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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?
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.
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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?.
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