Find all possible subsets that sum up to a given number

Question

I\'m learning Python and I have a problem with this seems to be simple task.

I want to find all possible combination of numbers that sum up to a given number.
for

Answer 1

That solution doesn't work, right? It will never add a number to a subset more than once, so you will never get, for example, [1,1,2]. It will never skip a number, either, so you will never get, for example, [1,3].

So the problem with your solution is twofold: One, you are not actually generating all possible subsets in the range 1..number. Two, The set of all subsets will exclude things that you should be including, because it will not allow a number to appear more than once.

This kind of problem can be generalized as a search problem. Imagine that the numbers you want to try are nodes on a tree, and then you can use depth-first search to find all paths through the tree that represent a solution. It's an infinitely large tree, but luckily, you never need to search all of it.