A. Apply the dynamic programming algorithm discussed in Chapter 7 to fill the given table for a knapsack instance of 7 items having values 10, 5, 15, 7, 6, 18, 3 and sizes 2, 3, 5, 7, 1, 4, 1. The knapsack capacity is C=13. The first row and the first column are already filled. The value of the optimal solution is also given. OsjsC=13 | 0|1 2|3|4|5 6 78 9 10 | 11 | 12| 13 | |00|0|0|0| 이 | 0|0|0|0|0| o| 0| 0 | 0 V=10, S;=2 |1 0 V;=5, S;=3|20 V;=15, S3=5| 3 0 V=7, S;=7|4 0 V;=6, S;=1|50 V=18, S;=4 6 0 V;=3, S;=1| 7 0 52 B. A way to find the items forming an optimal solution is to sort the items in decreasing order according to 's where Vi and Si are the value and the size of item į. If there is a sequence of successive items starting from the item 1 where their total size is equal to C (The knapsack capacity), then they form an optimal solution. Use this method to find and optimal solution (indicate its items, total yalue and total size).

A. Apply the dynamic programming algorithm discussed in Chapter 7 to fill the given table for a knapsack instance of 7 items having values 10, 5, 15, 7, 6, 18, 3 and sizes 2, 3, 5, 7, 1, 4, 1. The knapsack capacity is C=13. The first row and the first column are already filled. The value of the optimal solution is also given. OsjsC=13 | 0|1 2|3|4|5 6 78 9 10 | 11 | 12| 13 | |00|0|0|0| 이 | 0|0|0|0|0| o| 0| 0 | 0 V=10, S;=2 |1 0 V;=5, S;=3|20 V;=15, S3=5| 3 0 V=7, S;=7|4 0 V;=6, S;=1|50 V=18, S;=4 6 0 V;=3, S;=1| 7 0 52 B. A way to find the items forming an optimal solution is to sort the items in decreasing order according to 's where Vi and Si are the value and the size of item į. If there is a sequence of successive items starting from the item 1 where their total size is equal to C (The knapsack capacity), then they form an optimal solution. Use this method to find and optimal solution (indicate its items, total yalue and total size).

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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