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The subset sum problem is a decision problem in computer science. In its most general formulation, there is a multiset S {\displaystyle S} of integers and a target-sum T {\displaystyle T} , and the question is to decide whether any subset of the integers sum to precisely T {\displaystyle T}. The problem is known to be NP. Moreover, some restricted variants of it are NP-complete too, for example:
SSP can also be regarded as an optimization problem: find a subset whose sum is at most T, and subject to that, as close as possible to T. It is NP-hard, but there are several algorithms that can solve it reasonably quickly in practice.
SSP is a special case of the knapsack problem and of the multiple subset sum problem.