How does the quicksort algorithm work?

How does the quicksort algorithm work?

The quicksort algorithm is a popular 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.

Here is a step-by-step explanation of how the quicksort algorithm works:

1. Choose a pivot element from the array. This can be done in various ways, such as selecting the first, last, or middle element of the array.

2. Partition the array by rearranging its elements such that all elements less than the pivot come before it, and all elements greater than the pivot come after it. This step is commonly known as the partitioning step.

3. Recursively apply steps 1 and 2 to the sub-arrays formed by the partitioning step. 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. Combine the sorted sub-arrays to obtain the final sorted array. This step is usually done implicitly, as the elements are sorted in place during the partitioning step.

The key idea behind quicksort is that it is a divide-and-conquer algorithm, which means it breaks down the sorting problem into smaller sub-problems and solves them independently. By selecting a pivot element and partitioning the array, quicksort efficiently sorts the elements by repeatedly dividing the array into smaller parts and sorting them individually.

The efficiency of quicksort largely depends on the choice of the pivot element. Ideally, the pivot should be chosen in a way that divides the array into two roughly equal-sized sub-arrays. This ensures that the algorithm performs well in most cases. However, in the worst-case scenario where the pivot is always the smallest or largest element, quicksort can have a time complexity of O(n^2). On average, quicksort has a time complexity of O(n log n), making it one of the fastest sorting algorithms in practice.