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 8, Problem 2P
(a)
Program Plan Intro
To give an
(b)
Program Plan Intro
To give an algorithm of running time of
(c)
Program Plan Intro
To give a stable sorting element that uses constant amount of storage space.
(d)
Program Plan Intro
To give RADIX-SORT algorithm that sorts n -records with b -bits keys in
(e)
Program Plan Intro
To describe the counting sort so that it sorted the records in
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The search algorithm developed will be used for users to search the catalog for all items matching the search keyword(s), and there are a
total of 15000 items in the catalog. During development, three different algorithms were created.
• Algorithm A runs in constant time, with a maximum runtime of 1.10 seconds and returns all matching results.
●
Algorithm B runs in logarithmic time, with a maximum runtime of 0.3 seconds, and returns only the first result.
●
Algorithm C runs in linear time, with a maximum runtime of 1.50 seconds and returns all matching results.
Which algorithm would be the least suitable for the requirements stated? In your answer, justify your choice by explaining why you picked that
algorithm, and why you did not pick the other two algorithms.OND OND OND DAD
Consider an n by n matrix, where each of the n2 entries is a
positive integer.
If the entries in this matrix are unsorted, then determining
whether a target number t appears in the matrix can only be done
by searching through each of the n2 entries. Thus, any search
algorithm has a running time of O(n²).
However, suppose you know that this n by n matrix satisfies the
following properties:
• Integers in each row increase from left to right.
• Integers in each column increase from top to bottom.
An example of such a matrix is presented below, for n=5.
4 7 11 15
2 5 8 12 19
3 6 9 16 22
10 13 14 17 24
1
18 21 23 | 26 | 30
Here is a bold claim: if the n by n matrix satisfies these two
properties, then there exists an O(n) algorithm to determine
whether a target number t appears in this matrix.
Determine whether this statement is TRUE or FALSE. If the
statement is TRUE, describe your algorithm and explain why your
algorithm runs in O(n) time. If the statement is FALSE, clearly
explain why no…
Write a psuedo algorithm that solves the coin-row problem with dynamic programming, as a result, returns the maximum value of money that can be collected from the table under the specified conditions, but did not tell which coins should be taken from the table to reach this value (i.e. which elements of the array that comes as input to the algorithm). . Make the necessary changes in the algorithm that solves the Sequential Money problem with dynamic programming, make the algorithm return the values of the coins included in the maximum solution it finds in a series or a list. What are the time and space complexities of your algorithm, specify them separately.
Chapter 8 Solutions
Introduction to Algorithms
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