Board size N6

4 total solutions exist for N=6 · showing the first search path

1 / 1922

Speed

6×6 board. Place one queen per row so no two share a column or diagonal. Starting from row 0.

Queen columns per row

row 0—

row 1—

row 2—

row 3—

row 4—

row 5—

Solutions found so far

Total for N=6

n-queens.js

1function solve(row) {

2 if (row === N) {

3 solutions.push([...queens]);

4 return;

5 }

7 for (let col = 0; col < N; col++) {

8 if (isSafe(row, col)) {

9 queens[row] = col; // place

10 solve(row + 1); // recurse

11 queens[row] = null; // undo

12 }

13 }

14}

16function isSafe(r, c) {

17 return every placed queen q at (qr, qc)

18 has qc !== c

19 && |qr - r| !== |qc - c|;

20}

Slide N from 4 to 8 · Red ✕ marks attacked squares · Backtracking undoes dead ends automatically

About the N-Queens algorithm

Place N queens on an N×N board so none attack each other. The canonical backtracking example — try, conflict, undo, retry.

Category: Backtracking
Difficulty: Medium
Time complexity: O(N!)
Space complexity: O(N)