There’s a beautiful algorithm for solving this problem in time O(n + Sort), where Sort is the amount of time required to sort the input array. The idea behind the algorithm is to sort the array and then ask the following question: what is the smallest positive integer you cannot make using the first k … Read more
You could use itertools to iterate through every combination of every possible size, and filter out everything that doesn’t sum to 10: import itertools numbers = [1, 2, 3, 7, 7, 9, 10] target = 10 result = [seq for i in range(len(numbers), 0, -1) for seq in itertools.combinations(numbers, i) if sum(seq) == target] print(result) … Read more
Subset Sum is the first NP-complete problem I learned at Macalester. This question is viewed 36000+ times yet I don’t see a sufficient answer that explains the algorithm in detail with logic. So I thought I make an attempt to do so. Assumption: For the sake of simplicity first I made the assumption that the … Read more
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: def subset_sum(numbers, target, partial=[]): s = sum(partial) # check if the partial sum is equals to target if s == target: print “sum(%s)=%s” % (partial, target) if s >= … Read more