52. N-Queens II - Hard

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.."]
]

use dfs / backtracking

time = O(n!), space = O(n)

class Solution {
    Set<Integer> usedCols = new HashSet<>();
    Set<Integer> diag1 = new HashSet<>();
    Set<Integer> diag2 = new HashSet<>();
    int count = 0;
    
    public int totalNQueens(int n) {
        helper(0, n);
        return count;
    }
    
    private void helper(int row, int n) {
        if(row == n) {
            count++;
            return;
        }
        
        for(int col = 0; col < n; col++) {
            if(isValid(row, col)) {
                usedCols.add(col);
                diag1.add(row + col);
                diag2.add(row - col);
                helper(row + 1, n);
                usedCols.remove(col);
                diag1.remove(row + col);
                diag2.remove(row - col);
            }
        }
    }
    
    private boolean isValid(int row, int col) {
        return !(usedCols.contains(col) || diag1.contains(row + col) || diag2.contains(row - col));
    }
}