Question

Implement a quick sort algorithm that will accept an integer array of size n and in random order. Develop or research three different approaches as how you can pick the pivot. Write the code so the quick sort can choose among the above three different ways of picking the pivot. Run the algorithm for different sets of random data and make sure that for each set of data, you run the algorithm with all three options for the pivot selection. Record the number of key operations for each case. Report the numbers in a way that will allow you to draw a conclusion about which pivot selection approach was more efficient and how much variations you see between the different runs.

Answer 1

Answer:

#include <cstdlib>  

#include <iostream>  

#include <array>  

using namespace std;  

const string APP_NAME = "Quick Sort Algorithm";  

const array<string, 3> MENU_OPTIONS = {  

"Simulate with Random data",  

"Enter data",  

"Exit program"  

};  

void printMenuOptions() {  

cout << endl << "---------------------------" << endl;  

cout << APP_NAME << endl;  

cout << "---------------------------" << endl;  

for (int i=0; i<MENU_OPTIONS.size(); i++) {  

cout << i+1 << ". " << MENU_OPTIONS[i] << endl;  

}  

cout << endl << "Select an option: ";  

}  

int getRandomInt(int min, int max) {  

return min + (static_cast<int>(rand() % (max - min + 1)));  

}  

bool inArray(int value, int* arr, int size) {  

bool found = false;  

for (int i=0; i<size; i++) {  

if (arr[i] == value) {  

found = true;  

}  

}  

return found;  

}  

void generateRandomArrays(int size, int* arr0, int* arr1, int* arr2, int* arr3) {  

int value;  

bool ok = false;  

for (int i=0; i<size; i++) {  

while (!ok) {  

value = getRandomInt(1, size*10);  

if (!inArray(value, arr0, size)) {  

arr0[i] = value;  

arr1[i] = value;  

arr2[i] = value;  

arr3[i] = value;  

ok = true;  

}  

}  

ok = false;  

}  

}  

void print(int* data, int size) {  

for (int i=0; i<size; i++) {  

cout << data[i] << " ";  

}  

}  

int getPivot(int first, int last, int approach) {  

int pivot;  

switch (approach) {  

case 2:  

pivot = first;  

break;  

case 3:  

pivot = last;  

break;  

case 1:  

default:  

pivot = (first + last) / 2;  

}  

return pivot;  

}  

void swap(int* data, int i, int j) {  

int temp = data[i];  

data[i] = data[j];  

data[j] = temp;  

}  

int quickSort(int* data, int first, int last, int approach) {  

int ops = 0;  

int i = first;  

int j = last;  

int pivot = getPivot(i, j, approach);  

while (i <= j) {  

while (data[i] < data[pivot]) {  

i++;  

}  

while (data[j] > data[pivot]) {  

j--;  

}  

if (i <= j) {  

ops++;  

swap(data, i, j);  

i++;  

j--;  

}  

}  

if (j > first) {  

ops += quickSort(data, first, j, approach);  

}  

if (i < last) {  

ops += quickSort(data, i, last, approach);  

}  

return ops;  

}  

void simulate(int size, bool display) {  

int* data0 = new int[size];  

int* data1 = new int[size];  

int* data2 = new int[size];  

int* data3 = new int[size];  

int ops1, ops2, ops3;  

generateRandomArrays(size, data0, data1, data2, data3);  

ops1 = quickSort(data1, 0, size-1, 1);  

ops2 = quickSort(data2, 0, size-1, 2);  

ops3 = quickSort(data3, 0, size-1, 3);  

if (display) {  

cout << "Unsorted Array: ";  

print(data0, size);  

}  

cout << endl << endl << "> QuickSort #1: pivot is at the median" << endl;  

cout << "Swaps done: " << ops1 << endl;  

if (display) {  

cout << "Sorted Array: ";  

print(data1, size);  

}  

cout << endl << endl << "> QuickSort #2: pivot is at the start" << endl;  

cout << "Swaps done: " << ops2 << endl;  

if (display) {  

cout << "Sorted Array: ";  

print(data2, size);  

}  

cout << endl << endl << "> QuickSort #3: pivot is at the end" << endl;  

cout << "Swaps done: " << ops3 << endl;  

if (display) {  

cout << "Sorted Array: ";  

print(data3, size);  

}  

}  

void enterArray(int size, bool display) {  

// declare some variables  

int* data0 = new int[size];  

int* data1 = new int[size];  

int* data2 = new int[size];  

int* data3 = new int[size];  

int ops1, ops2, ops3;  

int value;  

for (int i=0; i<size; i++) {  

cout << "Enter value " << i+1 << " of " << size << ": ";  

cin >> value;  

data0[i] = value;  

data1[i] = value;  

data2[i] = value;  

data3[i] = value;  

}  

ops1 = quickSort(data1, 0, size-1, 1);  

ops2 = quickSort(data2, 0, size-1, 2);  

ops3 = quickSort(data3, 0, size-1, 3);  

if (display) {  

cout << "Unsorted Array: ";  

print(data0, size);  

}  

cout << endl << endl << "> QuickSort #1: pivot is at the median" << endl;  

cout << "Swaps done: " << ops1 << endl;  

if (display) {  

cout << "Sorted Array: ";  

print(data1, size);  

}  

cout << endl << endl << "> QuickSort #2: pivot is at the start" << endl;  

cout << "Swaps done: " << ops2 << endl;  

if (display) {  

cout << "Sorted Array: ";  

print(data2, size);  

}  

cout << endl << endl << "> QuickSort #3: pivot is at the end" << endl;  

cout << "Swaps done: " << ops3 << endl;  

if (display) {  

cout << "Sorted Array: ";  

print(data3, size);  

}  

}  

int main(int argc, char** argv) {  

int choice;  

char option;  

int num;  

bool end = false;  

bool display = false;  

while (!end) {  

printMenuOptions();  

cin >> choice;  

switch (choice) {  

case 1:  

cout << endl << "Enter size of array (elements will be integers randomly generated): ";  

cin >> num;  

if (num > 0) {  

cout << "Values will be randomly generated from 1 to " << num*10 << endl;  

cout << "Do you want to display the sorted arrays? <y/N>: ";  

cin >> option;  

display = (option == 'y') ? true : false;  

simulate(num, display);  

} else {  

cout << endl << "Incorrect size." << endl;  

}  

break;  

case 2:  

cout << endl << "Enter size of array (you will enter the numbers): ";  

cin >> num;  

if (num > 0) {  

cout << "Do you want to display the sorted arrays? <y/N>: ";  

cin >> option;  

display = (option == 'y') ? true : false;  

enterArray(num, display);  

} else {  

cout << endl << "Incorrect size." << endl;  

}  

break;  

case 3:  

end = true;  

break;  

default:  

cout << endl << "Incorrect option. Try again." << endl;  

}  

}  

return 0;  

}