Like most DP problems, you can either do it tabulated in order or do a DFS + memo-ization. In this case, the fastest solutions all do the tabulated method. However, I believe the only reason they are winning are because the range of target is small. If you have a very large target, with huge intervals between the numbers you have been given, I'm pretty sure only the DFS + memo-ization (using HashMap) is going to perform well. Someone please correct me if I am wrong?
Combination Sum IV