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Backtracking•Pattern: Backtracking•Medium

N-Queens — place N queens on N×N board without conflict

Problem Intuition & Objective

Find all valid N-Queens placements.

Time ComplexityO(n!)
Optimal
Space ComplexityO(n)
Memory Bounds
Optimal Algorithmic Approach

Row-by-row backtracking with column and diagonal conflict sets.

Core Invariants & Edge Cases

  • Place one queen per row; track used columns and both diagonals
  • Diagonals: col-row is unique for '/' diagonal, col+row for '\'
  • Use sets to check conflicts in O(1)
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