<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>all distinct solutions to the <strong>n-queens puzzle</strong></em>. You may return the answer in <strong>any order</strong>.</p>

<p>Each solution contains a distinct board configuration of the n-queens&#39; placement, where <code>&#39;Q&#39;</code> and <code>&#39;.&#39;</code> both indicate a queen and an empty space, respectively.</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> [[&quot;.Q..&quot;,&quot;...Q&quot;,&quot;Q...&quot;,&quot;..Q.&quot;],[&quot;..Q.&quot;,&quot;Q...&quot;,&quot;...Q&quot;,&quot;.Q..&quot;]]
<strong>Explanation:</strong> There exist two distinct solutions to the 4-queens puzzle as shown above
</pre>

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

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> [[&quot;Q&quot;]]
</pre>

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

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

/*
".Q.."
"...Q"
"Q..."
"..Q."


["..Q.","Q...","...Q",".Q.."]]
*/

class Solution {
public:
    vector<string> convertToBoard(vector<vector<char>> &state) {
        int n = state.size();
        
        vector<string> board;
        for(int row=0; row<n; row++) {
            string currRow(state[row].begin(), state[row].end());
            board.push_back(currRow);
        }
        
        return board;
    }
    
    void dfs(int row, vector<vector<char>> state, unordered_set<int> columns, unordered_set<int> diagonals, unordered_set<int> antiDiagonals, vector<vector<string>> &arrangements) {
        int n = state.size();
        
        if(row == n) {
            // valid arrangement found
            arrangements.push_back(convertToBoard(state));
            return;
        }
        
        for(int col=0; col<n; col++) {
            int diagonal = row-col;
            int antiDiagonal = row+col;
            
            if(columns.count(col) || diagonals.count(diagonal) || antiDiagonals.count(antiDiagonal)) {
                continue;
            }
            
            columns.insert(col);
            diagonals.insert(diagonal);
            antiDiagonals.insert(antiDiagonal);
            state[row][col] = 'Q';
            
            dfs(row+1, state, columns, diagonals, antiDiagonals, arrangements);
            
            // backtracking
            columns.erase(col);
            diagonals.erase(diagonal);
            antiDiagonals.erase(antiDiagonal);
            state[row][col] = '.';
        }
    }
    
    vector<vector<string>> solveNQueens(int n) {
        vector<vector<char>> state(n, vector<char>(n, '.'));
        
        unordered_set<int> columns;
        unordered_set<int> diagonals;
        unordered_set<int> antiDiagonals;
        
        vector<vector<string>> arrangements;
        
        dfs(0, state, columns, diagonals, antiDiagonals, arrangements);
        
        return arrangements;
    }
};
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