Here, We will discuss about Quick sort in C, their algorithm, implementation in C, time & space complexity and their applications.

**What is Quick Sort?**

**Quick Sort** is one of the famous *comparison-based sorting algorithms* based on divide and conquers algorithmic technique. It uses recursive calls for sorting the element.

The algorithm starts by picking an item, called **pivot**, and moving all smaller items before it, while all greater elements after it.

Selecting a random pivot in an array result in an improved complexity in most of the cases.

It reduces the space complexity and removes the use of the auxiliary array that is used in merge sort.

**Algorithm**

The recursive algorithm consists of four steps:

- If there are one or no elements in the array to be sorted, return.
- Pick an element in the array as the pivot.
- Split the array into two parts – one with elements larger than the pivot and the other with elements smaller than the pivot.
- Recursively repeat the algorithm for the halves of the original array.

**Implementation in C**

#### Program code in C:

```
#include<stdio.h>
void quicksort(int num[30], int first, int last)
{
int i, j, pivot, temp;
if(first < last)
{
pivot = first;
i = first;
j = last;
while(i < j)
{
while(num[i] <= num[temp] && i<last)
i++;
while(num[j] > num[pivot])
j--;
if(i > j)
{
temp = num[i];
num[i] = num[j];
num[j] = temp;
}
}
temp = num[pivot];
num[pivot] = num[j];
num[j] = temp;
quicksort(num, first, j-1);
quicksort(num, j+1, last);
}
}
int main(){
int i, n, num[30];
printf("how many elements you want? ");
scanf("%d",&n);
printf("Enter %d elements: ",n);
for(i=0; i<n; i++)
scanf("%d",&num[i]);
quicksort(num, 0, n-1);
printf("Order of Sorted elements: ");
for(i=0; i<n; i++)
printf("%d",num[i]);
return 0;
}
```

Code language: C++ (cpp)

#### Output:

`how many elements you want? 5 Enter 5 elements: 4 75 74 2 54 Order of Sorted elements: 2 4 54 74 7`

**Time and Space Complexity**

Time Complexity | |

Worst Case | O(n^{2}) |

Best Case | O(n log n) |

Average Case | O(n log n) |

Space Complexity | |

Worst Case | O(1) |

**Applications**

Quick Sort is implemented when

- the programming language is good for recursion
- time complexity matters
- space complexity matters

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