算法导论：堆排序

//goal: heap sort
//time: 9/7/2014
//author: zrss
//reference: introduction to algorithms

#include <cstdio>
#include <cstring>

#define MAX_DATA 10

class MaxHeap {
public:
    MaxHeap(int *data, int size);

    void heap_sort(void); //堆排序，升序

    void output(void);

private:
    void max_heapify(int i, int size); //使以i为根的子树成为最大堆，假设i左右子树均为最大堆
    void build_maxheap(int size); //自底向上使用max_heapify调整，建堆

private:
    int size;
    int array[MAX_DATA]; //从下标0开始存储
};

MaxHeap::MaxHeap(int *data, int size):size(size) {
    if (size > MAX_DATA)
        return;

    memcpy(array, data, sizeof(int) * size);
}

void MaxHeap::max_heapify(int i, int size) {
    bool check = true;

    while (check) {
        int l = (i << 1) + 1;
        int r = l + 1;

        int largest = i;

        //与子节点比较
        if (l < size && array[l] > array[i])
            largest = l;

        if (r < size && array[r] > array[largest])
            largest = r;

        if (largest != i) {
            int temp = array[largest];
            array[largest] = array[i];
            array[i] = temp;

            i = largest; //从被交换的子节点位置继续调整
        }
        else
            check = false; //父节点不小于子节点，满足最大堆性质，停止调整
    }
}

void MaxHeap::build_maxheap(int size) {
    int leaf_start_index = size >> 1; //后续元素为叶子节点

    //从第一个父节点开始调整
    for (int i = leaf_start_index - 1; i >= 0; --i)
        max_heapify(i, size);
}

void MaxHeap::heap_sort(void) {
    int cur_size = size;

    while (cur_size > 1) {
        //调整成堆
        build_maxheap(cur_size);

        //将最大值与堆末尾元素交换
        int temp = array[cur_size - 1];
        array[cur_size - 1] = array[0];
        array[0] = temp;

        --cur_size;
    }
}

void MaxHeap::output(void) {
    for (int i = 0; i < size; ++i)
        printf("%d ", array[i]);
}