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I am currently looking for ideas on how to find all possible sums of a set of numbers with these rules. I have these numbers to work with and I want to find all possible sums so that you can only use a single number at max 4 times and each time you pick 7 of these numbers.

{ 0, 1, 5, 22, 98, 453, 2031, 8698, 22854, 83661, 262349, 636345 and 1479181 }

Acceptable examples would be

0 + 0 + 0 + 0 + 83661 + 83661 + 2031

Unacceptable example would be

0 + 0 + 0 + 0 + 0 + 83661 + 2031

The only way I can think of is a series of nested loops but I am having trouble with that as well. Would there be any other options to do this. I am using Java but I don't really think that matters.

user3070528
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  • Have you thought of doing this using recursion? That would probably work best for your purposes. – Akshay Aug 06 '14 at 16:36
  • There should be algorithms around for finding all combinations--i.e. if you have a set, find all subsets that have exactly 7 elements. Now do that with a multi-set that contains 4 copies of each element from your original set. (But that will get you a lot of duplicate subsets...) – ajb Aug 06 '14 at 16:40

1 Answers1

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You can achieve this by building a new List of elements that contains each element of the given set duplicated 4 times . then use a DFS strategy method to build possible possible sum combination. to have an idea about how to implement DFS check this answer

Mifmif
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