LeetCode 494 Target Sum - Walkthrough

Trace Target Sum on $nums = [1, 1, 1, 1, 1]$ with target $S = 3$. Sum is $5$. We need $(5 + 3) / 2 = 4$ as the positive subset sum. Find subsets summing to $4$. Count $dp[s]$ = number of ways to make sum $s$. After processing all five $1$s: $dp[0]=1$, $dp[1]=5$, $dp[2]=10$, $dp[3]=10$, $dp[4]=5$, $dp[5]=1$.

Answer: $dp[4] = 5$ ways. These correspond to choosing $4$ ones as positive and $1$ as negative: $+1+1+1+1-1 = 3$.