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#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;
        // Move elements greater than key to one position ahead
        while (j >= 0 && arr[j] > key) {
            arr[j + 1] = arr[j];
            j--;
        }
        arr[j + 1] = key;
    }
}

void printArray(int arr[], int n) {
    for (int i = 0; i < n; i++)
        cout << arr[i] << " ";
    cout << endl;
}

int main() {
    int arr[] = {64, 34, 25, 12, 22, 11, 90, 5};
    int n = sizeof(arr) / sizeof(arr);
    cout << "Array before sorting:\n";
    printArray(arr, n);

    insertionSort(arr, n);

    cout << "Array after Insertion Sort:\n";
    printArray(arr, n);
    return 0;
}
  



  #include <iostream>
using namespace std;

int partition(int arr[], int l, int r) {
    int pivot = arr[r], i = l;
    for (int j = l; j < r; j++) {
        if (arr[j] <= pivot) {
            swap(arr[i], arr[j]);
            i++;
        }
    }
    swap(arr[i], arr[r]);
    return i;
}

int quickSelect(int arr[], int l, int r, int k) {
    if (l <= r) {
        int pi = partition(arr, l, r);
        if (pi == k)
            return arr[pi];
        else if (k < pi)
            return quickSelect(arr, l, pi - 1, k);
        else
            return quickSelect(arr, pi + 1, r, k);
    }
    return -1;
}

int main() {
    int arr[] = {10, 4, 5, 8, 6, 11, 26};
    int n = sizeof(arr) / sizeof(arr);
    int k = 3; // For 4th smallest (index 3)
    int kth = quickSelect(arr, 0, n - 1, k);
    cout << "The " << k + 1 << "th smallest element is: " << kth << endl;
    return 0;
}




3 

#include <iostream>
using namespace std;

void merge(int arr[], int l, int m, int r) {
    int n1 = m - l + 1, n2 = r - m;
    int *L = new int[n1], *R = new int[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++];
    delete[] L;
    delete[] R;
}

void mergeSort(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);
    }
}

void printArray(int arr[], int n) {
    for (int i = 0; i < n; i++)
        cout << arr[i] << " ";
    cout << endl;
}

int main() {
    int arr[] = {85, 14, 60, 53, 27, 41, 33, 10};
    int n = sizeof(arr) / sizeof(arr);
    cout << "Original array:\n";
    printArray(arr, n);

    mergeSort(arr, 0, n - 1);

    cout << "Sorted array (Merge Sort):\n";
    printArray(arr, n);
    return 0;
}