LeetCode-in-All
51. N-Queens
Hard
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 all distinct solutions to the n-queens puzzle. You may return the answer in any order.
Each solution contains a distinct board configuration of the n-queens’ placement, where 'Q' and '.' both indicate a queen and an empty space, respectively.
Example 1:
Input: n = 4
Output: [[“.Q..”,”…Q”,”Q…”,”..Q.”],[”..Q.”,”Q…”,”…Q”,”.Q..”]]
Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above
Example 2:
Input: n = 1
Output: [[“Q”]]
Constraints:
1 <= n <= 9
Solution
class Solution {
/**
* @param Integer $n
* @return String[][]
*/
public function solveNQueens($n) {
$pos = array_fill(0, $n + 2 * $n - 1 + 2 * $n - 1, false);
$pos2 = array_fill(0, $n, 0);
$ans = array();
$this->helper($n, 0, $pos, $pos2, $ans);
return $ans;
}
private function helper($n, $row, &$pos, &$pos2, &$ans) {
if ($row == $n) {
$this->construct($n, $pos2, $ans);
return;
}
for ($i = 0; $i < $n; $i++) {
$index = $n + 2 * $n - 1 + $n - 1 + $i - $row;
if ($pos[$i] || $pos[$n + $i + $row] || $pos[$index]) {
continue;
}
$pos[$i] = true;
$pos[$n + $i + $row] = true;
$pos[$index] = true;
$pos2[$row] = $i;
$this->helper($n, $row + 1, $pos, $pos2, $ans);
$pos[$i] = false;
$pos[$n + $i + $row] = false;
$pos[$index] = false;
}
}
private function construct($n, $pos, &$ans) {
$sol = array();
for ($r = 0; $r < $n; $r++) {
$queenRow = array_fill(0, $n, '.');
$queenRow[$pos[$r]] = 'Q';
array_push($sol, implode($queenRow));
}
array_push($ans, $sol);
}
}