Consider the knapsack problem: given n items of known weights w,., w, and values v,., v, anda knapsack of capacity W, find the most valuable subset of the items that fit int the knapcak . In order todesign a dynamic programming algorithm, we have driven the recurrence relation below that expresses asolution to an instance of the knapsack problem in terms of solutions to its smaller subinstances. For 1 0if j-w < 0F[i – 1, j]and we define the initial conditions as follows: F[0,j] = 0 for j>0 and F[i,0] = 0 for i > 02.1)Solve the knapsack instance given below using the recurrence given above.Apply the dynamic programming to the following instance of the knapsack problem where the capacityW = 4. Fill out the cells in the table using the recurrence given. You will not receive any credit if you donot use the recurrence relation. Write your results to the table below.сараcity jitemweighti123value$25$22112225252525$26$27312525474742651426i = 3 j= 3F[3,3] =i = 3 j= 4F[3,4] =i = 4 j = 2F[4, 2] =i = 4 j= 3F[4, 3] =i = 4 j= 4F[4, 4] =1.2.3.

Solution : By using the given formula we have to fill the remaining cells of the given table .…

Smax { Fli – 1, jl, vị + F[i – 1, j- wil } if j-w¿ > 0 if j-wi <0 F[i – 1, j] d we define the initial conditions as follows: F[0,j] = 0 for j>0 and F[i,0] = 0 for i 20 Solve the knapsack instance given below using the recurrence given above. ply the dynamic programming to the following instance of the knapsack problem where the capacity = 4. Fill out the cells in the table using the recurrence given. You will not receive any credit if you do t use the recurrence relation. Write your results to the table below. сараcity j item weight value i 1 2 3 4 $25 $22 1 1 25 25 25 25 $26 $27 3 1 25 25 47 47 4 3 26 51 4 26 = 3 j= 3 F[3,3] = = 3 j = 4 F[3,4] = = 4 j = 2 F[4,2] = = 4 j = 3 F[4,3] = = 4 j = 4 F[4, 4] = 2.

Smax { Fli – 1, jl, vị + F[i – 1, j- wil } if j-w¿ > 0 if j-wi <0 F[i – 1, j] d we define the initial conditions as follows: F[0,j] = 0 for j>0 and F[i,0] = 0 for i 20 Solve the knapsack instance given below using the recurrence given above. ply the dynamic programming to the following instance of the knapsack problem where the capacity = 4. Fill out the cells in the table using the recurrence given. You will not receive any credit if you do t use the recurrence relation. Write your results to the table below. сараcity j item weight value i 1 2 3 4 $25 $22 1 1 25 25 25 25 $26 $27 3 1 25 25 47 47 4 3 26 51 4 26 = 3 j= 3 F[3,3] = = 3 j = 4 F[3,4] = = 4 j = 2 F[4,2] = = 4 j = 3 F[4,3] = = 4 j = 4 F[4, 4] = 2.

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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