N-Queens Problem — Algorithm Visualizer

Step 1:Empty 5x5 board. Place 5 queens with no conflicts.

N-Queens Problem

Advanced
Time Complexity
O(n²)O(n!)O(n log n)O(n)O(log n)O(1)n →
O(N!)

The N-Queens problem asks: how can N chess queens be placed on an N×N chessboard so that no two queens threaten each other?

A queen can attack any piece in the same row, column, or diagonal. Therefore, a solution requires that no two queens share the same row, column, or diagonal.

How it works (Backtracking):

1. Place queens one row at a time
2. For each row, try each column
3. Check if the position is safe (no conflicts)
4. If safe, place the queen and move to the next row
5. If no safe column exists, backtrack to the previous row

This visualization shows the 4-Queens problem on a 4×4 board.

Time Complexity: O(N!) — in the worst case

Space Complexity: O(N²) — for the board

The N-Queens problem is a classic example of backtracking algorithms and constraint satisfaction problems.

Related algorithms

Frequently asked questions

What is N-Queens Problem?
The N-Queens problem asks: how can N chess queens be placed on an N×N chessboard so that no two queens threaten each other?
What is the complexity of N-Queens Problem?
Time (average): O(N!) · Space: O(N²)
Who is this N-Queens Problem visualizer for?
The N-Queens Problem visualization targets advanced-level learners in the Backtracking category. Useful for students, interview prep, and hands-on review.
What algorithms are related to N-Queens Problem?
In the same category (Backtracking) you can explore: Sudoku Solver, Maze Pathfinding. Each has an interactive visualization.