对于给定的一组关键字：41,62,13,84,35,96,57,39,79,61,15,83，分别写出：插入排序、堆排序、快速排序、冒泡排序的排序过程，请用c++语言实现上述排序，写在同一个程序里，头文件里不包括vector、algorithm

插入排序：

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--;
        }
        arr[j + 1] = key;
    }
}

堆排序：

void heapify(int arr[], int n, int i) {
    int largest = i; 
    int l = 2 * i + 1; 
    int r = 2 * i + 2; 

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

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

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

void heapSort(int arr[], int n) {
    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);
    }
}

快速排序：

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);
    }
}

冒泡排序：

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], arr[j + 1]);
}

完整程序实现如下：

#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--;
        }
        arr[j + 1] = key;
    }
}

void heapify(int arr[], int n, int i) {
    int largest = i; 
    int l = 2 * i + 1; 
    int r = 2 * i + 2; 

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

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

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

void heapSort(int arr[], int n) {
    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);
    }
}

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 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], arr[j + 1]);
}

int main() {
    int arr[] = {41, 62, 13, 84, 35, 96, 57, 39, 79, 61, 15, 83};
    int n = sizeof(arr) / sizeof(arr[0]);

    cout << "Original array:\n";
    for (int i = 0; i < n; i++)
        cout << arr[i] << " ";
    cout << endl;

    insertionSort(arr, n);
    cout << "Array sorted using insertion sort:\n";
    for (int i = 0; i < n; i++)
        cout << arr[i] << " ";
    cout << endl;

    heapSort(arr, n);
    cout << "Array sorted using heap sort:\n";
    for (int i = 0; i < n; i++)
        cout << arr[i] << " ";
    cout << endl;

    quickSort(arr, 0, n - 1);
    cout << "Array sorted using quick sort:\n";
    for (int i = 0; i < n; i++)
        cout << arr[i] << " ";
    cout << endl;

    bubbleSort(arr, n);
    cout << "Array sorted using bubble sort:\n";
    for (int i = 0; i < n; i++)
        cout << arr[i] << " ";
    cout << endl;

    return 0;
}