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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Question
Chapter 31, Problem 3P
a.
Program Plan Intro
To show that the running time of the straightforward recursive method for computing
b.
Program Plan Intro
To show how to compute
c.
Program Plan Intro
To show how to compute
d.
Program Plan Intro
To find the running time of these three methods under the more reasonable cost measure for the elementary arithmetic operations.
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Students have asked these similar questions
Recall that in the deterministic approach for choosing the pivot in the SELECT algorithm, first we split the
elements of the array into groups of size 5. We want to see how the running time of SELECT changes by
varying the size of groups. Consider the following cases:
(a) Split the array into groups of size 3
(b) Split the array into groups of size 7
For each case, write the corresponding recursion for the running time of the SELECT algorithm, draw the
corresponding recursion tree for the worst case, and use it to solve the recursion for the worst case.
For full credit, your answers must use O(.) notation (You do NOT need to use strong induction to prove
your result).
Another recursive algorithm is applied to some data A = (a₁, ..., am) where
m = 2* (i.e. 2, 4, 8,16 ...) where x is an integer ≥ 1. The running time T is
characterised using the following recurrence equations:
T(1) = c when the size of A is 1
T(m) = 2T (2) + c otherwise
Determine the running time complexity of this algorithm.
2. Expand the following recurrence to help you find a closed-form solution, and then use induction to prove
your answer is correct.
T(n) = T(n-1) + 5 for n> 0; T(0) = 8.
3. Give a recursive algorithm for the sequential search and explain its running time.
Chapter 31 Solutions
Introduction to Algorithms
Ch. 31.1 - Prob. 1ECh. 31.1 - Prob. 2ECh. 31.1 - Prob. 3ECh. 31.1 - Prob. 4ECh. 31.1 - Prob. 5ECh. 31.1 - Prob. 6ECh. 31.1 - Prob. 7ECh. 31.1 - Prob. 8ECh. 31.1 - Prob. 9ECh. 31.1 - Prob. 10E
Ch. 31.1 - Prob. 11ECh. 31.1 - Prob. 12ECh. 31.1 - Prob. 13ECh. 31.2 - Prob. 1ECh. 31.2 - Prob. 2ECh. 31.2 - Prob. 3ECh. 31.2 - Prob. 4ECh. 31.2 - Prob. 5ECh. 31.2 - Prob. 6ECh. 31.2 - Prob. 7ECh. 31.2 - Prob. 8ECh. 31.2 - Prob. 9ECh. 31.3 - Prob. 1ECh. 31.3 - Prob. 2ECh. 31.3 - Prob. 3ECh. 31.3 - Prob. 4ECh. 31.3 - Prob. 5ECh. 31.4 - Prob. 1ECh. 31.4 - Prob. 2ECh. 31.4 - Prob. 3ECh. 31.4 - Prob. 4ECh. 31.5 - Prob. 1ECh. 31.5 - Prob. 2ECh. 31.5 - Prob. 3ECh. 31.5 - Prob. 4ECh. 31.6 - Prob. 1ECh. 31.6 - Prob. 2ECh. 31.6 - Prob. 3ECh. 31.7 - Prob. 1ECh. 31.7 - Prob. 2ECh. 31.7 - Prob. 3ECh. 31.8 - Prob. 1ECh. 31.8 - Prob. 2ECh. 31.8 - Prob. 3ECh. 31.9 - Prob. 1ECh. 31.9 - Prob. 2ECh. 31.9 - Prob. 3ECh. 31.9 - Prob. 4ECh. 31 - Prob. 1PCh. 31 - Prob. 2PCh. 31 - Prob. 3PCh. 31 - Prob. 4P
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