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Consider the 0/1/2/3 Knapsack Problem. Unlike 0/1 Knapsack problem which restricts xi to be either O or 1, 0/1/2/3 Knapsack Problem allows xi to be either O or 1 or 2 or 3 (that is, we assume that 3 copies of each object i are available, for all i). (a) Obtain the dynamic programming functional equation to solve (find optimal profit) the 0/1/2/3 Knapsack Problem. (b) Give an algorithm to implement your functional equation. (c) What is the complexity of your algorithm?

Consider the 0/1/2/3 Knapsack Problem. Unlike 0/1 Knapsack problem which restricts xi to be either O or 1, 0/1/2/3 Knapsack Problem allows xi to be either O or 1 or 2 or 3 (that is, we assume that 3 copies of each object i are available, for all i). (a) Obtain the dynamic programming functional equation to solve (find optimal profit) the 0/1/2/3 Knapsack Problem. (b) Give an algorithm to implement your functional equation. (c) What is the complexity of your algorithm?

Database System Concepts
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
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Consider the 0/1/2/3 Knapsack Problem. Unlike 0/1 Knapsack problem which restricts xi to be either 0 or 1, 0/1/2/3 Knapsack Problem allows xi to be either 0 or 1 or 2 or 3 (that is, we assume that 3 copies of each object i are available, for all i). (a) Obtain the dynamic programming functional equation to solve (find optimal profit) the 0/1/2/3 Knapsack Problem. (b) Give an algorithm to implement your functional equation. (c) What is the complexity of your algorithm?
Transcribed Image Text:Consider the 0/1/2/3 Knapsack Problem. Unlike 0/1 Knapsack problem which restricts xi to be either 0 or 1, 0/1/2/3 Knapsack Problem allows xi to be either 0 or 1 or 2 or 3 (that is, we assume that 3 copies of each object i are available, for all i). (a) Obtain the dynamic programming functional equation to solve (find optimal profit) the 0/1/2/3 Knapsack Problem. (b) Give an algorithm to implement your functional equation. (c) What is the complexity of your algorithm?
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