使用堆排序对数组排序

Question

我正在做算法的中期审查，我试图用Java实现所有的伪代码，以便更好地理解算法。但是在堆排序部分，我的代码有一些问题。我的输入数组是

{10,16,4,10,14,7,9,3,2,8,1}

第一个元素只是表示我想要排序的元素的数量。换句话说，需要排序的元素从索引1开始。

我的build max heap输出是：16 14 10 8 7 9 3 2 4 1

堆排序的输出是：1 3 2 4 7 8 9 10 14 16

看起来我的build max堆部分工作得很好，但我在堆排序部分也找不到bug。

public class Midterm{
  public static void main(String[] args){
    int[] C = {10,16,4,10,14,7,9,3,2,8,1};
    /*for convenience, the first element in array C represent the
    number of elements needed to be heapified;
    */
    Midterm heap = new Midterm();
    int n = C.length - 1;
    for (int i = (n / 2); i > 0; i--){
      heap.maxHeapify(C, i, n);
    }

    int index = 1;
    while(index <= n){
      System.out.print(C[index] + " ");
      index++;
    }
    System.out.println();

    Midterm heap2 = new Midterm();
    heap2.heapSort(C);
    int index2 = 1;
    while(index2 <= n){
      System.out.print(C[index2] + " ");
      index2++;
    }
    System.out.println();

  }

  public void heapSort(int[] A){
    int n = A.length - 1;
    for (int i = n; i >= 2; i--){
      exchange(A, 1, i);
      maxHeapify(A, 1, i - 1);
    }
  }
  public void maxHeapify(int[] A, int i, int n){
    int left = 2 *i, right = 2 * i + 1;
    int largest;
    if (left < n && A[left] > A[i]){
      largest = left;
    }else{
      largest = i;
    }
    if (right < n && A[right] > A[largest]){
      largest = right;
    }
    if (largest != i){
      exchange(A, i, largest);
      maxHeapify(A, largest,n);
    }
  }
  private void exchange(int[] A, int i , int j){
    int temp = A[i];
    A[i] = A[j];
    A[j] = temp;
  }
}

Answer 1

检查下面的代码。

public class HeapSort
  {
   public void sort(int arr[])
    {
     int n = arr.length;

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

    // One by one extract an element from heap
    for (int i=n-1; i>=0; i--)
    {
        // Move current root to end
        int temp = arr[0];
        arr[0] = arr[i];
        arr[i] = temp;

        // call max heapify on the reduced heap
        heapify(arr, i, 0);
    }
}

// To heapify a subtree rooted with node i which is
// an index in arr[]. n is size of heap
void heapify(int arr[], int n, int i)
{
    int largest = i;  // Initialize largest as root
    int l = 2*i + 1;  // left = 2*i + 1
    int r = 2*i + 2;  // right = 2*i + 2

    // If left child is larger than root
    if (l < n && arr[l] > arr[largest])
        largest = l;

    // If right child is larger than largest so far
    if (r < n && arr[r] > arr[largest])
        largest = r;

    // If largest is not root
    if (largest != i)
    {
        int swap = arr[i];
        arr[i] = arr[largest];
        arr[largest] = swap;

        // Recursively heapify the affected sub-tree
        heapify(arr, n, largest);
    }
}

/* A utility function to print array of size n */
static void printArray(int arr[])
{
    int n = arr.length;
    for (int i=0; i<n; ++i)
        System.out.print(arr[i]+" ");
    System.out.println();
}

// Driver program
public static void main(String args[])
{
    int arr[] = {12, 11, 13, 5, 6, 7};
    int n = arr.length;

    HeapSort ob = new HeapSort();
    ob.sort(arr);

    System.out.println("Sorted array is");
    printArray(arr);
 }
}

Answer 2

您的代码中有2个错误：

1.堆排序的for循环从last元素到first元素，所以

for (int i = n; i >= 2; i--){

应该是：

for (int i = n; i >= 1; i--){

因为索引从0开始。

2.在执行交换（a，1，i）后，正确的调用应该是：

maxHeapify(A, 1, i)