Hard Algorithms Dynamic Programming
Discuss advanced DP techniques: bitmask DP, digit DP, DP on trees.
Answer
Bitmask DP uses integer bits to represent subsets, solving problems like TSP, assignment, and subset optimization in O(2^n * poly(n)). Digit DP counts numbers with certain properties by processing digits, tracking tight bound and state (e.g., count numbers with digit sum S). Tree DP solves tree problems by computing values bottom-up: subtree aggregation, rerooting for all-roots answers. These techniques extend DP applicability to complex combinatorial and structural problems.
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