- N-Queens
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
JavaScript Solution
/**
* @param {number} n
* @return {string[][]}
*/
var solveNQueens = function(n) {
let col = Array(n).fill(0)
let pie = na = new Array(2*n - 1).fill(0)
let board = []
let res = []
for(let i=0; i< n; i++){
board.push(Array(n).fill('.'))
}
return dfs(0,n,col,pie,na,board,res),res
};
let dfs = (row, n, col, pie, na, board, res)=>{
if(row==n){
let rows =[]
for(let i=0;i<n;i++){
rows.push(board[i].join(''))
}
res.push(rows)
return
}
for(let i=0; i < n; i++){
if(!col[i] && !pie[row + i] && !na[row - i + n - 1] ){
[ col[i], pie[row + i], na[row - i + n - 1] ] = [1,1,1]
board[row][i] = 'Q'
dfs(row + 1, n, col, pie, na, board, res)
board[row][i] = '.'
[ col[i], pie[row + i], na[row - i + n - 1] ] = [0,0,0]
}
}
return
}