const chess: GridStatus[][] = new Array(n).fill(0)
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.map(_ => new Array(n).fill(0));
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backTracking(chess, n, 0);
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return resCount;
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function backTracking(chess: GridStatus[][], n: number, startRowIndex: number): void {
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if (startRowIndex === n) {
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resCount++;
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return;
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}
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for (let j = 0; j < n; j++) {
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if (checkValid(chess, startRowIndex, j, n) === true) {
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chess[startRowIndex][j] = 1;
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backTracking(chess, n, startRowIndex + 1);
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chess[startRowIndex][j] = 0;
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}
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}
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}
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};
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function checkValid(chess: GridStatus[][], i: number, j: number, n: number): boolean {
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// 向上纵向检查
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let tempI: number = i - 1,
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tempJ: number = j;
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while (tempI >= 0) {
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if (chess[tempI][tempJ] === 1) return false;
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tempI--;
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}
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// 斜向左上检查
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tempI = i - 1;
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tempJ = j - 1;
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while (tempI >= 0 && tempJ >= 0) {
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if (chess[tempI][tempJ] === 1) return false;
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tempI--;
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tempJ--;
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}
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// 斜向右上检查
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tempI = i - 1;
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tempJ = j + 1;
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while (tempI >= 0 && tempJ < n) {
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if (chess[tempI][tempJ] === 1) return false;
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tempI--;
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tempJ++;
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}
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return true;
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}
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```
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C
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```c
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//path[i]为在i行，path[i]列上存在皇后
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int *path;
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int pathTop;
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int answer;
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//检查当前level行index列放置皇后是否合法
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int isValid(int index, int level) {
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int i;
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//updater为若斜角存在皇后，其所应在的列
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//用来检查左上45度是否存在皇后
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int lCornerUpdater = index - level;
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//用来检查右上135度是否存在皇后
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int rCornerUpdater = index + level;
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for(i = 0; i < pathTop; ++i) {
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//path[i] == index检查index列是否存在皇后
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//检查斜角皇后：只要path[i] == updater，就说明当前位置不可放置皇后。
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//path[i] == lCornerUpdater检查左上角45度是否有皇后
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//path[i] == rCornerUpdater检查右上角135度是否有皇后
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if(path[i] == index || path[i] == lCornerUpdater || path[i] == rCornerUpdater)
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return 0;
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//更新updater指向下一行对应的位置
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++lCornerUpdater;
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--rCornerUpdater;
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}
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return 1;
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}
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//回溯算法：level为当前皇后行数
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void backTracking(int n, int level) {
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//若path中元素个数已经为n，则证明有一种解法。answer+1
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if(pathTop == n) {
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++answer;
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return;
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}
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int i;
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for(i = 0; i < n; ++i) {
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//若当前level行，i列是合法的放置位置。就将i放入path中
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if(isValid(i, level)) {
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path[pathTop++] = i;
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backTracking(n, level + 1);
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//回溯
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--pathTop;
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}
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}
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}
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int totalNQueens(int n){
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answer = 0;
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pathTop = 0;
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path = (int *)malloc(sizeof(int) * n);
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backTracking(n, 0);
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return answer;
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}
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```
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Java
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```java
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class Solution {
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int count = 0;
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public int totalNQueens(int n) {
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char[][] board = new char[n][n];
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for (char[] chars : board) {
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Arrays.fill(chars, '.');
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}
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backTrack(n, 0, board);
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return count;
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}
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private void backTrack(int n, int row, char[][] board) {
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if (row == n) {
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count++;
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return;
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}
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for (int col = 0; col < n; col++) {
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if (isValid(row, col, n, board)) {
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board[row][col] = 'Q';
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backTrack(n, row + 1, board);
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board[row][col] = '.';
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}
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}
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}
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private boolean isValid(int row, int col, int n, char[][] board) {
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// 检查列
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for (int i = 0; i < row; ++i) {
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if (board[i][col] == 'Q') {
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return false;
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}
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}
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// 检查45度对角线
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for (int i = row - 1, j = col - 1; i >= 0 && j >= 0; i--, j--) {
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if (board[i][j] == 'Q') {
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return false;
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}
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}
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// 检查135度对角线
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for (int i = row - 1, j = col + 1; i >= 0 && j <= n - 1; i--, j++) {
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if (board[i][j] == 'Q') {
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return false;
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}
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}
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return true;
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}
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}
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```
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<p align="center">
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<a href="https://programmercarl.com/other/kstar.html" target="_blank">
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<img src="../pics/网站星球宣传海报.jpg" width="1000"/>
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</a>
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