This problem can be solved with a recursive combinations of all possible sums filtering out those that reach the target. Here is the algorithm in Python: This type of algorithms are very well explained in the following Stanford’s Abstract Programming lecture – this video is very recommendable to understand how recursion works to generate permutations of solutions. … Read more
Art of Computer Programming Volume 4: Fascicle 3 has a ton of these that might fit your particular situation better than how I describe. Gray Codes An issue that you will come across is of course memory and pretty quickly, you’ll have problems by 20 elements in your set — 20C3 = 1140. And if … Read more
Have a look at itertools.combinations: Return r length subsequences of elements from the input iterable. Combinations are emitted in lexicographic sort order. So, if the input iterable is sorted, the combination tuples will be produced in sorted order. Since 2.6, batteries are included!