52. N-Queens II

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LeetCode

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Problem

The n-queens puzzle is the problem of placing n queens on an n x 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 1:

Input: n = 4
Output: 2
Explanation: There are two distinct solutions to the 4-queens puzzle as shown.

Example 2:

Input: n = 1
Output: 1

Code

class Solution {
    int res = 0;
    public int totalNQueens(int n) {
        helper(new int[n], 0);
        return res;
    }

    private void helper(int[] queens, int pos){
        if(pos == queens.length){
            res++;
            return;
        }

        for(int i = 0; i < queens.length; i++){
            queens[pos] = i;
            if(isValid(queens, pos)){
                helper(queens, pos + 1);
            }
        }
    }

    private boolean isValid(int[] queens, int pos){
        for(int i = 0; i < pos; i++){
            if(queens[i] == queens[pos]){
                return false;
            }

            if(Math.abs(queens[i] - queens[pos]) == Math.abs(i - pos)){
                return false;
            }
        }

        return true;
    }
}

time: O(N!) space: O(N)