Challenge: Partition Reconstruction

The DP tells you if a partition exists, but not which elements to use. To reconstruct, track how each sum was achieved. Modify the DP: when $dp[s - nums[i]]$ is true and you set $dp[s] = true$, record that element $i$ contributed to sum $s$.

Or backtrack: start at target sum, for each element check if $dp[target - nums[i]]$ was true before adding element $i$. If so, include it and continue. Try reconstructing the partition for $[1, 5, 11, 5]$. Which elements form the subset summing to $11$?