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Which of the following cases is definite to give O(nlogn) time complexity always for quick sort to sort the array
A[0…n], for any set of values of array A Case 1: Choosing middle element as pivot. Case 2: Choosing pivot element as (2∘)th element initially followed by (21)th element, followed by (22)th element of array A and so on. Case 3: Choosing median element as pivot. Case 4: Choosing the pivot element randomly from the array A. Case 5: Choosing pivot such that the array is partitioned into almost two equal subarrays.
- a)Only 1 and 4
- b)Only 1, 2 and 3
- c)Only 3 and 5
- d)Only 1, 3 and 4
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Which of the following cases is definite to give O(nlogn) time complex...
Only case 3 and 5 ensures O(nlogn) time complexity always.
Case 1: Choosing middle element doesn't mean that pivots location is in middle, after the
partition algorithm. In the worst case pivot may go either first or last location (O(n2)).
Similarly Case 2, Case 4 does not guarantee O(nlogn). But cases 3 and 5 are similar and make sure that pivot always goes to the middle location, after the partition algorithm.
Most Upvoted Answer
Which of the following cases is definite to give O(nlogn) time complex...
Understanding Time Complexity in Quick Sort
To determine which cases guarantee an O(n log n) time complexity for Quick Sort, we must analyze how different pivot selection strategies affect the performance.
Case 1: Choosing the Middle Element as Pivot
- This strategy can lead to poor performance in sorted or nearly sorted arrays.
- It does not always guarantee balanced partitions, which can degrade performance to O(n^2) in the worst case.
Case 2: Sequential Pivot Selection
- Choosing the pivot element in a fixed sequential manner (2nd, 21st, 22nd, etc.) does not ensure balanced partitions.
- This approach can lead to unbalanced partitions, resulting in an O(n^2) complexity.
Case 3: Choosing the Median Element as Pivot
- The median guarantees that the partitions are as balanced as possible, leading to O(n log n) time complexity consistently.
- This method optimally divides the array into two roughly equal halves.
Case 4: Random Pivot Selection
- Randomly choosing a pivot can average out to O(n log n) for large datasets.
- While it can still reach O(n^2) in rare scenarios, the average-case performance is O(n log n).
Case 5: Balanced Partitioning
- This method ensures that the array is divided into two equal or nearly equal parts.
- Like the median selection, it consistently maintains O(n log n) time complexity.
Conclusion
Thus, the correct answer is option 'C' - only Cases 3 and 5 guarantee O(n log n) time complexity consistently for any input. Cases 1, 2, and 4 do not provide such a guarantee under all circumstances.
To determine which cases guarantee an O(n log n) time complexity for Quick Sort, we must analyze how different pivot selection strategies affect the performance.
Case 1: Choosing the Middle Element as Pivot
- This strategy can lead to poor performance in sorted or nearly sorted arrays.
- It does not always guarantee balanced partitions, which can degrade performance to O(n^2) in the worst case.
Case 2: Sequential Pivot Selection
- Choosing the pivot element in a fixed sequential manner (2nd, 21st, 22nd, etc.) does not ensure balanced partitions.
- This approach can lead to unbalanced partitions, resulting in an O(n^2) complexity.
Case 3: Choosing the Median Element as Pivot
- The median guarantees that the partitions are as balanced as possible, leading to O(n log n) time complexity consistently.
- This method optimally divides the array into two roughly equal halves.
Case 4: Random Pivot Selection
- Randomly choosing a pivot can average out to O(n log n) for large datasets.
- While it can still reach O(n^2) in rare scenarios, the average-case performance is O(n log n).
Case 5: Balanced Partitioning
- This method ensures that the array is divided into two equal or nearly equal parts.
- Like the median selection, it consistently maintains O(n log n) time complexity.
Conclusion
Thus, the correct answer is option 'C' - only Cases 3 and 5 guarantee O(n log n) time complexity consistently for any input. Cases 1, 2, and 4 do not provide such a guarantee under all circumstances.
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Which of the following cases is definite to give O(nlogn) time complexity always for quick sort to sort the arrayA[0…n], for any set of values of array A Case 1: Choosing middle element as pivot. Case 2: Choosing pivot element as (2)th element initially followed by (21)th element, followed by (22)th element of array A and so on. Case 3: Choosing median element as pivot. Case 4: Choosing the pivot element randomly from the array A. Case 5: Choosing pivot such that the array is partitioned into almost two equal subarrays.a)Only 1 and 4b)Only 1, 2 and 3c)Only 3 and 5d)Only 1, 3 and 4Correct answer is option 'C'. Can you explain this answer?
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Which of the following cases is definite to give O(nlogn) time complexity always for quick sort to sort the arrayA[0…n], for any set of values of array A Case 1: Choosing middle element as pivot. Case 2: Choosing pivot element as (2)th element initially followed by (21)th element, followed by (22)th element of array A and so on. Case 3: Choosing median element as pivot. Case 4: Choosing the pivot element randomly from the array A. Case 5: Choosing pivot such that the array is partitioned into almost two equal subarrays.a)Only 1 and 4b)Only 1, 2 and 3c)Only 3 and 5d)Only 1, 3 and 4Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Which of the following cases is definite to give O(nlogn) time complexity always for quick sort to sort the arrayA[0…n], for any set of values of array A Case 1: Choosing middle element as pivot. Case 2: Choosing pivot element as (2)th element initially followed by (21)th element, followed by (22)th element of array A and so on. Case 3: Choosing median element as pivot. Case 4: Choosing the pivot element randomly from the array A. Case 5: Choosing pivot such that the array is partitioned into almost two equal subarrays.a)Only 1 and 4b)Only 1, 2 and 3c)Only 3 and 5d)Only 1, 3 and 4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following cases is definite to give O(nlogn) time complexity always for quick sort to sort the arrayA[0…n], for any set of values of array A Case 1: Choosing middle element as pivot. Case 2: Choosing pivot element as (2)th element initially followed by (21)th element, followed by (22)th element of array A and so on. Case 3: Choosing median element as pivot. Case 4: Choosing the pivot element randomly from the array A. Case 5: Choosing pivot such that the array is partitioned into almost two equal subarrays.a)Only 1 and 4b)Only 1, 2 and 3c)Only 3 and 5d)Only 1, 3 and 4Correct answer is option 'C'. Can you explain this answer?.
Which of the following cases is definite to give O(nlogn) time complexity always for quick sort to sort the arrayA[0…n], for any set of values of array A Case 1: Choosing middle element as pivot. Case 2: Choosing pivot element as (2)th element initially followed by (21)th element, followed by (22)th element of array A and so on. Case 3: Choosing median element as pivot. Case 4: Choosing the pivot element randomly from the array A. Case 5: Choosing pivot such that the array is partitioned into almost two equal subarrays.a)Only 1 and 4b)Only 1, 2 and 3c)Only 3 and 5d)Only 1, 3 and 4Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Which of the following cases is definite to give O(nlogn) time complexity always for quick sort to sort the arrayA[0…n], for any set of values of array A Case 1: Choosing middle element as pivot. Case 2: Choosing pivot element as (2)th element initially followed by (21)th element, followed by (22)th element of array A and so on. Case 3: Choosing median element as pivot. Case 4: Choosing the pivot element randomly from the array A. Case 5: Choosing pivot such that the array is partitioned into almost two equal subarrays.a)Only 1 and 4b)Only 1, 2 and 3c)Only 3 and 5d)Only 1, 3 and 4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following cases is definite to give O(nlogn) time complexity always for quick sort to sort the arrayA[0…n], for any set of values of array A Case 1: Choosing middle element as pivot. Case 2: Choosing pivot element as (2)th element initially followed by (21)th element, followed by (22)th element of array A and so on. Case 3: Choosing median element as pivot. Case 4: Choosing the pivot element randomly from the array A. Case 5: Choosing pivot such that the array is partitioned into almost two equal subarrays.a)Only 1 and 4b)Only 1, 2 and 3c)Only 3 and 5d)Only 1, 3 and 4Correct answer is option 'C'. Can you explain this answer?.
Solutions for Which of the following cases is definite to give O(nlogn) time complexity always for quick sort to sort the arrayA[0…n], for any set of values of array A Case 1: Choosing middle element as pivot. Case 2: Choosing pivot element as (2)th element initially followed by (21)th element, followed by (22)th element of array A and so on. Case 3: Choosing median element as pivot. Case 4: Choosing the pivot element randomly from the array A. Case 5: Choosing pivot such that the array is partitioned into almost two equal subarrays.a)Only 1 and 4b)Only 1, 2 and 3c)Only 3 and 5d)Only 1, 3 and 4Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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Which of the following cases is definite to give O(nlogn) time complexity always for quick sort to sort the arrayA[0…n], for any set of values of array A Case 1: Choosing middle element as pivot. Case 2: Choosing pivot element as (2)th element initially followed by (21)th element, followed by (22)th element of array A and so on. Case 3: Choosing median element as pivot. Case 4: Choosing the pivot element randomly from the array A. Case 5: Choosing pivot such that the array is partitioned into almost two equal subarrays.a)Only 1 and 4b)Only 1, 2 and 3c)Only 3 and 5d)Only 1, 3 and 4Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Which of the following cases is definite to give O(nlogn) time complexity always for quick sort to sort the arrayA[0…n], for any set of values of array A Case 1: Choosing middle element as pivot. Case 2: Choosing pivot element as (2)th element initially followed by (21)th element, followed by (22)th element of array A and so on. Case 3: Choosing median element as pivot. Case 4: Choosing the pivot element randomly from the array A. Case 5: Choosing pivot such that the array is partitioned into almost two equal subarrays.a)Only 1 and 4b)Only 1, 2 and 3c)Only 3 and 5d)Only 1, 3 and 4Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Which of the following cases is definite to give O(nlogn) time complexity always for quick sort to sort the arrayA[0…n], for any set of values of array A Case 1: Choosing middle element as pivot. Case 2: Choosing pivot element as (2)th element initially followed by (21)th element, followed by (22)th element of array A and so on. Case 3: Choosing median element as pivot. Case 4: Choosing the pivot element randomly from the array A. Case 5: Choosing pivot such that the array is partitioned into almost two equal subarrays.a)Only 1 and 4b)Only 1, 2 and 3c)Only 3 and 5d)Only 1, 3 and 4Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Which of the following cases is definite to give O(nlogn) time complexity always for quick sort to sort the arrayA[0…n], for any set of values of array A Case 1: Choosing middle element as pivot. Case 2: Choosing pivot element as (2)th element initially followed by (21)th element, followed by (22)th element of array A and so on. Case 3: Choosing median element as pivot. Case 4: Choosing the pivot element randomly from the array A. Case 5: Choosing pivot such that the array is partitioned into almost two equal subarrays.a)Only 1 and 4b)Only 1, 2 and 3c)Only 3 and 5d)Only 1, 3 and 4Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice GATE tests.
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