a4_solution

# a4_solution - CS325 Winter 2013 HW4 Due Feb 22nd in class 1...

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CS325 Winter 2013: HW4 Due Feb 22nd in class 1. Knapsack without repetitions. Consider the following knapsack problem: The total weight limit W = 10 and Item Weight Value 1 6 \$30 2 3 \$14 3 4 \$16 4 2 \$9 Solve this problem using the dynamic programming algorithm presented in class. Please show the two dimensional table L ( w,j ) for w = 0 , 1 ,...,W and j = 1 , 2 , 3 , 4. L 0 1 2 3 4 5 6 7 8 9 10 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 30 30 30 30 30 2 0 0 0 14 14 14 30 30 30 44 44 3 0 0 0 14 16 16 30 30 30 44 46 4 0 0 9 14 16 23 30 30 39 44 46 2. Give a dynamic programming algorithm for solving the following problem. Input: A list of n positive integers a 1 ,a 2 ,...,a n and a number t . Goal: Decide if some subset of the a i ’s add up to t . (You can use each a i at most once.) The running time should be O ( nt ). Consider the subproblem L ( i,s ), which returns the answer of “Does a subset of a 1 i sum up to s ?”. Below are some substeps that will help you develop your algorithm. a What are the two options we have regarding item i toward answering the subproblem L ( )?

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a4_solution - CS325 Winter 2013 HW4 Due Feb 22nd in class 1...

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