a) What is the Dynamic Programming recurrence formula for the 0/1 knapsack? Show thesubproblem overlapping of the following 0/1 knapsack problem?Max Weight of Bag = 7 kgItemWeightBenefit1312241532025b) MMM takes part in programming contests. His favourite topic is dynamic programming(DP).As he said, that he likes problems on DP, because "you spend a lot of time on thinking and alittle time on coding".In this problem you are to solve a version of the knapsack problem(link), one of the mostfamous examples of DP problem.You are given N items, each has two parameters: a weight and a cost. Let's define M as thesum of the weights of all the items.Your task is to determine the most expensive cost of a knapsack, which capacity equals to 1,2, .., M. A cost of a knapsack equals the sum of the costs of all the elements of the knapsack.Also, when you have a knapsack with a capacity equal to C, then you can fill it with items,****whose sum of weights is not greater than C.In the test case, M equals to 9.For C = 1, it's optimal to choose {1} items;For C = 2, it's optimal to choose {5} items;For C = 3, it's optimal to choose {1, 5} items;For C = 4, it's optimal to choose {4, 5} items;For C = 5, it's optimal to choose {1, 4, 5} items;For C = 6, it's optimal to choose {3, 4, 5} items;For C = 7, it's optimal to choose {1, 3, 4, 5} items;For C = 8, it's optimal to choose {2, 3, 4, 5} items;For C = 9, it's optimal to choose {1, 2, 3, 4, 5} items.Find the recurrence formula of the DP problem mentioned above3.

Note: Solving the first question as per the guidelines, i.e., a. Dynamic Programming of 0/1…

a) What is the Dynamic Programming recurrence formula for the 0/1 knapsack? Show the subproblem overlapping of the following 0/1 knapsack problem? Max Weight of Bag = 7 kg Item Weight Benefit 1 3 12 2 4 15 3 3 20 4 6 25

a) What is the Dynamic Programming recurrence formula for the 0/1 knapsack? Show the subproblem overlapping of the following 0/1 knapsack problem? Max Weight of Bag = 7 kg Item Weight Benefit 1 3 12 2 4 15 3 3 20 4 6 25

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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