I want to know about the algorithm used to solve this problem PRSN. I saw some of the answers, I could able to understand that this problem was solved using dynamic programming, but what is the exact trick that solves the problem?

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Why donâ€™t you search for â€śBribe the Prisonersâ€ť on Google? It was a straight lift from Google Code Jam 2009. http://www.algorithmatica.com/bribe-the-prisoners/

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