Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 15, Problem 10P
(a)
Program Plan Intro
To show that there is an optimal investment strategy in each year that put all money into a single investment.
(b)
Program Plan Intro
To show that problem of planning optimal investment strategy exhibits optimal substructure.
(c)
Program Plan Intro
To design and describe an
(d)
Program Plan Intro
To show that the problem of maximizing income at end of 10 years have no longer exhibits optimal substructure.
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The list below is the grades of a student. To pass the course, the following requirements need to be met:
• The mininum grade cannot be less than 50
The average must be great than 75
The number of grades that are less than 60 cannot be more 3.
Check the grades and let me know if the student has passed the course or not.
grade =
[90, 70, 80, 85, 99, 86, 44, 66, 90, 70, 80, 85, 99, 86, 44, 66, 90, 70,
80, 85, 99, 86, 44, 66, 85, 99, 86, 44, 66, 90, 70, 80, 85, 99, 86, 44,
66, 85, 99, 86, 44, 66, 90, 70, 80, 85, 99, 86, 44, 66]
8. Pizza
Mario owns a pizzeria. Mario makes all of his pizzas from 10 different ingredients, using 3 ingredients on each pizza. Mario's cousin Luigi owns a pizzeria
as well. Luigi makes all his pizzas from 9 ingredients, using 4 ingredients on each pizza. Mario and Luigi have made a bet: Mario believes that customers
can order a larger selection of pizzas in his pizzeria than they can order in Luigi's pizzeria. Use functions for this assignment.
Implement a factorial() function yourself (do not use the one from the math module)
• When choosing k items from n possible items, the number of possibilities can be obtained using the following formula:
()
n!
k!(n-k)!
Make a function called choose with two parameters n and k, that implements the above formula.
• Write a program that calculates the number of pizzas Mario and Luigi can make. The outcome should look like this:
Mario can make 120 pizzas.
Luigi can make 126 pizzas.
Luigi has won the bet.
Project Optimization and regression: Exact and approximate methods to solve 0-1 Knapsack problem
Description
The 0/1 Knapsack Problem and Logistics
Transportation companies such as TNT and Royal Mail face daily problems in logistics. Consider the following simple logistics problem, which you will solve:
An airline cargo company has 1 aeroplane which it flies from the UK to the US on a daily basis to transport some cargo. In advance of a flight, it receives bids for deliveries from (many) customers. Customers state the weight of the cargo item they would like delivered, and the amount they are prepared to pay. The airline is constrained by the total amount of weight the plane is allowed to carry. The company must choose a subset of the packages (bids) to carry in order to make the maximum possible profit, given the weight limit that they must respect.
In mathematical form the problem is: Given a set of N items each with weight wi and value vi, for i=1 to N, choose a subset of items…
Chapter 15 Solutions
Introduction to Algorithms
Ch. 15.1 - Prob. 1ECh. 15.1 - Prob. 2ECh. 15.1 - Prob. 3ECh. 15.1 - Prob. 4ECh. 15.1 - Prob. 5ECh. 15.2 - Prob. 1ECh. 15.2 - Prob. 2ECh. 15.2 - Prob. 3ECh. 15.2 - Prob. 4ECh. 15.2 - Prob. 5E
Ch. 15.2 - Prob. 6ECh. 15.3 - Prob. 1ECh. 15.3 - Prob. 2ECh. 15.3 - Prob. 3ECh. 15.3 - Prob. 4ECh. 15.3 - Prob. 5ECh. 15.3 - Prob. 6ECh. 15.4 - Prob. 1ECh. 15.4 - Prob. 2ECh. 15.4 - Prob. 3ECh. 15.4 - Prob. 4ECh. 15.4 - Prob. 5ECh. 15.4 - Prob. 6ECh. 15.5 - Prob. 1ECh. 15.5 - Prob. 2ECh. 15.5 - Prob. 3ECh. 15.5 - Prob. 4ECh. 15 - Prob. 1PCh. 15 - Prob. 2PCh. 15 - Prob. 3PCh. 15 - Prob. 4PCh. 15 - Prob. 5PCh. 15 - Prob. 6PCh. 15 - Prob. 7PCh. 15 - Prob. 8PCh. 15 - Prob. 9PCh. 15 - Prob. 10PCh. 15 - Prob. 11PCh. 15 - Prob. 12P
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