Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Which one of the following is the recurrence ...
Start Learning for Free
Which one of the following is the recurrence equation for the worst case time complexity of the Quicksort algorithm for sorting n(≥ 2) numbers? In the recurrence equations given in the options below, c is a constant.
- a)T(n) = 2T (n/2) + cn
- b)T(n) = T(n – 1) + T(0) + cn
- c)T(n) = 2T (n – 2) + cn
- d)T(n) = T(n/2) + cn
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Which one of the following is the recurrence equation for the worst ca...
In worst case, the chosen pivot is always placed at a corner position and recursive call is made for following.
a) for subarray on left of pivot which is of size n-1 in worst case.
b) for subarray on right of pivot which is of size 0 in worst case.
a) for subarray on left of pivot which is of size n-1 in worst case.
b) for subarray on right of pivot which is of size 0 in worst case.
Most Upvoted Answer
Which one of the following is the recurrence equation for the worst ca...
Explanation:
Quicksort Algorithm:
Quicksort is a sorting algorithm that follows the divide-and-conquer approach. It works by selecting a pivot element from the array and partitioning the other elements into two sub-arrays, according to whether they are less than or greater than the pivot. The sub-arrays are then recursively sorted.
Recurrence Equation:
A recurrence equation is used to represent the time complexity of an algorithm in terms of its smaller subproblems.
The given recurrence equation options are as follows:
a) T(n) = 2T(n/2) + cn
b) T(n) = T(n-1) + T(0) + cn
c) T(n) = 2T(n-2) + cn
d) T(n) = T(n/2) + cn
Let's analyze each option to determine which one represents the worst-case time complexity of the Quicksort algorithm for sorting n^2 numbers.
Option A:
T(n) = 2T(n/2) + cn
This option represents the time complexity of an algorithm that divides the problem into two equal-sized subproblems and combines their solutions. This equation does not account for the partitioning step in the Quicksort algorithm, where the pivot element is selected and the array is divided into sub-arrays.
Option B:
T(n) = T(n-1) + T(0) + cn
This option represents the time complexity of an algorithm that recursively solves subproblems with decreasing sizes. The term T(n-1) represents the time complexity of sorting the left sub-array, T(0) represents the time complexity of sorting the right sub-array (which is empty), and cn represents the time complexity of the partitioning step. This equation accurately represents the worst-case time complexity of the Quicksort algorithm.
Option C:
T(n) = 2T(n-2) + cn
This option represents the time complexity of an algorithm that divides the problem into two subproblems, each with a size reduced by 2. However, in the Quicksort algorithm, the size of the subproblems is reduced by approximately half, not by 2.
Option D:
T(n) = T(n/2) + cn
This option represents the time complexity of an algorithm that recursively solves subproblems with half the size of the original problem. However, it does not account for the partitioning step in the Quicksort algorithm.
Conclusion:
Among the given options, option B accurately represents the worst-case time complexity of the Quicksort algorithm for sorting n^2 numbers.
Quicksort Algorithm:
Quicksort is a sorting algorithm that follows the divide-and-conquer approach. It works by selecting a pivot element from the array and partitioning the other elements into two sub-arrays, according to whether they are less than or greater than the pivot. The sub-arrays are then recursively sorted.
Recurrence Equation:
A recurrence equation is used to represent the time complexity of an algorithm in terms of its smaller subproblems.
The given recurrence equation options are as follows:
a) T(n) = 2T(n/2) + cn
b) T(n) = T(n-1) + T(0) + cn
c) T(n) = 2T(n-2) + cn
d) T(n) = T(n/2) + cn
Let's analyze each option to determine which one represents the worst-case time complexity of the Quicksort algorithm for sorting n^2 numbers.
Option A:
T(n) = 2T(n/2) + cn
This option represents the time complexity of an algorithm that divides the problem into two equal-sized subproblems and combines their solutions. This equation does not account for the partitioning step in the Quicksort algorithm, where the pivot element is selected and the array is divided into sub-arrays.
Option B:
T(n) = T(n-1) + T(0) + cn
This option represents the time complexity of an algorithm that recursively solves subproblems with decreasing sizes. The term T(n-1) represents the time complexity of sorting the left sub-array, T(0) represents the time complexity of sorting the right sub-array (which is empty), and cn represents the time complexity of the partitioning step. This equation accurately represents the worst-case time complexity of the Quicksort algorithm.
Option C:
T(n) = 2T(n-2) + cn
This option represents the time complexity of an algorithm that divides the problem into two subproblems, each with a size reduced by 2. However, in the Quicksort algorithm, the size of the subproblems is reduced by approximately half, not by 2.
Option D:
T(n) = T(n/2) + cn
This option represents the time complexity of an algorithm that recursively solves subproblems with half the size of the original problem. However, it does not account for the partitioning step in the Quicksort algorithm.
Conclusion:
Among the given options, option B accurately represents the worst-case time complexity of the Quicksort algorithm for sorting n^2 numbers.
Attention Computer Science Engineering (CSE) Students!
To make sure you are not studying endlessly, EduRev has designed Computer Science Engineering (CSE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Computer Science Engineering (CSE).
|
Explore Courses for Computer Science Engineering (CSE) exam
|
|
Similar Computer Science Engineering (CSE) Doubts
Top Courses for Computer Science Engineering (CSE)View all
Which one of the following is the recurrence equation for the worst case time complexity of the Quicksort algorithm for sorting n(≥ 2) numbers? In the recurrence equations given in the options below, c is a constant.a)T(n) = 2T (n/2) + cnb)T(n) = T(n – 1) + T(0) + cnc)T(n) = 2T (n – 2) + cnd)T(n) = T(n/2) + cnCorrect answer is option 'B'. Can you explain this answer?
Question Description
Which one of the following is the recurrence equation for the worst case time complexity of the Quicksort algorithm for sorting n(≥ 2) numbers? In the recurrence equations given in the options below, c is a constant.a)T(n) = 2T (n/2) + cnb)T(n) = T(n – 1) + T(0) + cnc)T(n) = 2T (n – 2) + cnd)T(n) = T(n/2) + cnCorrect answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Which one of the following is the recurrence equation for the worst case time complexity of the Quicksort algorithm for sorting n(≥ 2) numbers? In the recurrence equations given in the options below, c is a constant.a)T(n) = 2T (n/2) + cnb)T(n) = T(n – 1) + T(0) + cnc)T(n) = 2T (n – 2) + cnd)T(n) = T(n/2) + cnCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one of the following is the recurrence equation for the worst case time complexity of the Quicksort algorithm for sorting n(≥ 2) numbers? In the recurrence equations given in the options below, c is a constant.a)T(n) = 2T (n/2) + cnb)T(n) = T(n – 1) + T(0) + cnc)T(n) = 2T (n – 2) + cnd)T(n) = T(n/2) + cnCorrect answer is option 'B'. Can you explain this answer?.
Which one of the following is the recurrence equation for the worst case time complexity of the Quicksort algorithm for sorting n(≥ 2) numbers? In the recurrence equations given in the options below, c is a constant.a)T(n) = 2T (n/2) + cnb)T(n) = T(n – 1) + T(0) + cnc)T(n) = 2T (n – 2) + cnd)T(n) = T(n/2) + cnCorrect answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Which one of the following is the recurrence equation for the worst case time complexity of the Quicksort algorithm for sorting n(≥ 2) numbers? In the recurrence equations given in the options below, c is a constant.a)T(n) = 2T (n/2) + cnb)T(n) = T(n – 1) + T(0) + cnc)T(n) = 2T (n – 2) + cnd)T(n) = T(n/2) + cnCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one of the following is the recurrence equation for the worst case time complexity of the Quicksort algorithm for sorting n(≥ 2) numbers? In the recurrence equations given in the options below, c is a constant.a)T(n) = 2T (n/2) + cnb)T(n) = T(n – 1) + T(0) + cnc)T(n) = 2T (n – 2) + cnd)T(n) = T(n/2) + cnCorrect answer is option 'B'. Can you explain this answer?.
Solutions for Which one of the following is the recurrence equation for the worst case time complexity of the Quicksort algorithm for sorting n(≥ 2) numbers? In the recurrence equations given in the options below, c is a constant.a)T(n) = 2T (n/2) + cnb)T(n) = T(n – 1) + T(0) + cnc)T(n) = 2T (n – 2) + cnd)T(n) = T(n/2) + cnCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
Download more important topics, notes, lectures and mock test series for Computer Science Engineering (CSE) Exam by signing up for free.
Here you can find the meaning of Which one of the following is the recurrence equation for the worst case time complexity of the Quicksort algorithm for sorting n(≥ 2) numbers? In the recurrence equations given in the options below, c is a constant.a)T(n) = 2T (n/2) + cnb)T(n) = T(n – 1) + T(0) + cnc)T(n) = 2T (n – 2) + cnd)T(n) = T(n/2) + cnCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Which one of the following is the recurrence equation for the worst case time complexity of the Quicksort algorithm for sorting n(≥ 2) numbers? In the recurrence equations given in the options below, c is a constant.a)T(n) = 2T (n/2) + cnb)T(n) = T(n – 1) + T(0) + cnc)T(n) = 2T (n – 2) + cnd)T(n) = T(n/2) + cnCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Which one of the following is the recurrence equation for the worst case time complexity of the Quicksort algorithm for sorting n(≥ 2) numbers? In the recurrence equations given in the options below, c is a constant.a)T(n) = 2T (n/2) + cnb)T(n) = T(n – 1) + T(0) + cnc)T(n) = 2T (n – 2) + cnd)T(n) = T(n/2) + cnCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Which one of the following is the recurrence equation for the worst case time complexity of the Quicksort algorithm for sorting n(≥ 2) numbers? In the recurrence equations given in the options below, c is a constant.a)T(n) = 2T (n/2) + cnb)T(n) = T(n – 1) + T(0) + cnc)T(n) = 2T (n – 2) + cnd)T(n) = T(n/2) + cnCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Which one of the following is the recurrence equation for the worst case time complexity of the Quicksort algorithm for sorting n(≥ 2) numbers? In the recurrence equations given in the options below, c is a constant.a)T(n) = 2T (n/2) + cnb)T(n) = T(n – 1) + T(0) + cnc)T(n) = 2T (n – 2) + cnd)T(n) = T(n/2) + cnCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Computer Science Engineering (CSE) tests.
|
|
Explore Courses for Computer Science Engineering (CSE) exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup