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N-Queens Problem (Backtracking)

Solve the classic N-Queens puzzle using backtracking algorithm with interactive visualization

N-Queens Problem (Backtracking)

The N-Queens problem is a classic example of backtracking algorithm. Place N queens on an N×N chessboard such that no two queens attack each other.

Theory & Concepts

Definition:

Backtracking is an algorithmic approach that considers searching every possible combination in order to solve computational problems. It builds solutions incrementally and abandons candidates that cannot lead to a valid solution.

Key Points:

  • Systematic exploration of solution space
  • Prune branches that cannot lead to valid solutions
  • Recursive approach with state space tree
  • Time complexity: O(N!) in worst case, optimized with pruning

Applications:

  • Constraint satisfaction problems
  • Puzzle solving (Sudoku, N-Queens, Maze)
  • Graph coloring and scheduling problems
  • Combinatorial optimization

University Guidelines

Exam Weightage
8-10 marks Marks

Syllabus Coverage:

  • Backtracking algorithm design
  • State space tree representation
  • Pruning strategies and optimization
  • N-Queens problem solution
  • Time and space complexity analysis

Common Questions:

  • Solve N-Queens for given board size
  • Explain backtracking with state space tree
  • Compare backtracking with other approaches
  • Analyze time complexity of backtracking algorithms

Exam Tips:

Draw state space tree for small examples
Show pruning conditions clearly
Explain recursive calls and backtrack steps
Calculate time complexity with pruning

Algorithm Details

O(N!) worst case, optimized with pruning
Time Complexity
O(N) for recursion stack
Space Complexity

Algorithm Steps:

  1. 1Start with empty board and first row
  2. 2Place queen in safe position in current row
  3. 3Check if placement conflicts with previous queens
  4. 4If safe, recursively solve for next row
  5. 5If no safe position, backtrack to previous row
  6. 6Continue until all queens are placed or no solution exists

Problem Setup

Recommended: 4-8 (larger boards may take longer)

Problem Description:

Place 4 queens on a 4×4 chessboard such that no two queens attack each other. Queens can attack horizontally, vertically, and diagonally.