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 16.1, Problem 5E
Program Plan Intro
To modify the Activity-Selection problem in such a way that the total value of activities scheduled is maximized, that is,
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Let's consider the bar cutting problem: Suppose we have a bar of length n. p is the selling price of a bar of length i; Let's assume that (i=1, 2, ..., n). Our goal is to split the bar into parts of integer length to get maximum profit.
(a) Design a dynamic programming algorithm for this problem. Instead of pseudocode, a well-explained explanation is preferred. Also mention the time and place complexity of your algorithm. (Hint: Define the function F(n) as the maximum profit that can be obtained for a stick of length n and construct an iterative relation.)
(b) Apply the dynamic programming algorithm you designed for the following example: You have a stick of length 6. Selling prices of parts: pi=1, P2=6, p3=7, p=11, p=14, po=15.
Suppose that there are m students who want to take part in n projects. A student
is allowed to join in a particular project only if the student is qualified for the project. Each
project can only have a limited number of students, and each student can take part in at most
one project. The goal is to maximize the number of students that are admitted to the projects.
Show how to solve this problem by transforming it into a maximum flow problem. What is the
running time of your algorithm?
A robot can move horizontally or vertically to any square in the same row or in the same column of a board. Find the number of the shortest paths by which a robot can move from one corner of a board to the diagonally opposite corner. The length of a path is measured by the number of squares it passes through, including the first and the least squares. Write the recurrence relation if you solve the problem by a dynamic programming algorithm.
Chapter 16 Solutions
Introduction to Algorithms
Ch. 16.1 - Prob. 1ECh. 16.1 - Prob. 2ECh. 16.1 - Prob. 3ECh. 16.1 - Prob. 4ECh. 16.1 - Prob. 5ECh. 16.2 - Prob. 1ECh. 16.2 - Prob. 2ECh. 16.2 - Prob. 3ECh. 16.2 - Prob. 4ECh. 16.2 - Prob. 5E
Ch. 16.2 - Prob. 6ECh. 16.2 - Prob. 7ECh. 16.3 - Prob. 1ECh. 16.3 - Prob. 2ECh. 16.3 - Prob. 3ECh. 16.3 - Prob. 4ECh. 16.3 - Prob. 5ECh. 16.3 - Prob. 6ECh. 16.3 - Prob. 7ECh. 16.3 - Prob. 8ECh. 16.3 - Prob. 9ECh. 16.4 - Prob. 1ECh. 16.4 - Prob. 2ECh. 16.4 - Prob. 3ECh. 16.4 - Prob. 4ECh. 16.4 - Prob. 5ECh. 16.5 - Prob. 1ECh. 16.5 - Prob. 2ECh. 16 - Prob. 1PCh. 16 - Prob. 2PCh. 16 - Prob. 3PCh. 16 - Prob. 4PCh. 16 - Prob. 5P
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