If an array is already sorted, what is the time complexity of Quick Sort?
Practice Questions
Q1
If an array is already sorted, what is the time complexity of Quick Sort?
O(n)
O(n log n)
O(n^2)
O(log n)
Questions & Step-by-Step Solutions
If an array is already sorted, what is the time complexity of Quick Sort?
Step 1: Understand what Quick Sort is. Quick Sort is a sorting algorithm that works by selecting a 'pivot' element and partitioning the array into two parts: elements less than the pivot and elements greater than the pivot.
Step 2: Recognize that Quick Sort's efficiency depends on how well it can partition the array. Ideally, it should split the array into two equal halves.
Step 3: Consider the case when the array is already sorted. In this situation, if we always choose the first or last element as the pivot, the partitioning will not be balanced.
Step 4: When the array is sorted, each partitioning step will only reduce the size of the problem by one element, leading to many recursive calls.
Step 5: Calculate the number of comparisons made. In the worst case, Quick Sort will make n comparisons for the first element, n-1 for the second, and so on, resulting in a total of n + (n-1) + (n-2) + ... + 1 comparisons.
Step 6: The total number of comparisons can be simplified to n(n+1)/2, which is O(n^2).
Step 7: Conclude that when the array is already sorted, Quick Sort has a worst-case time complexity of O(n^2).
Time Complexity of Quick Sort – Understanding how the performance of Quick Sort varies based on the input array's order.
Worst Case Scenario – Recognizing that the worst-case time complexity occurs with specific input conditions, such as a sorted array.
