What is the time complexity of the worst-case scenario for Quick Sort when the p
Practice Questions
Q1
What is the time complexity of the worst-case scenario for Quick Sort when the pivot is the smallest or largest element?
O(n)
O(n log n)
O(n^2)
O(log n)
Questions & Step-by-Step Solutions
What is the time complexity of the worst-case scenario for Quick Sort when the pivot is the smallest or largest element?
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: Identify the worst-case scenario. The worst-case scenario for Quick Sort happens when the pivot chosen is either the smallest or the largest element in the array.
Step 3: Explain what happens in this scenario. If the pivot is the smallest or largest element, one of the partitions will have zero elements, and the other will have all the remaining elements. This means that the algorithm will not effectively reduce the problem size.
Step 4: Calculate the number of comparisons. In the worst case, Quick Sort will make comparisons for every element in the array for each recursive call, leading to a total of n + (n-1) + (n-2) + ... + 1 comparisons.
Step 5: Sum the comparisons. The total number of comparisons can be expressed as n(n-1)/2, which simplifies to O(n^2).
Step 6: Conclude the time complexity. Therefore, the worst-case time complexity of Quick Sort when the pivot is the smallest or largest element is O(n^2).
