N皇后问题 Java 代码实现 | 回溯算法详解

public class NQueen {

private int n; // 棋盘大小
private int[] board; // 存储每一行中皇后的位置

public NQueen(int n) {
    this.n = n;
    board = new int[n];
}

// 判断当前位置是否合法
private boolean isValid(int row, int col) {
    for (int i = 0; i < row; i++) {
        if (board[i] == col || Math.abs(row - i) == Math.abs(col - board[i])) {
            return false;
        }
    }
    return true;
}

// 回溯法求解N皇后问题
private void backtrack(int row) {
    if (row == n) {
        printBoard();
        return;
    }
    for (int i = 0; i < n; i++) {
        if (isValid(row, i)) {
            board[row] = i;
            backtrack(row + 1);
        }
    }
}

// 打印棋盘
private void printBoard() {
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            if (board[i] == j) {
                System.out.print('Q' + ' ');
            } else {
                System.out.print('*' + ' ');
            }
        }
        System.out.println();
    }
    System.out.println();
}

public void solve() {
    backtrack(0);
}

public static void main(String[] args) {
    NQueen nQueen = new NQueen(8);
    nQueen.solve();
}

}