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Dynamic Programming•Pattern: 0/1 Knapsack•Medium

Partition equal subset sum

Problem Intuition & Objective

Determine if an array can be partitioned into two subsets with equal sum.

Time ComplexityO(n × sum/2)
Optimal
Space ComplexityO(sum/2)
Memory Bounds
Optimal Algorithmic Approach

0/1 knapsack with boolean DP array.

Core Invariants & Edge Cases

  • Total sum must be even; target = sum/2
  • 0/1 knapsack DP: dp[j] = can we achieve sum j?
  • Traverse nums outer, sums inner in reverse
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