<p>The <strong>n-queens</strong> puzzle is the problem of placing <code>n</code> queens on an <code>n x n</code> chessboard such that no two queens attack each other.</p>

<p>Given an integer <code>n</code>, return <em>the number of distinct solutions to the&nbsp;<strong>n-queens puzzle</strong></em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/13/queens.jpg" style="width: 600px; height: 268px;" />
<pre>
<strong>Input:</strong> n = 4
<strong>Output:</strong> 2
<strong>Explanation:</strong> There are two distinct solutions to the 4-queens puzzle as shown.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 9</code></li>
</ul>

class Solution {

vector<int> curr;
vector<bool> col, a, b;
int ans = 0;
int tot;

void sol_map(int row) {
    if (row == -1)
        return;
//cout << row << endl;
    if (row == tot) {
        ans++;
        sol_map(row-1);
        return;
    }

    if (curr[row] != -1) {
        col[curr[row]] = false;
        a[row+curr[row]] = false;
        b[row+tot-1-curr[row]] = false;
    }

    int curr_col;
    for (curr_col=curr[row]+1; curr_col<tot; curr_col++) {
        if (!check_valid(row, curr_col))
            continue;
        else break;
    }
    
    if (curr_col == tot) {
        curr[row] = -1;
        sol_map(row-1);
    } else {
        curr[row] = curr_col;
        col[curr_col] = true;
        a[row+curr_col] = true;
        b[row+tot-1-curr_col] = true;
        sol_map(row+1);
    }

}

bool check_valid(int row_index, int col_index) {
    if (col[col_index]==true || a[row_index+col_index]==true || b[row_index+tot-1-col_index]==true)
        return false;
    else return true;
}

public:
    int totalNQueens(int n) {
        curr = vector<int>(n, -1);
        col = vector<bool>(n, false);
        a = vector<bool>(2*n-1, false);
        b = vector<bool>(2*n-1, false);
        tot = n;
        sol_map(0);
        return ans;
    }
};
15597