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Consider the Quicksort algorithm. Suppose there is a procedure for finding a pivot element which splits the list into two sub-lists each of which contains at least one-fifth of the elements. Let T(n) be the number of comparisons required to sort n elements. Then
- a)T(n) <= 2T(n/5) + n
- b)T(n) <= T(n/5) + T(4n/5) + n
- c)T(n) <= 2T(4n/5) + n
- d)T(n) <= 2T(n/2) + n
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Consider the Quicksort algorithm. Suppose there is a procedure for fin...
For the case where n/5 elements are in one subset, T(n/5) comparisons are needed for the first subset with n/5 elements, T(4n/5) is for the rest 4n/5 elements, and n is for finding the pivot.
If there are more than n/5 elements in one set then other set will have less than 4n/5 elements and time complexity will be less than T(n/5) + T(4n/5) + n because recursion tree will be more balanced.
Most Upvoted Answer
Consider the Quicksort algorithm. Suppose there is a procedure for fin...
Explanation:
The given question is related to the Quicksort algorithm and asks for the relation between the number of comparisons required to sort n elements (T(n)) and the pivot element selection strategy. Let's analyze the options one by one.
Option A: T(n) = 2T(n/5)
This option suggests that the number of comparisons required to sort n elements is twice the number of comparisons required to sort n/5 elements. However, this contradicts the given condition that the pivot element splits the list into two sub-lists, each containing at least one-fifth of the elements. Hence, this option is incorrect.
Option B: T(n) = T(n/5) * T(4n/5)
This option suggests that the number of comparisons required to sort n elements is equal to the number of comparisons required to sort n/5 elements multiplied by the number of comparisons required to sort 4n/5 elements. This option satisfies the given condition that the pivot element splits the list into two sub-lists, each containing at least one-fifth of the elements. Therefore, this option is correct.
Option C: T(n) = 2T(4n/5)
This option suggests that the number of comparisons required to sort n elements is twice the number of comparisons required to sort 4n/5 elements. However, this contradicts the given condition that the pivot element splits the list into two sub-lists, each containing at least one-fifth of the elements. Hence, this option is incorrect.
Option D: T(n) = 2T(n/2) * n
This option suggests that the number of comparisons required to sort n elements is twice the number of comparisons required to sort n/2 elements multiplied by n. This option does not consider the condition of the pivot element splitting the list into two sub-lists, each containing at least one-fifth of the elements. Hence, this option is incorrect.
Therefore, the correct answer is Option B: T(n) = T(n/5) * T(4n/5) as it satisfies the given condition of the pivot element selection strategy.
The given question is related to the Quicksort algorithm and asks for the relation between the number of comparisons required to sort n elements (T(n)) and the pivot element selection strategy. Let's analyze the options one by one.
Option A: T(n) = 2T(n/5)
This option suggests that the number of comparisons required to sort n elements is twice the number of comparisons required to sort n/5 elements. However, this contradicts the given condition that the pivot element splits the list into two sub-lists, each containing at least one-fifth of the elements. Hence, this option is incorrect.
Option B: T(n) = T(n/5) * T(4n/5)
This option suggests that the number of comparisons required to sort n elements is equal to the number of comparisons required to sort n/5 elements multiplied by the number of comparisons required to sort 4n/5 elements. This option satisfies the given condition that the pivot element splits the list into two sub-lists, each containing at least one-fifth of the elements. Therefore, this option is correct.
Option C: T(n) = 2T(4n/5)
This option suggests that the number of comparisons required to sort n elements is twice the number of comparisons required to sort 4n/5 elements. However, this contradicts the given condition that the pivot element splits the list into two sub-lists, each containing at least one-fifth of the elements. Hence, this option is incorrect.
Option D: T(n) = 2T(n/2) * n
This option suggests that the number of comparisons required to sort n elements is twice the number of comparisons required to sort n/2 elements multiplied by n. This option does not consider the condition of the pivot element splitting the list into two sub-lists, each containing at least one-fifth of the elements. Hence, this option is incorrect.
Therefore, the correct answer is Option B: T(n) = T(n/5) * T(4n/5) as it satisfies the given condition of the pivot element selection strategy.
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Consider the Quicksort algorithm. Suppose there is a procedure for finding a pivot element which splits the list into two sub-lists each of which contains at least one-fifth of the elements. Let T(n) be the number of comparisons required to sort n elements. Thena)T(n) <= 2T(n/5) + nb)T(n) <= T(n/5) + T(4n/5) + nc)T(n) <= 2T(4n/5) + nd)T(n) <= 2T(n/2) + nCorrect answer is option 'B'. Can you explain this answer?
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Consider the Quicksort algorithm. Suppose there is a procedure for finding a pivot element which splits the list into two sub-lists each of which contains at least one-fifth of the elements. Let T(n) be the number of comparisons required to sort n elements. Thena)T(n) <= 2T(n/5) + nb)T(n) <= T(n/5) + T(4n/5) + nc)T(n) <= 2T(4n/5) + nd)T(n) <= 2T(n/2) + nCorrect 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 Consider the Quicksort algorithm. Suppose there is a procedure for finding a pivot element which splits the list into two sub-lists each of which contains at least one-fifth of the elements. Let T(n) be the number of comparisons required to sort n elements. Thena)T(n) <= 2T(n/5) + nb)T(n) <= T(n/5) + T(4n/5) + nc)T(n) <= 2T(4n/5) + nd)T(n) <= 2T(n/2) + nCorrect 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 Consider the Quicksort algorithm. Suppose there is a procedure for finding a pivot element which splits the list into two sub-lists each of which contains at least one-fifth of the elements. Let T(n) be the number of comparisons required to sort n elements. Thena)T(n) <= 2T(n/5) + nb)T(n) <= T(n/5) + T(4n/5) + nc)T(n) <= 2T(4n/5) + nd)T(n) <= 2T(n/2) + nCorrect answer is option 'B'. Can you explain this answer?.
Consider the Quicksort algorithm. Suppose there is a procedure for finding a pivot element which splits the list into two sub-lists each of which contains at least one-fifth of the elements. Let T(n) be the number of comparisons required to sort n elements. Thena)T(n) <= 2T(n/5) + nb)T(n) <= T(n/5) + T(4n/5) + nc)T(n) <= 2T(4n/5) + nd)T(n) <= 2T(n/2) + nCorrect 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 Consider the Quicksort algorithm. Suppose there is a procedure for finding a pivot element which splits the list into two sub-lists each of which contains at least one-fifth of the elements. Let T(n) be the number of comparisons required to sort n elements. Thena)T(n) <= 2T(n/5) + nb)T(n) <= T(n/5) + T(4n/5) + nc)T(n) <= 2T(4n/5) + nd)T(n) <= 2T(n/2) + nCorrect 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 Consider the Quicksort algorithm. Suppose there is a procedure for finding a pivot element which splits the list into two sub-lists each of which contains at least one-fifth of the elements. Let T(n) be the number of comparisons required to sort n elements. Thena)T(n) <= 2T(n/5) + nb)T(n) <= T(n/5) + T(4n/5) + nc)T(n) <= 2T(4n/5) + nd)T(n) <= 2T(n/2) + nCorrect answer is option 'B'. Can you explain this answer?.
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