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Combinatorial optimization typically deals with optimizing over a finite set of objects that have some combinatorial structure (e.g. trees, matchings, matroids). Approximation algorithms, polyhedral methods, and integer programming are all on topic.

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Sequential prize searching

A solution to the problem is an ordered list of $n$ rooms. If $n=N$, Dieter Kadelka's suggestion (searching the rooms in order of decreasing $p_i/c_i$) can be followed and gives an optimal solution c …
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