What is the time complexity of quicksort in the best case?
Practice Questions
Q1
What is the time complexity of quicksort in the best case?
O(n)
O(n log n)
O(n^2)
O(log n)
Questions & Step-by-Step Solutions
What is the time complexity of quicksort in the best case?
Step 1: Understand what quicksort does. Quicksort is a sorting algorithm that works by selecting a 'pivot' element from the array and partitioning the other elements into two groups: those less than the pivot and those greater than the pivot.
Step 2: In the best case scenario, the pivot divides the array into two equal halves. This means that each time we pick a pivot, we split the array into two parts of equal size.
Step 3: When the array is divided into two equal halves, we can represent the number of comparisons needed to sort the array as a tree structure. Each level of the tree represents a division of the array.
Step 4: The height of this tree is log(n) because we keep dividing the array in half until we reach single elements.
Step 5: At each level of the tree, we need to look at all n elements to partition them around the pivot. Therefore, the work done at each level is O(n).
Step 6: Since there are log(n) levels and each level takes O(n) time, we multiply these together: O(n) * O(log n) = O(n log n).
Step 7: Therefore, the time complexity of quicksort in the best case is O(n log n).
