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Dynamic Programming: 0/1 Knapsack - Donald Bren School …

2015 Goodrich and Ta m a s s i a 0/1 Knapsack 1 Dynamic programming : 0/1 Knapsack Presentation for use with the textbook, Algorithm Design and Applications, by M. T. Goodrich and R. Tamassia, Wiley, 2015 2015 Goodrich and Ta m a s s i a Dynamic programming 2 The 0/1 Knapsack Problem Given: A set S of n items, with each item i having n wi - a positive weight n bi - a positive benefit Goal: Choose items with maximum total benefit but with weight at most W. If we are not allowed to take fractional amounts, then this is the 0/1 Knapsack problem. n In this case, we let T denote the set of items we take n Objective: maximize n Constraint: Tiib TiiWw 2015 Goodrich and Ta m a s s i a 0/1 Knapsack 3 Given: A set S of n items, with each item i having n bi - a positive benefit n wi - a positive weight Goal: Choose items with maximum total benefit but with weight at most W.

© 2015 Goodrich and Tamassia Dynamic Programming 2 The 0/1 Knapsack Problem Given: A set S of n items, with each item i having n w i - a positive weight n b i - a ...

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