# Quick Sort

Quick Sort is a popular sorting algorithm that is based on the divide-and-conquer paradigm, where a large problem is broken down into smaller sub-problems, and the solutions to these sub-problems are combined to form a complete solution to the original problem. The quick sort algorithm operates by choosing a pivot element from an unsorted list and partitioning the list around this pivot, such that all elements smaller than the pivot are placed to the left of the pivot and all elements larger than the pivot are placed to the right of the pivot. The pivot is then placed in its final position in the sorted list. The quick sort algorithm is then recursively applied to the sub-lists to the left and right of the pivot until the entire list is sorted.

The quick sort algorithm has an average time complexity of O(n log n), which is considered optimal for sorting algorithms. This means that, for large datasets, the time required to sort the data will increase linearly with the size of the dataset, but at a slower rate than the size of the dataset. Additionally, quick sort is an in-place sorting algorithm, which means that it operates on the original list and does not require additional memory to sort the data.

Quick sort can be implemented in several programming languages, including Python, C++, Java and many others. Here is a code example of the quick sort algorithm in Python:

```
def quick_sort(arr, low, high):
if low < high:
pivot_index = partition(arr, low, high)
quick_sort(arr, low, pivot_index-1)
quick_sort(arr, pivot_index+1, high)
def partition(arr, low, high):
pivot = arr[high]
i = low - 1
for j in range(low, high):
if arr[j] <= pivot:
i = i + 1
arr[i], arr[j] = arr[j], arr[i]
arr[i + 1], arr[high] = arr[high], arr[i + 1]
return i + 1
```

The quick sort algorithm starts by calling the quick_sort function, which takes an array arr, a low index low and a high index high as arguments. If the low index is less than the high index, the algorithm selects the pivot and partitions the list around the pivot. The pivot is selected using the partition function, which takes the array arr, the low index low and the high index high as arguments.

In the partition function, the pivot is selected as the last element in the list, and an index i is initialized to the low index minus one. The function then iterates through the list, starting from the low index and ending at the high index, using the variable j. If the current element at index j is less than or equal to the pivot, the index i is incremented and the elements at indices i and j are swapped.

Once the partition function has completed, the pivot is placed in its final position in the sorted list by swapping the element at index i + 1 with the pivot. The partition function then returns the index of the pivot, which is stored in the variable pivot_index.

Finally, the quick_sort function is recursively called on the sub-lists to the left and right of the pivot, using the quick_sort