The O(n log n) average-case running time analysis of quicksort relies on several assumptions. Which of the following does not need to be assumed:Group of answer choicesThat the result of each partitioning step is an arrangement in which the pivot value ends up close to the middle of the partitioned arrayThat the result of each partitioning step is an arrangement in which the pivot value is equally likely to end up in each position of the partitioned arrayThat each comparison of two elements can be carried out in O(1) timeThat each function call can be carried out in O(1) timeThat each swap of two elements can be carried out in O(1) time
Question
The O(n log n) average-case running time analysis of quicksort relies on several assumptions. Which of the following does not need to be assumed:Group of answer choicesThat the result of each partitioning step is an arrangement in which the pivot value ends up close to the middle of the partitioned arrayThat the result of each partitioning step is an arrangement in which the pivot value is equally likely to end up in each position of the partitioned arrayThat each comparison of two elements can be carried out in O(1) timeThat each function call can be carried out in O(1) timeThat each swap of two elements can be carried out in O(1) time
Solution 1
The assumption that does not need to be made for the O(n log n) average-case running time analysis of quicksort is: That each function call can be carried out in O(1) time.
This is because the time complexity of a function call in quicksort is not constant. The time it takes to execute a function call depends on the size of the subarray being sorted, which can vary. Therefore, it is not accurate to assume that each function call can be carried out in O(1) time.
Solution 2
The assumption that does not need to be made for the O(n log n) average-case running time analysis of quicksort is: That each function call can be carried out in O(1) time.
This is because the time complexity of a function call in quicksort is not constant. The time it takes to execute a function call depends on the size of the subarray being sorted, which can vary. Therefore, it is not accurate to assume that each function call can be carried out in O(1) time.
Similar Questions
Consider a modification to QuickSort where each time the partition function is called, the median of the partition array is always found (in constant time) and used as the pivot. The worst-case running time for the algorithm is: Group of answer choices Θ(nlogn) Θ(n^2) Θ(n) Θ(logn)
The time complexity of quicksort is ……..a.O(n)b.O(logn)c.O(n2)d.O(n logn)
What is the time complexity of the quicksort algorithm in the worst case?
The running time of quick sort depends heavily on the selection of Select one:Pivot elementNo of inputs Arrangement of elements in array Size of elements
Quicksort uses Hoare partitioning. Assume an array contains ten keys: 6 3 1 7 9 5 8 2 4 0. After a first round of simple Hoare partitioning (not median-of-three), the array looks like so: Group of answer choices 5 3 1 0 4 2 6 8 9 7 2 3 1 0 4 5 6 8 9 7 3 1 5 2 4 0 6 7 9 8 2 3 0 1 5 4 6 7 8 9 5 3 1 4 0 2 6 7 9 8
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