Algorithm Design Questions
The quicksort algorithm is a sorting algorithm that follows the divide-and-conquer approach. It works by selecting a pivot element from the array and partitioning the other elements into two sub-arrays, according to whether they are less than or greater than the pivot. The sub-arrays are then recursively sorted using the same process until the entire array is sorted.
Here is a step-by-step explanation of the quicksort algorithm:
1. Choose a pivot element from the array. This can be any element, but commonly the first or last element is chosen.
2. Partition the array by rearranging its elements such that all elements less than the pivot are placed before it, and all elements greater than the pivot are placed after it. The pivot element is now in its final sorted position.
3. Recursively apply steps 1 and 2 to the sub-arrays formed by the partitioning. This means selecting new pivot elements for each sub-array and partitioning them until the sub-arrays contain only one element or are empty.
4. Once the recursion reaches the base case (sub-arrays with one element or empty), the entire array is sorted.
The quicksort algorithm has an average time complexity of O(n log n), making it one of the most efficient sorting algorithms. However, in the worst-case scenario where the pivot is consistently chosen as the smallest or largest element, the time complexity can degrade to O(n^2). To mitigate this, various optimizations can be implemented, such as choosing a random pivot or using the median-of-three method to select a pivot.