DATABASE SYSTEMS-MINDTAPV2.0
13th Edition
ISBN: 9780357427873
Author: Coronel
Publisher: CENGAGE L
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Chapter 9, Problem 6RQ
What is the minimal data rule in conceptual design? Why is it important?
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You are given a rope of length n meters and scissors that can cut the rope into any two pieces. For
simplification, only consider cutting the rope at an integer position by the meter metric.
Each cut has a cost associated with it, c(m), which is the cost of cutting the rope at position m. (You can call
c(m) at any time to return the cost value.)
The goal is to cut the rope into k smaller pieces, minimizing the total cost of cutting.
B
Provide the pseudo-code of your dynamic programming algorithm f(n,k) that will return the minimum
cost of cutting the rope of length n into k pieces. Briefly explain your algorithm.
What is the benefit of using dynamic programming for this problem?
What are the key principles of dynamic programming used in your algorithm?
Determine whether each of the problems below is NP-Complete or P
A. 3-SAT
B. Traveling Salesman Problem
C. Minimum Spanning Tree
D. Checking if a positive integer is prime or not.
E. Given a set of linear inequalities with integer variables, finding a set of values for the variables that
satisfies all inequalities and maximizes or minimizes a given linear objective function.
1. Based on our lecture on NP-Complete, can an NP-Complete problem not have a polynomial-time
algorithm? Explain your answer.
2. Prove the conjecture that if any problem in NP is not polynomial-time solvable, then no NP-Complete
problem is polynomial-time solvable. (You can't use Theorem 1 and 2 directly)
3. After you complete your proof in b), discuss how this conjecture can be used to solve the problem of
whether P=NP.
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