Sorting Algorithms (DSA - 4)

Bubble Sort

Time Complexity:

Best: O(n²) (when the array is already sorted)
Average: O(n²)
Worst: O(n²)
Space Complexity: O(1)

#include <iostream>
#include <vector>
using namespace std;

void bubbleSort(vector<int>& arr) {
    int n = arr.size();
    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], arr[j + 1]);
            }
        }
    }
}

int main() {
    vector<int> arr = {64, 34, 25, 12, 22, 11, 90};
    bubbleSort(arr);
    for (int num : arr) {
        cout << num << " ";
    }
    return 0;
}

Selection Sort

Time Complexity:

Best: O(n²)
Average: O(n²)
Worst: O(n²)
Space Complexity: O(1)

#include <iostream>
#include <vector>
using namespace std;

void selectionSort(vector<int>& arr) {
    int n = arr.size();
    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(arr[i], arr[min_idx]);
    }
}

int main() {
    vector<int> arr = {64, 25, 12, 22, 11};
    selectionSort(arr);
    for (int num : arr) {
        cout << num << " ";
    }
    return 0;
}

Insertion Sort

Time Complexity:

Best: O(n) (when the array is already sorted)
Average: O(n²)
Worst: O(n²)
Space Complexity: O(1)

#include <iostream>
#include <vector>
using namespace std;

void insertionSort(vector<int>& arr) {
    int n = arr.size();
    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;
        }
        arr[j + 1] = key;
    }
}

Merge Sort

Time Complexity:

Best: O(nlogn)
Average: O(nlogn)
Worst: O(nlogn)
Space Complexity: O(n)

#include <iostream>
#include <vector>
using namespace std;

void merge(vector<int>& arr, int l, int m, int r) {
    int n1 = m - l + 1;
    int n2 = r - m;
    vector<int> L(n1);
    vector<int> 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++];
        } else {
            arr[k++] = R[j++];
        }
    }

    while (i < n1) {
        arr[k++] = L[i++];
    }

    while (j < n2) {
        arr[k++] = R[j++];
    }
}

void mergeSort(vector<int>& arr, int l, int r) {
    if (l < r) {
        int m = l + (r - l) / 2;
        mergeSort(arr, l, m);
        mergeSort(arr, m + 1, r);
        merge(arr, l, m, r);
    }
}

Quick Sort

Time Complexity:

Best: O(nlogn)
Average: O(nlogn)
Worst: O(n²) (when the pivot is the smallest or largest element)
Space Complexity: O(logn) (due to recursion stack)

#include <iostream>
#include <vector>
using namespace std;

int partition(vector<int>& arr, int low, int high) {
    int pivot = arr[high];
    int i = low - 1;
    for (int j = low; j < high; ++j) {
        if (arr[j] <= pivot) {
            ++i;
            swap(arr[i], arr[j]);
        }
    }
    swap(arr[i + 1], arr[high]);
    return i + 1;
}

void quickSort(vector<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);
    }
}

Heap Sort

Time Complexity:

Best: O(nlogn)
Average: O(nlogn)
Worst: O(nlogn)
Space Complexity: O(1)

#include <iostream>
#include <vector>
using namespace std;

void heapify(vector<int>& arr, int n, int i) {
    int largest = i;
    int left = 2 * i + 1;
    int right = 2 * i + 2;

    if (left < n && arr[left] > arr[largest])
        largest = left;

    if (right < n && arr[right] > arr[largest])
        largest = right;

    if (largest != i) {
        swap(arr[i], arr[largest]);
        heapify(arr, n, largest);
    }
}

void heapSort(vector<int>& arr) {
    int n = arr.size();

    for (int i = n / 2 - 1; i >= 0; --i)
        heapify(arr, n, i);

    for (int i = n - 1; i >= 0; --i) {
        swap(arr[0], arr[i]);
        heapify(arr, i, 0);
    }
}