There is no known Greedy strategy that is optimal for
solving the 0/1 Knapsack problem. For each of the following
strategies give a counterexample, i.e. descibe an instance where
that strategy will fail to produce an optimal result.
(a) Lightest item first.
(b)Most valuable item first.
(c)Item with the best value to weight ratio first.
There is no known Greedy strategy that is optimal for solving the 0/1 Knapsack problem. For...
Consider the following greedy algorithm for the knapsack problem: each time we pick the item with the highest value to weight ratio to the bag. Skip items that will make the total weight exceeded the capacity of the bag. Find a counterexample to show that this approach will not work, and the result could be 100 times worse than the optimal solution. That is, construct a table of set of items with weight and values and find a bag capacity...
"Greedy, but Better": Given a knapsack problem with a weight capacity C, and n items, and each item has a weight W[1:n] and monetary value P[1:n]. You have to determine which items to take so that the total weight is C, and the total value (profit) is maximized. In this case we are considering an integer problem, so you can either take an item, or not take an item, you cannot take it fractionally. If you recall, the greedy algorithm...
5) (10 pts) Greedy Algorithms The 0-1 Knapsack problem is as follows: you are given a list of items, each item has an integer weight and integer value. The goal of the problem is to choose a subset of the items which have a sum of weights less than or equal to a given W with a maximal sum of values. For example, if we had the following five items (each in the form (weight, value)): 11(6, 13), 2(4, 10),...
1. Fractional Knapsack Problem Algorithm Which best describes the tightest range of the number of items with only fractional inclusion (i.e. not entirely included or excluded) in the knapsack? (Let n denote the number of items for possible inclusion.) A) At least 0 items and at most n items B) At least 1 items and at most n items C) Exactly n items D) At least 0 items and at most n-1 items E) At least 1 items and at...
Consider the following greedy strategies for this problem: 1. Select the earliest finishing interval and discard overlapping intervals. Keep doing this until all intervals have been eliminated (either selected or discarded). 2. Select the earliest starting interval and discard overlapping intervals. Keep doing this until all intervals have been eliminated (either selected or discarded). 3. Select the pair of non-overlapping intervals that have the smallest gap between them: find a pair of intervals i # j such that s; -...
In the bin packing problem, items of different weights (or sizes) must be packed into a finite number of bins each with the capacity C in a way that minimizes the number of bins used. The decision version of the bin packing problem (deciding if objects will fit into <= k bins) is NP-complete. There is no known polynomial time algorithm to solve the optimization version of the bin packing problem. In this practice problem you will be examining three...
Hey guys, I need some help solving this problem. thank
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Pontfolio Optimization Task 4 Suppose the shares of two different companies give you the same return on average. Does it make sense to distribute your money and buy some shares of each company? Or would it be better to invest all the money into only a single company? Common sense says: "distribute" Why? Let's see... What at all could we gain if the return is...
Help needed with Python 3: Dictionaries and Sets.
The problem is one that asks the user to create a completed
program that prompts the user for the name of a data file, and
reads the contents of that data file, then creates variables in a
form suitable for computing the answer to some questions.
The format should be in the same manner as the attached .py
file. All subsequent assignment details (.py and .csv files) can be
found at this...
Problem Definition: Problem: Given an array of integers find all pairs of integers, a and b, where a – b is equal to a given number. For example, consider the following array and suppose we want to find all pairs of integers a and b where a – b = 3 A = [10, 4, 6, 16, 1, 6, 12, 13] Then your method should return the following pairs: 4, 1 15, 12 13, 10 A poor solution: There are...
CEMEX a. Did CEMEX use a multidomestic strategy? Justify your answer. b. Did CEMEX use a global strategy? Justify your answer. c. Did CEMEX use a transnational strategy? Justify your answer. On June 7, 2007 Mexico-based CEMEX won a majority stake in Australia’s Rinker Group. The $15.3 billion takeover, which came on top of the major acquisition in 2005 of the RMC Corporation – then the world’s largest ready-mix concrete company and the single largest purchaser of cement – made...