Editorial for Christmas Cards


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This problem is a straightforward dynamic programming problem. The two states for the problem are dp[\text{current card}][\text{maximum card}]. First, you must make the observation that cards in any solution will always be played in the order they are found in the deck. The current card is the card that you are deciding whether or not to play. The maximum card is the highest card that you can play. For each state, you either do not play the card (dp[\text{current}+1][\text{maximum}]), or you do play the card (dp[\text{current}+1][\text{maximum}+d[i]]+c[i])

Time Complexity: \mathcal{O}(N^2)


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