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The Subset Sum problem is described as follows: given a set of positive integers S and a target sum t, is there a subset of S whose sum is t? It is one of the well-know, so-called "hard" problems in computing. It's actually a very simple problem, and the computer program to solve it is not extremely complicated. What's hard about it is the running time – all known exact algorithms have running time that is proportional to an exponential function of the number of elements in the set (for worst-case instances of the problem).
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