Sorting Algorithms in C++
Introduction to Sorting Algorithms
Sorting algorithms are a fundamental concept in computer science. They are used to rearrange a collection of elements into a particular order, such as ascending or descending. In this tutorial, we will explore various sorting algorithms, their implementations, and their efficiencies.
1. Bubble Sort
Bubble Sort is a simple sorting algorithm that repeatedly steps through the list, compares adjacent elements and swaps them if they are in the wrong order. The pass through the list is repeated until the list is sorted.
Example Code:
#include <iostream>
using namespace std;
void bubbleSort(int arr[], int n) {
for (int i = 0; i < n-1; i++) {
for (int j = 0; j < n-i-1; j++) {
if (arr[j] > arr[j+1]) {
// Swap arr[j] and arr[j+1]
int temp = arr[j];
arr[j] = arr[j+1];
arr[j+1] = temp;
}
}
}
}
void printArray(int arr[], int size) {
for (int i = 0; i < size; i++) {
cout << arr[i] << " ";
}
cout << endl;
}
int main() {
int arr[] = {64, 34, 25, 12, 22, 11, 90};
int n = sizeof(arr)/sizeof(arr[0]);
bubbleSort(arr, n);
cout << "Sorted array: \n";
printArray(arr, n);
return 0;
}
Output:
11 12 22 25 34 64 90
2. Selection Sort
Selection Sort is an in-place comparison sorting algorithm. It has an O(n^2) time complexity, making it inefficient on large lists. The algorithm divides the input list into two parts: the sublist of items already sorted, built up from left to right at the front (left) of the list, and the sublist of items remaining to be sorted that occupy the rest of the list.
Example Code:
#include <iostream>
using namespace std;
void selectionSort(int arr[], int n) {
for (int i = 0; i < n-1; i++) {
int min_idx = i;
for (int j = i+1; j < n; j++) {
if (arr[j] < arr[min_idx]) {
min_idx = j;
}
}
// Swap the found minimum element with the first element
int temp = arr[min_idx];
arr[min_idx] = arr[i];
arr[i] = temp;
}
}
void printArray(int arr[], int size) {
for (int i = 0; i < size; i++) {
cout << arr[i] << " ";
}
cout << endl;
}
int main() {
int arr[] = {64, 25, 12, 22, 11};
int n = sizeof(arr)/sizeof(arr[0]);
selectionSort(arr, n);
cout << "Sorted array: \n";
printArray(arr, n);
return 0;
}
Output:
11 12 22 25 64
3. Insertion Sort
Insertion Sort is a simple sorting algorithm that builds the final sorted array one item at a time. It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge sort.
Example Code:
#include <iostream>
using namespace std;
void insertionSort(int arr[], int n) {
for (int i = 1; i < n; i++) {
int key = arr[i];
int j = i - 1;
while (j >= 0 && arr[j] > key) {
arr[j + 1] = arr[j];
j = j - 1;
}
arr[j + 1] = key;
}
}
void printArray(int arr[], int size) {
for (int i = 0; i < size; i++) {
cout << arr[i] << " ";
}
cout << endl;
}
int main() {
int arr[] = {12, 11, 13, 5, 6};
int n = sizeof(arr)/sizeof(arr[0]);
insertionSort(arr, n);
cout << "Sorted array: \n";
printArray(arr, n);
return 0;
}
Output:
5 6 11 12 13
4. Merge Sort
Merge Sort is an efficient, stable, comparison-based, divide and conquer sorting algorithm. Most implementations produce a stable sort, meaning that the implementation preserves the input order of equal elements in the sorted output.
Example Code:
#include <iostream>
using namespace std;
void merge(int arr[], int l, int m, int r) {
int n1 = m - l + 1;
int n2 = r - m;
int L[n1], R[n2];
for (int i = 0; i < n1; i++) {
L[i] = arr[l + i];
}
for (int j = 0; j < n2; j++) {
R[j] = arr[m + 1 + j];
}
int i = 0, j = 0, k = l;
while (i < n1 && j < n2) {
if (L[i] <= R[j]) {
arr[k] = L[i];
i++;
} else {
arr[k] = R[j];
j++;
}
k++;
}
while (i < n1) {
arr[k] = L[i];
i++;
k++;
}
while (j < n2) {
arr[k] = R[j];
j++;
k++;
}
}
void mergeSort(int arr[], int l, int r) {
if (l >= r) {
return;
}
int m = l + (r - l) / 2;
mergeSort(arr, l, m);
mergeSort(arr, m + 1, r);
merge(arr, l, m, r);
}
void printArray(int arr[], int size) {
for (int i = 0; i < size; i++) {
cout << arr[i] << " ";
}
cout << endl;
}
int main() {
int arr[] = {12, 11, 13, 5, 6, 7};
int arr_size = sizeof(arr)/sizeof(arr[0]);
cout << "Given array is \n";
printArray(arr, arr_size);
mergeSort(arr, 0, arr_size - 1);
cout << "\nSorted array is \n";
printArray(arr, arr_size);
return 0;
}
Output:
Given array is
12 11 13 5 6 7
Sorted array is
5 6 7 11 12 13
5. Quick Sort
Quick Sort is an efficient sorting algorithm, serving as a systematic method for placing the elements of an array in order. Developed by Tony Hoare in 1959, it is still a commonly used algorithm for sorting.
Example Code:
#include <iostream>
using namespace std;
void swap(int* a, int* b) {
int t = *a;
*a = *b;
*b = t;
}
int partition(int arr[], int low, int high) {
int pivot = arr[high];
int i = (low - 1);
for (int j = low; j <= high - 1; j++) {
if (arr[j] < pivot) {
i++;
swap(&arr[i], &arr[j]);
}
}
swap(&arr[i + 1], &arr[high]);
return (i + 1);
}
void quickSort(int arr[], int low, int high) {
if (low < high) {
int pi = partition(arr, low, high);
quickSort(arr, low, pi - 1);
quickSort(arr, pi + 1, high);
}
}
void printArray(int arr[], int size) {
for (int i = 0; i < size; i++) {
cout << arr[i] << " ";
}
cout << endl;
}
int main() {
int arr[] = {10, 7, 8, 9, 1, 5};
int n = sizeof(arr) / sizeof(arr[0]);
quickSort(arr, 0, n - 1);
cout << "Sorted array: \n";
printArray(arr, n);
return 0;
}
Output:
1 5 7 8 9 10
Conclusion
Sorting algorithms are crucial for the performance of many applications. Each algorithm has its own advantages and is suitable for different situations. Understanding these algorithms helps in selecting the right one for a particular problem, leading to efficient and effective solutions.