Introduction to Algorithms
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 33.2, Problem 7E
Program Plan Intro

To output all k intersections in O((n+k)lgn) time.

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You are standing in front of an infinitely long straight fence; that is, the fence extends infinitely to your left and to your right. The fence has a single gate in it but you do not know where it is. Your goal is to minimize the distance you need to walk in order to find the gate. If n (which is unknown) is the distance to the gate in yards, design and an analyze an efficient algorithm for finding the gate in terms of n.
Which function grows faster f(n) = log 2n or g(n) = n0.3log3n
In Python, generate a random matrix A with 100 entries each of which is an independent numberpseudo-randomly drawn (uniformly) from the interval (0, 1). Let B = A + AT . Use Python to calculatethe diagonal matrix D with the same eigenvalues as B. Then use the QR method to block-diagonalize Bover R. Do at least 100 steps of the QR switching. You should end up with a matrix E which is differentthan D. Answer the question of why.
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