LeetCode 416 Partition Equal Subset Sum - Boolean State Design

Define $dp[s]$ = true if some subset of numbers can sum to exactly $s$, false otherwise. Your target is $dp[S/2]$. Base case: $dp[0] = true$. An empty subset sums to 0. All other $dp[s]$ start as false. Transition: for each number $num$, update $dp[s] = dp[s] \text{ OR } dp[s - num]$ for all valid $s$.

If you could reach $s - num$ before, you can reach $s$ by adding $num$. Process sums in decreasing order to avoid using the same number twice.