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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
function solveNQueens(n: number): string[][] {
const result: string[][] = []
const board: number[] = []
const BOARD_ROW = Array(n).fill('.').join('')
const printBoard = () => board.map((col) => `${BOARD_ROW.slice(0, col)}Q${BOARD_ROW.slice(col + 1)}`)
const isSafePlace = (c: number): boolean => {
for (let row = 0; row < board.length; row++) {
const col = board[row]
if (c === col) {
return false
}
const diff = board.length - row
if (c === col + diff || c === col - diff) {
return false
}
}
return true
}
const backtrack = () => {
if (board.length === n) {
result.push(printBoard())
return
}
for (let col = 0; col < n; col++) {
if (isSafePlace(col)) {
board.push(col)
backtrack()
board.pop()
}
}
}
backtrack()
return result
}
export { solveNQueens }