What is the time complexity of the quicksort algorithm in the average case?
Practice Questions
Q1
What is the time complexity of the quicksort algorithm in the average case?
O(n)
O(n log n)
O(n^2)
O(log n)
Questions & Step-by-Step Solutions
What is the time complexity of the quicksort algorithm in the average case?
Step 1: Understand what time complexity means. It measures how the time to complete an algorithm grows as the size of the input (n) increases.
Step 2: Know that quicksort is a sorting algorithm that uses a method called 'divide and conquer'. This means it breaks the problem into smaller parts, solves each part, and then combines the results.
Step 3: In the average case, quicksort splits the list into two roughly equal halves each time it sorts. This is important for its efficiency.
Step 4: Each time quicksort splits the list, it takes O(n) time to rearrange the elements around a pivot (the element used to split the list).
Step 5: Since the list is split in half each time, the number of splits needed is log(n) (because you can keep halving until you reach 1).
Step 6: Combine the time taken for each split (O(n)) with the number of splits (log(n)). This gives you O(n log n) for the average case.
