堆排序算法

#include <stdio.h>#include <stdlib.h>#define LEFT(i) (i<<1) + 1#define RIGHT(i) (i<<1) + 2int N = 10;int heapSize = 10;void buildMaxHeap(int *parr);void maxHeapify(int *parr,int index);void heapSort(int *parr);void exchange(int &a, int &b);void main(){int arr[] = {16,14,8,7,10,9,3,2,4,1};heapSort(arr);for (int index = 0; index< N;index++){printf("%d/t",arr[index]);}getchar();}void exchange(int &a, int &b){int temp;temp = a;a = b;b = temp;}//keep the heap feature status.void maxHeapify(int *parr,int index){int l = LEFT(index);int r = RIGHT(index);int largest = 0;if (l < heapSize && parr[l] > parr[index]){largest = l;}elselargest = index;if (r < heapSize && parr[largest] < parr[r]){largest = r;}if (largest != index){exchange(parr[largest],parr[index]);maxHeapify(parr,largest);}elsereturn ;}void buildMaxHeap(int *parr){//here: non-leaf node is from 0 to N/2, //can be demonstrated using negativeapproach.for (int i = N/2;i >= 0;i--){maxHeapify(parr,i);}}void heapSort(int *parr){buildMaxHeap(parr);//get the max number and then heapify again from 0;for (int index = heapSize;index>=1;index--){exchange(parr[0],parr[heapSize-1]);heapSize--;maxHeapify(parr,0);}}

 

其实需要说明的一点是：堆中叶子节点的下标是从N/2+1开始，这点只需反证法就很明了。

而且本程序的核心就是maxHeapify函数，该函数用来保持最大堆得性质，parent>son。