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sol10

# sol10 - CIS 435 Spring 2002 Jim Calvin Homework#10...

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CIS 435, Spring 2002, Jim Calvin Homework #10 Solutions 16.2-3 Suppose we have n items with weights w 1 w 2 ≤ ··· ≤ w n and values v 1 v 2 ≥ ··· ≥ v n . The optimal algorithm is: take items 1 , 2 ,... ,k where k is the frst integer such that w 1 + w 2 + ··· + w k +1 >L . To show that this is optimal, we frst show that an optimal solution contains item 1 (assuming that L>w 1 ). IF not, replace any chosen item with 1 and the weight is no greater and the value is at least as high. Thus there is an optimal solution containing item 1. An optimal solution to the subproblem with items 2 through n must contain item 2, and so on. 16.2-4 ProF. Midas should drive as Far as he can on each tank oF gas without
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