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Relating to the level of difficulty of a calculation or the asymptotic running time of an algorithm.

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Algorithm about finding a combination that the sum is closest to a given number

. $$ \arg\min_{1\leq j_1,\cdots,j_n\leq k}{|x - \sum_{i=1}^n{P_{ij_i}}|} $$ An direct algorithm with time complexity $k^n$ is trivial. … This could be a cutdown, but the complexity is still exponential. Could I do better than this? Is there any relevant topic, algorithm or data structure that I'm missing? …
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