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 34.2, Problem 5E
Program Plan Intro
To show that any language in NP can be determined by an
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If we want to prove P = NP, we only need to pick up any one NPC problem and design a polynomial-time algorithm for the problem. If you want to prove P = NP, select one NPC problem based on your preference and describe your idea of a polynomial-time algorithm that solves the problem. It does not have to be a formal algorithm or pseudo-code, a description of your idea of designing such an algorithm would be fine.
Describe some algorithm A where A € NP and
A does not € P.
Let P2(x) be the least squares interpolating polynomial for f(x) := sin(πx) on the interval [0,1] (with weight function w(x) = 1). Determine nodes (x0,x1,x2) for the second-order Lagrange interpolating polynomial Pˆ2(x) so that P2 = Pˆ2. You are welcome to proceed theoretically or numerically using Python.
Chapter 34 Solutions
Introduction to Algorithms
Ch. 34.1 - Prob. 1ECh. 34.1 - Prob. 2ECh. 34.1 - Prob. 3ECh. 34.1 - Prob. 4ECh. 34.1 - Prob. 5ECh. 34.1 - Prob. 6ECh. 34.2 - Prob. 1ECh. 34.2 - Prob. 2ECh. 34.2 - Prob. 3ECh. 34.2 - Prob. 4E
Ch. 34.2 - Prob. 5ECh. 34.2 - Prob. 6ECh. 34.2 - Prob. 7ECh. 34.2 - Prob. 8ECh. 34.2 - Prob. 9ECh. 34.2 - Prob. 10ECh. 34.2 - Prob. 11ECh. 34.3 - Prob. 1ECh. 34.3 - Prob. 2ECh. 34.3 - Prob. 3ECh. 34.3 - Prob. 4ECh. 34.3 - Prob. 5ECh. 34.3 - Prob. 6ECh. 34.3 - Prob. 7ECh. 34.3 - Prob. 8ECh. 34.4 - Prob. 1ECh. 34.4 - Prob. 2ECh. 34.4 - Prob. 3ECh. 34.4 - Prob. 4ECh. 34.4 - Prob. 5ECh. 34.4 - Prob. 6ECh. 34.4 - Prob. 7ECh. 34.5 - Prob. 1ECh. 34.5 - Prob. 2ECh. 34.5 - Prob. 3ECh. 34.5 - Prob. 4ECh. 34.5 - Prob. 5ECh. 34.5 - Prob. 6ECh. 34.5 - Prob. 7ECh. 34.5 - Prob. 8ECh. 34 - Prob. 1PCh. 34 - Prob. 2PCh. 34 - Prob. 3PCh. 34 - Prob. 4P
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- (a) Writeup Prove Theorem 1 Using Theorem 1, describe an algorithm in words to check bipartiteness and analyze its run time.arrow_forwardIf a non-deterministic algorithms is required to solve a problem in polynomial time, the problem is probably in _________ class. (P, NP)arrow_forwardGiven a problem X and Y, if X reduces to Y in polynomial time, and Y is known to be NP-Complete, what can be said about X?arrow_forward
- We mentioned that if we want to prove P = NP, we only need to pick up any one NPC problem and design a polynomial-time algorithm for the problem. If you want to prove P = NP, select one NPC problem based on your preference and describe your idea of a polynomial-time algorithm that solves the problem. It does not have to be a formal algorithm or pseudo-code, a description of your idea of designing such an algorithm would be fine.arrow_forwardIf you are given a set S of integers and a number t, prove that this issue falls into the NP class. Is there a subset of S where the total number of items is t? Note: Complexity in Data Structures and Algorithmsarrow_forwardGive a decision procedure (algorithm) to answer the question: Given a finite automaton M, is L(M) infinite? Please explain step by step.arrow_forward
- Algorithm DEGENERATIONSGiven a rational proper parametrization P(t) = χ1 1(t) χ1 2(t) , χ2 1(t) χ2 2(t)∈ L(t)2,where L is a computable subfield of R, of an affine rational curve C, the algorithm computes DParrow_forwardAnswer True or False whether a function with growth rate is a member of the set of algorithms that grow with a certain complexity. Draw also the graph.arrow_forwardThe code shows an implementation of the Rabin-Karp algorithm in Python. What is the best and worst case of this algorithm? Explain with an example for each case, without going into mathematical detailsarrow_forward
- Let the sequence (n) be recursively defined by x1 = √2 and Xn+1 = √√2+xn, n≥ 1. Show that (n) converges and evaluate its limit.arrow_forwardFind the Worst case time Complexity of the following recursive functions T(n) = T(n-1)+n -1, T(1) = 0arrow_forwardProve Proposition U. Given a set of r symbols and frequencies, the Huffman algorithmbuilds an optimal prefix-free code.arrow_forward
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