9. Design and implement C/C++ Program to sort a given set of n integer elements using Quick Sort method and compute its time complexity. Run the program for varied values of n> 5000 and record the time taken to sort. Plot a graph of the time taken versus n. The elements can be read from a file or can be generated using the random number generator.
Step 1: Implement the Quick Sort Algorithm
Quick Sort is a divide-and-conquer algorithm that works by selecting a ‘pivot’ element and partitioning the array into elements less than and greater than the pivot.
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
// Function to swap two elements
void swap(int* a, int* b)
{
int t = *a;
*a = *b;
*b = t;
}
// Partition function for Quick Sort
int partition(int arr[], int low, int high)
{
int pivot = arr[high]; // Pivot element
int i = (low - 1); // Index of smaller element
for (int j = low; j <= high - 1; j++)
{
if (arr[j] < pivot)
{
i++; // Increment index of smaller element
swap(&arr[i], &arr[j]);
}
}
swap(&arr[i + 1], &arr[high]);
return (i + 1);
}
// Quick Sort function
void quickSort(int arr[], int low, int high)
{
if (low < high)
{
int pi = partition(arr, low, high);
// Recursively sort elements before and after partition
quickSort(arr, low, pi - 1);
quickSort(arr, pi + 1, high);
}
}
// Function to generate random numbers
void generateRandomNumbers(int arr[], int n)
{
for (int i = 0; i < n; i++)
{
arr[i] = rand() % 100000; // Generate random numbers between 0 and 99999
}
}
int main()
{
int n;
printf("Enter number of elements: ");
scanf("%d", &n); // Read the number of elements from the user
if (n <= 5000)
{
printf("Please enter a value greater than 5000\n");
return 1; // Exit if the number of elements is not greater than 5000
}
// Allocate memory for the array
int *arr = (int *)malloc(n * sizeof(int));
if (arr == NULL)
{
printf("Memory allocation failed\n");
return 1; // Exit if memory allocation fails
}
// Generate random numbers and store them in the array
generateRandomNumbers(arr, n);
// Measure the time taken to sort the array
clock_t start = clock();
quickSort(arr, 0, n - 1);
clock_t end = clock();
// Calculate and print the time taken to sort the array
double time_taken = ((double)(end - start)) / CLOCKS_PER_SEC;
printf("Time taken to sort %d elements: %f seconds\n", n, time_taken);
// Free the allocated memory
free(arr);
return 0;
}Step 2: Measure Time Taken
This program generates n random numbers, sorts them using the Quick Sort algorithm, and measures the time taken for the sorting process.
Step 3: Run the Program for Various Values of n
To collect data, run the program with different values of n greater than 5000, such as 6000, 7000, 8000, etc., and record the time taken for each if you didn’t get time then increase the value of n for example 20000, 40000, 60000 etc….
Step 4: Plot the Results
You can use a graphing tool like Python with matplotlib to plot the results.
import matplotlib.pyplot as plt
# Example data collected
n_values = [10000, 20000, 30000, 35000, 50000]
time_taken = [0.0000, 0.015000, 0.011000, 0.003000, 0.015000] # replace with actual times recorded
plt.plot(n_values, time_taken, marker='o')
plt.title('Quick Sort Time Complexity')
plt.xlabel('Number of Elements (n)')
plt.ylabel('Time taken (seconds)')
plt.grid(True)
plt.show()Enter number of elements: 10000
Time taken to sort 10000 elements: 0.0000 seconds
********************************************************************
Enter number of elements: 20000
Time taken to sort 20000 elements: 0.015000 seconds
********************************************************************
Enter number of elements: 30000
Time taken to sort 30000 elements: 0.011000 seconds
********************************************************************
Enter number of elements: 35000
Time taken to sort 35000 elements: 0.003000 seconds
********************************************************************
Enter number of elements: 50000
Time taken to sort 50000 elements: 0.015000 seconds