Lec4Knapsack

# Storing values of sub solutions construct the optimum

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Unformatted text preview: do n- 2 times : c = a + b; a = b; b = c return c Compute the values "bottom up” Only store needed values: the previous two Same O(n) time complexity, constant space Dynamic Programming •  Characterize the structure of the problem, ie show how a larger problem can be solved using solutions to sub- problems •  Recursively deﬁne the optimum •  Compute the optimum bottom up, storing values of sub solutions •  Construct the optimum from the stored data Optimal substructure !   Dynamic programming works when a problem has optimal substructure: we can construct the optimum of a larger problem from the optima of a "small set" of smaller problems. !   small: polynomial !   Not all problems h...
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