Coding Problems
Partition Equal Subset Sum | Leetcode 416
Welcome to our deep dive on Partition Equal Subset Sum (Leetcode 416). This problem beautifully maps directly into the legendary 0/1 Knapsack dynamic programming pattern.
Problem Statement
Given a non-empty array nums containing only positive integers, find if the array can be partitioned into two subsets such that the sum of elements in both subsets is equal.
Example 1:
nums = [1,5,11,5] => Output: true
(Explanation: The array can be partitioned as [1, 5, 5] and [11].)
Example 2:
nums = [1,2,3,5] => Output: false
(Explanation: The array cannot be partitioned into equal sum subsets. The total sum is 11, which cannot be halved into an integer).)
Core Concept: The 0/1 Knapsack Transformation
We want to split the array mathematically cleanly exactly into two subsets with an equal sum. Therefore, the target sum for one single subset must be strictly precisely Total Sum / 2.
- If
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