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 29, Problem 2P
a.
Program Plan Intro
To verify that complementary slackness holds in lines 29.53 and 29.57 of the linear
b.
Program Plan Intro
To prove that complementary slackness holds for any primal linear program and its corresponding dual.
c.
Program Plan Intro
To prove that a feasible solution
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Solve the following exercise using jupyter notebook for Python, to find the objective function, variables, constraint matrix and print the graph with the optimal solution.
A farm specializes in the production of a special cattle feed, which is a mixture of corn and soybeans. The nutritional composition of these ingredients and their costs are as follows:
- Corn contains 0.09 g of protein and 0.02 g of fiber per gram, with a cost of.$0.30 per gram.- Soybeans contain 0.60 g of protein and 0.06 g of fiber per gram, at a cost of $0.90 per gram.0.90 per gram.
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Exercise 4
20= 10+4+6
The rod-cutting problem consists of a rod of n units long that can be cut into integer-length
pieces. The sale price of a piece i units long is Pi for i = 1,...,n. We want to apply dynamic
programming to find the maximum total sale price of the rod. Let F(k) be the maximum price
for a given rod of length k.
1. Give the recurrence on F(k) and its initial condition(s).
2. What are the time and space efficiencies of your algorithm?
Now, consider the following instance of the rod-cutting problem: a rod of length n=5, and the
following sale prices P1=2, P2=3, P3-7, P4=2 and P5=5.
Develop a dynamic programming algorithm for the knapsack problem: given n items of know weights w1, . . . , wn and values v1, . . . ,vn and a knapsack of capacity W, find the most valuable subset of the items that fit into the knapsack. We assume that all the weights and the knapsack’s capacity are positive integers, while the item values are positive real numbers. (This is the 0-1 knapsack problem).
Analyze the structure of an optimal solution.
Give the recursive solution.
Give a solution to this problem by writing pseudo code procedures.
Analyze the running time for your algorithms.
Chapter 29 Solutions
Introduction to Algorithms
Ch. 29.1 - Prob. 1ECh. 29.1 - Prob. 2ECh. 29.1 - Prob. 3ECh. 29.1 - Prob. 4ECh. 29.1 - Prob. 5ECh. 29.1 - Prob. 6ECh. 29.1 - Prob. 7ECh. 29.1 - Prob. 8ECh. 29.1 - Prob. 9ECh. 29.2 - Prob. 1E
Ch. 29.2 - Prob. 2ECh. 29.2 - Prob. 3ECh. 29.2 - Prob. 4ECh. 29.2 - Prob. 5ECh. 29.2 - Prob. 6ECh. 29.2 - Prob. 7ECh. 29.3 - Prob. 1ECh. 29.3 - Prob. 2ECh. 29.3 - Prob. 3ECh. 29.3 - Prob. 4ECh. 29.3 - Prob. 5ECh. 29.3 - Prob. 6ECh. 29.3 - Prob. 7ECh. 29.3 - Prob. 8ECh. 29.4 - Prob. 1ECh. 29.4 - Prob. 2ECh. 29.4 - Prob. 3ECh. 29.4 - Prob. 4ECh. 29.4 - Prob. 5ECh. 29.4 - Prob. 6ECh. 29.5 - Prob. 1ECh. 29.5 - Prob. 2ECh. 29.5 - Prob. 3ECh. 29.5 - Prob. 4ECh. 29.5 - Prob. 5ECh. 29.5 - Prob. 6ECh. 29.5 - Prob. 7ECh. 29.5 - Prob. 8ECh. 29.5 - Prob. 9ECh. 29 - Prob. 1PCh. 29 - Prob. 2PCh. 29 - Prob. 3PCh. 29 - Prob. 4PCh. 29 - Prob. 5P
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