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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?
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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.
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Which one of the following is the recurrence equation for the worst ca...
Understanding Quicksort Time Complexity
Quicksort is a popular sorting algorithm that employs a divide-and-conquer strategy. To analyze its worst-case time complexity, we must understand how it breaks down the problem.
Recurrence Relation Explanation
In the worst case, Quicksort can degenerate into a situation where it consistently picks the smallest or largest element as the pivot. This results in unbalanced partitions. The recurrence relation that best describes this scenario is:
- T(n) = T(n - 1) + T(0) + cn
Here’s a breakdown of this relation:
- T(n - 1): This part represents the recursive call to sort the remaining elements. In the worst case, one subproblem will have n-1 elements, and the other will have 0.
- T(0): This represents the base case where no elements are left to sort, which contributes a constant time.
- cn: This term accounts for the time taken to partition the array around the pivot, which requires linear time.
Why Other Options Are Incorrect
- Option A (T(n) = 2T(n/2) + cn): This represents a balanced partitioning scenario, typical of the average case, not the worst case.
- Option C (T(n) = 2T(n - 2) + cn): This would imply that two nearly equal partitions are created, which is not the case in the worst scenario.
- Option D (T(n) = T(n/2) + cn): This suggests that only one recursive call happens, which is incorrect for the worst case.
Conclusion
Thus, the correct recurrence relation for the worst-case time complexity of the Quicksort algorithm is indeed T(n) = T(n - 1) + T(0) + cn, making option B the right choice.
Quicksort is a popular sorting algorithm that employs a divide-and-conquer strategy. To analyze its worst-case time complexity, we must understand how it breaks down the problem.
Recurrence Relation Explanation
In the worst case, Quicksort can degenerate into a situation where it consistently picks the smallest or largest element as the pivot. This results in unbalanced partitions. The recurrence relation that best describes this scenario is:
- T(n) = T(n - 1) + T(0) + cn
Here’s a breakdown of this relation:
- T(n - 1): This part represents the recursive call to sort the remaining elements. In the worst case, one subproblem will have n-1 elements, and the other will have 0.
- T(0): This represents the base case where no elements are left to sort, which contributes a constant time.
- cn: This term accounts for the time taken to partition the array around the pivot, which requires linear time.
Why Other Options Are Incorrect
- Option A (T(n) = 2T(n/2) + cn): This represents a balanced partitioning scenario, typical of the average case, not the worst case.
- Option C (T(n) = 2T(n - 2) + cn): This would imply that two nearly equal partitions are created, which is not the case in the worst scenario.
- Option D (T(n) = T(n/2) + cn): This suggests that only one recursive call happens, which is incorrect for the worst case.
Conclusion
Thus, the correct recurrence relation for the worst-case time complexity of the Quicksort algorithm is indeed T(n) = T(n - 1) + T(0) + cn, making option B the right choice.
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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) 2025 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) 2025 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) 2025 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) 2025 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).
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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.
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