N-Queens Problem Visualizer

Interactive Chess Queen Placement

Solve and visualize the classic N-Queens problem with interactive animations and multiple solutions.

Configuration

The N-Queens Problem:
Place N chess queens on an N×N board so that no two queens attack each other

About N-Queens

The N-Queens problem is a classic puzzle where you must place N chess queens on an N×N chessboard.

Rules:

• No two queens can be in the same row

• No two queens can be in the same column

• No two queens can be on the same diagonal

Complexity:

This is an NP-hard problem solved using backtracking

Features

  • Interactive board visualization
  • Find all solutions
  • Animate through solutions
  • Adjustable animation speed
  • Show attacked cells
  • Copy solution positions
  • Download all solutions
  • Support 1×1 to 12×12 boards

Solution Counts

4×4:2 solutions
5×5:10 solutions
6×6:4 solutions
8×8:92 solutions
10×10:724 solutions

Algorithm

Backtracking:

Places queens row by row

Pruning:

Skips invalid positions early

Recursion:

Explores all valid placements

Time Complexity:

O(N!) worst case

Applications

  • Algorithm design and analysis
  • Backtracking technique demonstration
  • Constraint satisfaction problems
  • Computer science education
  • Puzzle solving strategies
  • Optimization problems
  • Artificial intelligence
  • Combinatorial mathematics

History

Notable Facts:

1848: First published by chess player Max Bezzel

1850: Franz Nauck extended to N-Queens

Classic Problem: One of the most studied problems in computer science

27×27: Largest board with all solutions counted (234,907,967,154,122,528)