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
/**
* @param {number} n
* @return {string[][]}
*/
var solveNQueens = function(n) {
const board = Array.from({ length: n }, () => Array(n).fill('.'))
const res = []
const leftRow = new Array(n).fill(0)
const upperDiagonal = new Array(2 * n - 1).fill(0)
const lowerDiagonal = new Array(2 * n - 1).fill(0)
const solve = (col) => {
if (col === n) {
res.push(construct(board))
return
}
for (let row = 0; row < n; row++) {
if (
leftRow[row] === 0 &&
lowerDiagonal[row + col] === 0 &&
upperDiagonal[n - 1 + col - row] === 0
) {
board[row][col] = 'Q'
leftRow[row] = 1
lowerDiagonal[row + col] = 1
upperDiagonal[n - 1 + col - row] = 1
solve(col + 1)
board[row][col] = '.'
leftRow[row] = 0
lowerDiagonal[row + col] = 0
upperDiagonal[n - 1 + col - row] = 0
}
}
}
const construct = (board) => {
return board.map(row => row.join(''))
}
solve(0)
return res
}
export { solveNQueens }