Prove that greedy approach to fractional knapsack problem

Assignment Help Computer Engineering

Reference no: EM131834772

Problem

1. Prove that the greedy approach to the Fractional Knapsack problem yields an optimal solution.

2. Show that the worst-case number of entries computed by the refined dynamic programming algorithm for the 0-1 Knapsack problem is in ?(2 n). Do this by considering the instance in which W = 2n -2 and wi = 2i-1 for 1 ≤ i ≤ n.

3. Show that in the refined dynamic programming algorithm for the 0-1 Knapsack problem, the total number of entries computed is about (W + 1) × (n + 1) /2, when n = W + 1 and wi = 1 for all i.

Reference no: EM131834772

Questions Cloud

Which of the following autocorrelation sequences are extendi : Which of the following autocorrelation sequences are extendible? For those that are extendible, find an extension and determine whether or not the extension

Reflection coefficients corresponding : The reflection coefficients corresponding to a third-order all-pole model are and the modeling error is given by

Describe one type of learner analysis : Write a one page an explanation of one strength and one limitation of using a Class Café to conduct a learner analysis.

Reflection coefficients for a two-pole model of a signal : The reflection coefficients for a two-pole model of a signal x(n) are r1 = 0.25 and r2 = 0.25 and the "modeling error" is ?2 = 9.

Prove that greedy approach to fractional knapsack problem : Prove that the greedy approach to the Fractional Knapsack problem yields an optimal solution.

Describe three features of the course environment : Write in one pagea one-sentence description of an undergraduate or graduate online psychology course you might teach in the future.

Analyze your algorithm and show results using order notation : Use the dynamic programming approach to write an algorithm for Exercise. Analyze your algorithm and show the results using order notation.

Finite number of values of its unit sample response : You are told that it is always possible to determine whether or not a causal all-pole filter is stable from a finite number of values of its unit sample respons

What is the worst-case time complexity of the given approach : Assuming the keys are already sorted, what is the worst-case time complexity of this approach? Justify your answer.

User Account

All Pages