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Backtracking•Pattern: Backtracking•Medium

Permutations of a list (with duplicates)

Problem Intuition & Objective

Generate all unique permutations of a list that may contain duplicates.

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

Backtracking with sort + duplicate-skip condition.

Core Invariants & Edge Cases

  • Sort, then use backtracking with a used[] boolean array
  • Skip if nums[i] == nums[i-1] and !used[i-1] (avoid duplicate branches)
  • Swap-based approach (without sorting) for no duplicates
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