Starting Out with C++: Early Objects
8th Edition
ISBN: 9780133360929
Author: Tony Gaddis, Judy Walters, Godfrey Muganda
Publisher: Addison-Wesley
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Chapter 9.6, Problem 9.12CP
Explanation of Solution
Basic operations:
The basic operation is the initial step in the
- Normally, the algorithm executes the basic step in constant time rather than considering about the size of the input.
- So, it means that size of the bound does not affect the efficiency of the operations.
- The complexity of an algorithm can be found out by finding the number of basic steps required for an input.
Comparing the efficiency of an algorithm:
In the given question, one algorithm requires “
Expert Solution & Answer
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Students have asked these similar questions
One algorithm needs 10n basic operations to process an input of size n, and another algorithm needs 25n basic operations to process the same input. Which of the two algorithms is more efficient? Or are they equally efficient?
A certain computer algorithm executes twice as many operations when it is run with an input of size k as when it is run with an input of
size k - 1 (where k is an integer that is greater than 1). When the algorithm is run with an input of size 1, it executes seven operations. How
many operations does it execute when it is run with an input of size 24?
For each integernz 1, let s,-1 be the number of operations the algorithm executes when it is run with an input of size n. Then
for each integer 2 1. Therefore, So, S3. Sz.
is -Select-
and s,=
with constant
Select-
,which is
. So, for every integer n 2 0, s, =
It follows that for an input of size 24, the number
of operations executed by the algorithm is s
-Select-v
which equals
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Desd
A computer science student designed two candidate algorithms for a problem while working
on his part-time job The time complexity of these two algorithms are
T,(n) = 3 n logn and T2(n) = n6/5
a) Which algorithm is better? Why?
b) If we run both algorithms at the same time with an input size of 105, which algorithm
produces results faster than the other one? Why?
Chapter 9 Solutions
Starting Out with C++: Early Objects
Ch. 9.2 - Prob. 9.1CPCh. 9.2 - Prob. 9.2CPCh. 9.2 - Prob. 9.3CPCh. 9.2 - Prob. 9.4CPCh. 9.3 - True or false: Any sort can be modified to sort in...Ch. 9.3 - Prob. 9.6CPCh. 9.3 - Prob. 9.7CPCh. 9.3 - Prob. 9.8CPCh. 9.3 - Prob. 9.9CPCh. 9.6 - Prob. 9.10CP
Ch. 9.6 - Prob. 9.11CPCh. 9.6 - Prob. 9.12CPCh. 9.6 - Prob. 9.13CPCh. 9.6 - Prob. 9.14CPCh. 9.6 - Prob. 9.15CPCh. 9 - Prob. 1RQECh. 9 - Prob. 2RQECh. 9 - Prob. 3RQECh. 9 - Prob. 4RQECh. 9 - Prob. 5RQECh. 9 - Prob. 6RQECh. 9 - Prob. 7RQECh. 9 - A binary search will find the value it is looking...Ch. 9 - The maximum number of comparisons that a binary...Ch. 9 - Prob. 11RQECh. 9 - Prob. 12RQECh. 9 - Bubble sort places ______ number(s) in place on...Ch. 9 - Selection sort places ______ number(s) in place on...Ch. 9 - Prob. 15RQECh. 9 - Prob. 16RQECh. 9 - Why is selection sort more efficient than bubble...Ch. 9 - Prob. 18RQECh. 9 - Prob. 19RQECh. 9 - Prob. 20RQECh. 9 - Prob. 21RQECh. 9 - Charge Account Validation Write a program that...Ch. 9 - Lottery Winners A lottery ticket buyer purchases...Ch. 9 - Lottery Winners Modification Modify the program...Ch. 9 - Hit the Slopes Write a program that can be used by...Ch. 9 - String Selection Sort Modify the selectionSort...Ch. 9 - Binary String Search Modify the binarySearch...Ch. 9 - Search Benchmarks Write a program that has at...Ch. 9 - Sorting Benchmarks Write a program that uses two...Ch. 9 - Sorting Orders Write a program that uses two...Ch. 9 - Ascending Circles Program 8-31 from Chapter 8...Ch. 9 - Modified Bin Manager Class Modify the BinManager...Ch. 9 - Using Files-String Selection Sort Modification...Ch. 9 - Using Vectors String Selection Sort Modification...
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- Two algorithms A, B sort the same problem. When you go through each algorithm and break them down into their primitive operations, each can be represented as below A = n4 + 100n2 + 10n + 50 B = 10n3 + 2n2 + nlogn + 200 For very large values of n which of these algorithms explain why B will run in the shortest time to solve the problemarrow_forwardConsider the following algorithm segment. Assume that n is a positive integer. for i: = 1 to 3n S:= 0 for j:= 1 to i - 1 s:= s+j• (i - j+ 1) next j r:= s2 next i (a) What is the actual number of elementary operations (additions, subtractions, multiplications, divisions, and comparisons) that are performed when the algorithm segment is executed? For simplicity, count only comparisons that occur within if-then statements, and ignore those implied by for-next loops. Express your answer in terms of n. (Hint: See Example 11.3.3 and exercises 11.3.11a and 11.3.14a in the "Read It" link.) The number of operations isarrow_forwardThe two different algorithms that perform the same complexity process are called B and C. The total number of operations (operations) performed with algorithm B is 64n. The total number of operations performed with the C algorithm is 16 n ^ 2. Here is my question: Determine the problem size n0 where B is better than C for n> n0 please.arrow_forward
- Suppose that the running time of an algorithm A is T(n) = n2. If the time it takes for algorithm A to finish on an input of size n 10 is 100ms, what will be the time that it will take for A to finish on an input of size 20? Assume that the algorithm runs on the same machine.arrow_forward2) A computer science student designed two candidate algorithms for a problem while working on his part-time job The time complexity of these two algorithms are T1(n) = 3 n log n and T2(n) = nº/5 . a) Which algorithm is better? Why? b) If we run both algorithms at the same time with an input size of 105, which algorithm produces results faster than the other one? Why?arrow_forwardSuppose you have algorithms with five running times. Assume these are the exact running times. How much slower do each of these algorithms get when you (a) double the input or (b) increase the input size by one? Do both. This problem requires discrete math. I solved all of these but I had a quick question. My teacher wanted us to use the big 0 notation for these running times, but the problem is that I'm not sure if that's necessary for these problems for the question it's asking. I tried to the big 0 notations for the first three. For (a) I got 8n3. Which I'm not sure is right. For example, for 1b I got 3n2 + 3n + 1 for how much slower these get from the original. Is that correct? Was I supposed to do something more for the big 0 notation. You can check to see if these answers are correct. The big O notation formula is f(n) = 0(g(n)). (a) n2 For double size I got 4n2. I got 2n + 1 from the input the size by one. I think that's all I need to do. I got similar answers for theother…arrow_forward
- 2) A computer science student designed two candidate algorithms for a problem while working on his part-time job The time complexity of these two algorithms are T1(n) = 3 n logn and T2(n) = nº/5 . a) Which algorithm is better? Why? b) If we run both algorithms at the same time with an input size of 10°, which algorithm produces results faster than the other one? Why?arrow_forwardConsider the following algorithm segment. Assume that n is a positive integer. for i:=1 to 4n S := 0 for i:=1 to i - 1 s := s + j(i- j + 1) next j r:= s² next i (a) What is the actual number of elementary operations (additions, subtractions, multiplications, divisions, and comparisons) that are performed when the algorithm segment is executed? For simplicity, count only comparisons that occur within if-then statements, and ignore those implied by for-next loops. Express your answer in terms of n. (Hint: See Example 11.3.3 and exercises 11.3.11a and 11.3.14a in the "Read It" link.) The number of operations is (b) Apply the theorem on polynomial orders to the expression in part (a) to find that an order for the algorithm segment is narrow_forwardMethod A performs 10 n2 basic operations, while algorithm B does 300ln(n) basic operations, resulting in a difference of 10 n2. At what point does algorithm B begin to outperform algorithm A in terms of performance?arrow_forward
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