《算法导论》CLRS算法C++实现（三）P75 堆排序

第六章 堆排序

主要分为三个子算法。算法MAX-HEAPIFY(A, i)为调整堆，算法BUILD-MAX-HEAP(A)为建堆，算法HEAPSORT(A)为堆排序。运行环境Code::Blocks 10.05。

MAX-HEAPIFY(A, i)

l ← LEFT(i)
r ← RIGHT(i)
if l ≤ heap-size[A] and A[l] > A[i]
    then largest ← l
else largest ← i
if r ≤ heap-size[A] and A[r] > A[largest]
    then largest ← r
if largest ≠ i
    then swap(A[i], A[largest])
    MAX-HEAPIFY(A, largest)

BUILD-MAX-HEAP(A) 

heap-size[A] ← length[A]
for i ← ⌊length[A]/2⌋ down to 1
    do MAX-HEAPIFY(A, i)

 HEAPSORT(A)

BUILD-MAX-HEAP(A)
for i ← length[A] downto 2
    do exchange A[1] ↔ A[i]
    heap-size[A] ← heap-size[A] - 1
    MAX-HEAPIFY(A, 1)

C++代码实现

#include <iostream>

using namespace std;

//交换x和y

void swap(int* x, int* y)
{
    int temp;
    temp = *x;
    *x = *y;
    *y = temp;
}

//返回左孩子的下标
inline int left(int i)
{
    return 2 * i + 1;
}

//返回右孩子的下标
inline int right(int i)
{
    return 2 * i + 2;
}

//返回父结点
inline int parent(int i)
{
    if(i % 2)
        return (i - 1) / 2;
    return (i - 2) / 2;
}

void maxHeapify(int* arr, int i, int heapsize)
{
    int l = left(i);
    int r = right(i);
    int largest;
    if((l < heapsize) && (arr[l] > arr[i]))
        largest = l;
    else
        largest = i;
    if((r < heapsize) && (arr[r] > arr[largest]))
        largest = r;
    if(largest != i)
    {
        swap(arr[i], arr[largest]);
        maxHeapify(arr, largest, heapsize);
    }
}

void buildMaxHeap(int* arr, int length)
{
    int i;
    for(i = length / 2; i >= 0; i--)
    {
        maxHeapify(arr, i, length);
    }
}

void heapSort(int* arr, int length)
{
    int i, heapsize = length;
    buildMaxHeap(arr, length);
    for(i = heapsize - 1; i > 0; i--)
    {
        swap(arr[0], arr[i]);
        heapsize--;
        maxHeapify(arr, 0, heapsize);
    }
}

int main()
{
    int arr[] = {0, 2, 6, 98, 34, -5, 23, 11, 89, 100, 7};
    heapSort(arr, 11);
    for(int i = 0; i < 11; i++)
    {
        cout << arr[i] << " ";
    }
    cout << endl;
    return 0;
}