L52. N-Queens II

dfs

Problem:

The n-queens puzzle is the problem of placing n queens on an n×n chessboard such that no two queens attack each other.

Given an integer n, return the number of distinct solutions to the n-queens puzzle.

Example:

Input: 4
Output: 2
Explanation: There are two distinct solutions to the 4-queens puzzle as shown below.
[
 [".Q..",  // Solution 1
  "...Q",
  "Q...",
  "..Q."],

 ["..Q.",  // Solution 2
  "Q...",
  "...Q",
  ".Q.."]
]

Solution:

public int totalQueens(int n){
    if(n <= 1) return n;
    char[][] board = new char[n][n];
    for(int i = 0; i < n; i++){
        for(int j = 0; j < n; j++){
            char[i][j] = '.';
        }
    }
    int count = new int[1];
    dfs(board, count, n, 0);
    return count[0];
}
privat void dfs(char[][] board, int[] count, int n, int colIndex){
    if(colIndex == n){
        count[0]++;
        return;
    }
    for(int i = 0; i < n; i++){
        if(isValid(board, i, colIndex)){
            board[i][colIndex] = 'Q';
            dfs(board, count, n, colIndex+1);
            board[i][colIndex] = '.';
        }
    }
}
private boolean isValid(char[][] board, int x, int y){
    for(int i = 0; i < board.length; i++){
        for(int j = 0; j < y; j++){
            if(board[i][j] == 'Q' && (x == i || Math.abs(x-i) == Math.abs(y-j))){
                return false;
            }
        }
    }
    return true;
}