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NQueens.java
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82 lines (76 loc) · 2.52 KB
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package problems;
import java.util.ArrayList;
import java.util.List;
/**
* N皇后问题。有一个n*n的棋盘，往里放n个棋子（皇后），每个棋子所在的行、列、对角线都不能有另一个棋子。
*/
public class NQueens {
private List<List<String>> res = new ArrayList<>();
/**
* 使用回溯算法来求解，求出所有正确的解法
*/
public List<List<String>> solution(int n) {
int[] board = new int[n];
backtrack(0, board);
return res;
}
// 放置皇后
private void backtrack(int row, int[] board) {
if (row == board.length) {
ArrayList<String> b = new ArrayList<>();
for (int value : board) {
StringBuilder sb = new StringBuilder();
for (int j = 0; j < board.length; j++) {
if (j == value) sb.append("Q");
else sb.append(".");
}
b.add(sb.toString());
}
res.add(b);
return;
}
int n = board.length;
for (int col = 0; col < n; col++) {
// 排除不合法的选项
if (!isValid(board, row, col)) continue;
// 做选择
board[row] = col;
// 进入到下一层决策树
backtrack(row + 1, board);
// 撤销选择
board[row] = 0;
}
}
// 判断是否可以在board[row][col]位置上放置皇后
private boolean isValid(int[] board, int row, int col) {
int n = board.length;
int left = col - 1, right = col + 1;
// 逐行往上检查
for (int i = row - 1; i >= 0; i--) {
// 第i行的col列是否有棋子
if (board[i] == col) return false;
// 检查左上对角线：第i行的col列是否有棋子
if (left >= 0) {
if (board[i] == left) return false;
}
// 检查右上对角线：第i行的col的列是否有棋子
if (right < n) {
if (board[i] == right) return false;
}
--left;
++right;
}
return true;
}
public static void main(String[] args) {
NQueens eq = new NQueens();
List<List<String>> res = eq.solution(8);
for (List<String> board : res) {
System.out.println("Solution: ");
for (String row : board) {
System.out.println(row);
}
System.out.println();
}
}
}