quicksort

Quicksort is a sorting algorithm that follows a 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 are the steps involved in the quicksort algorithm:

  1. Select a pivot element from the array. This can be done in various ways, such as choosing the first, last, or middle element, or even selecting a random element.

  2. Partition the array by rearranging its elements around the pivot. This is done by maintaining two pointers, one from the left (low) and the other from the right (high) end of the array. The goal is to move elements smaller than the pivot to the left side and elements greater than the pivot to the right side.

  3. Compare each element from the left pointer with the pivot. If it is smaller, move the left pointer to the right. If it is larger or equal to the pivot, stop.

  4. Compare each element from the right pointer with the pivot. If it is greater, move the right pointer to the left. If it is smaller or equal to the pivot, stop.

  5. If the left pointer is still to the left of the right pointer, swap the elements at the left and right positions.

  6. Repeat steps 3-5 until the left pointer is no longer to the left of the right pointer.

  7. After the partitioning step, the pivot element is in its final sorted position. All elements to the left of the pivot are smaller, and all elements to the right are greater.

  8. Recursively apply the quicksort algorithm to the sub-arrays on either side of the pivot, repeating steps 1-7, until the entire array is sorted.

  9. At the end of the recursion, the array will be sorted in ascending order.

Note: The efficiency of quicksort heavily depends on the choice of pivot. In the worst-case scenario, the pivot is always the smallest or largest element, resulting in a time complexity of O(n^2). However, on average, quicksort has a time complexity of O(n log n), making it one of the fastest sorting algorithms.