LeetCode 416 Partition Equal Subset Sum - Implementation

function canPartition(nums)
    total := sum of all nums
    if total is odd then
        return false
    target := total / 2
    dp := array of size (target + 1), all false
    dp[0] := true
    for each num in nums
        for w from target down to num
            dp[w] := dp[w] OR dp[w - num]
    return dp[target]

Time: $O(n \times target)$ where $target = sum/2$. Space: $O(target)$.

The backwards loop prevents using the same element twice. If you looped forward, dp[w - num] might already include num from this iteration.

This is the standard 0/1 knapsack space reduction. You'll see it in most subset sum variants.