N-Queens Problem Resource - aloalgo
aloalgo logoaloalgo
Beta
Problems👑 Leaderboard
New
Login

N-Queens Problem

Place N queens on an N×N chessboard so that no two queens attack each other. This is the classic backtracking problem.

The Problem

Backtracking Solution

Optimized with Sets

Track attacked columns and diagonals with sets for O(1) conflict checks.

Understanding Diagonals

Count Solutions Only

Bitmask Optimization

Use bitmasks for the fastest possible implementation.

Step-by-Step Example (N=4)

Related Problems

  • N-Queens II: Count solutions (shown above)
  • Sudoku Solver: Similar constraint propagation
  • Word Search: Grid backtracking
  • Combination Sum: Choice + backtrack pattern

Key Takeaways

  1. Row by row: Place one queen per row, try each column
  2. Track constraints: Use sets for columns and diagonals
  3. Diagonal math: row-col and row+col identify diagonals
  4. Early pruning: Skip invalid placements immediately
Was this helpful?

Company

Contact UsPrivacy Policy

Practice

Study planAll problems

Learn

ResourcesCheat SheetDSA Glossary
© 2026 aloalgo. All rights reserved.