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In this article we will discuss how to implement QuickSort using random pivoting. In QuickSort we first partition the array in place such that all elements to the left of the pivot element are smaller, while all elements to the right of the pivot are greater that the pivot. Then we recursively call the same procedure for left and right subarrays.

Unlike merge sort we don’t need to merge the two sorted arrays. Thus Quicksort requires lesser auxillary space than Merge Sort, which is why it is often preferred to Merge Sort.Using a randomly generated pivot we can further improve the time complexity of QuickSort.

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We have discussed at two popular methods for partioning the arrays-Hoare’s vs Lomuto partition scheme

It is advised that the reader has read that article or knows how to implement the QuickSort using either of the two partition schemes.

Algorithm for random pivoting using Lomuto Partitioning

Algorithm for random pivoting using Hoare Partitioning

Below is the CPP implementation of the Algorithms

`/* C++ implementation QuickSort using Lomuto's partition ` `#include <cstdlib> ` `using` `namespace` `std; ` `/* This function takes last element as pivot, places ` `the pivot element at its correct position in sorted ` `array, and places all smaller (smaller than pivot) ` `to left of pivot and all greater elements to right ` `int` `partition(` `int` `arr[], ` `int` `low, ` `int` `high) ` `int` `pivot = arr[high]; ` `// pivot ` `int` `i = (low - 1); ` `// Index of smaller element ` `for` `(` `int` `j = low; j <= high - 1; j++) { ` `// If current element is smaller than or ` `if` `(arr[j] <= pivot) { ` `i++; ` `// increment index of smaller element ` `} ` `swap(arr[i + 1], arr[high]); ` `} ` `// Generates Random Pivot, swaps pivot with ` `int` `partition_r(` `int` `arr[], ` `int` `low, ` `int` `high) ` `// Generate a random number in between ` `srand` `(` `time` `(NULL)); ` `swap(arr[random], arr[high]); ` `return` `partition(arr, low, high); ` `arr[] --> Array to be sorted, ` `high --> Ending index */` `{ ` `/* pi is partitioning index, arr[p] is now ` `int` `pi = partition_r(arr, low, high); ` `// Separately sort elements before ` `quickSort(arr, low, pi - 1); ` `} ` `void` `printArray(` `int` `arr[], ` `int` `size) ` `int` `i; ` `printf` `(` `'%d '` `, arr[i]); ` `} ` `// Driver program to test above functions ` `{ ` `int` `n = ` `sizeof` `(arr) / ` `sizeof` `(arr[0]); ` `printf` `(` `'Sorted array:'` `); ` `return` `0; ` |

`partition scheme. */` `#include <iostream> ` `/* This function takes last element as pivot, places ` `the pivot element at its correct position in sorted ` `array, and places all smaller (smaller than pivot) ` `to left of pivot and all greater elements to right ` `int` `partition(` `int` `arr[], ` `int` `low, ` `int` `high) ` `int` `pivot = arr[low]; ` `// or equal to pivot ` `i++; ` `// or equal to pivot ` `j--; ` `if` `(i >= j) ` `} ` `// end element and calls the partition function ` `// In Hoare partition the low element is selected ` `int` `partition_r(` `int` `arr[], ` `int` `low, ` `int` `high) ` `// Generate a random number in between ` `srand` `(` `time` `(NULL)); ` `swap(arr[random], arr[low]); ` `return` `partition(arr, low, high); ` `arr[] --> Array to be sorted, ` `high --> Ending index */` `{ ` `/* pi is partitioning index, arr[p] is now ` `int` `pi = partition_r(arr, low, high); ` `// Separately sort elements before ` `quickSort(arr, low, pi); ` `} ` `void` `printArray(` `int` `arr[], ` `int` `n) ` `for` `(` `int` `i = 0; i < n; i++) ` `printf` `(` `'` `); ` `int` `main() ` `int` `arr[] = { 10, 7, 8, 9, 1, 5 }; ` `quickSort(arr, 0, n - 1); ` `printArray(arr, n); ` `} ` |

Output:

**Notes**

- Using random pivoting we improve the expected or average time complexity to O (N log N). The Worst Case complexity is still O ( N^2 ).

**rand ()**

rand() function is used in C to generate random numbers. If we generate a sequence of random number with rand() function, it will create the same sequence again and again every time program runs. Say if we are generating 5 random numbers in C with the help of rand() in a loop, then every time we compile and run the program our output must be the same sequence of numbers.**Syntax:**

`#include <stdio.h> ` `int` `main(` `void` `) ` `// This program will create same sequence of ` `printf` `(` `' %d '` `, ` `rand` `()); ` `} ` |

**NOTE:** This program will create same sequence of random numbers on every program run.

Output 1:

Output 2:

Output n:

**srand()**

The srand() function sets the starting point for producing a series of pseudo-random integers. If srand() is not called, the rand() seed is set as if srand(1) were called at program start. Any other value for seed sets the generator to a different starting point.**Syntax:**

**Note:** The pseudo-random number generator should only be seeded once, before any calls to rand(), and the start of the program. It should not be repeatedly seeded, or reseeded every time you wish to generate a new batch of pseudo-random numbers.

Standard practice is to use the result of a call to **srand(time(0))** as the seed. However, time() returns a time_t value which vary everytime and hence the pseudo-random number vary for every program call.

`#include <stdio.h> ` `#include<time.h> ` `// Driver program ` `{ ` `// This program will create different sequence of ` `// Use current time as seed for random generator ` `printf` `(` `' %d '` `, ` `rand` `()); ` `return` `0; ` |

**NOTE:** This program will create different sequence of random numbers on every program run.

Output 1:

Output 2:

Output n:

**How srand() and rand() are related to each other?**

srand() sets the seed which is used by rand to generate “random” numbers. If you don’t call srand before your first call to rand, it’s as if you had called srand(1) to set the seed to one.

In short, **srand() — Set Seed for rand() Function**.

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