优先队列（二叉堆）的插入程序

《数据结构与算法分析》习题6.2，这题是问答题，心血来潮下决心用程序实现，编程菜鸟前前后后调试了大概一天时间才完成两种算法，下面是第一种算法，时间复杂度为O(NlogN)。

#include<stdio.h>
#include<stdlib.h>
typedef struct heapStruct
{
    int Capacity;
    int Size;
    int *Elements;
}*priorityQueue;
priorityQueue initQueue(int n)
{
    priorityQueue H;
    H = (priorityQueue)malloc(sizeof(priorityQueue));
    if(H == NULL)
        printf("Out of space!!!");
    
    H->Elements = (int *)malloc((n+1)*sizeof(int));
    if(H->Elements == NULL)
        printf("Out of space!!!");

    H->Capacity = n;
    H->Size = 0;
    H->Elements[0] = -1;

    return H;
}
int isFull(priorityQueue H)
{
    return H->Size == H->Capacity;
}
int isEmpty(priorityQueue H)
{
    return H->Size == 0;
}
void Insert(int X, priorityQueue H)
{
    int i;

    if(isFull(H))
    {
        printf("Priority queue is full");
        return;
    }
    for(i = ++H->Size; H->Elements[i/2] > X; i /= 2)
        H->Elements[i] = H->Elements[i/2];
    H->Elements[i] = X;
}
void printQueue(priorityQueue H)
{
    int i;
    if(isEmpty(H))
        printf("H is NULL");
    for(i=1; i<=H->Size; i++)
        printf("%d ", H->Elements[i]);
}
void main()
{
    int input[15] = {10,12,1,14,6,5,8,15,3,9,7,4,11,13,2};
    int i;
    priorityQueue H = initQueue(20);
    
    for(i = 0; i < 15; i++)
        Insert(input[i], H);

    printQueue(H);
}       

第二种算法是将N个关键字以任意顺序放入书中，保持结构特性。为了保持二叉堆的性质可能需要将父节点下滤，时间复杂度为O（N）。使用Swap函数的时候遇到问题，后面将会总结一下Swap函数。

#include<stdio.h>
#include<stdlib.h>
typedef struct heapStruct
{
    int Capacity;
    int Size;
    int *Elements;
}*priorityQueue;
int isFull(priorityQueue H)
{
    return H->Size == H->Capacity;
}
int isEmpty(priorityQueue H)
{
    return H->Size == 0;
}
void Swap(int *a, int *b)
{
    int Tmp = *a;
    *a = *b; 
    *b = Tmp;
}
void percolateDown(int i, priorityQueue H)
{
    int j;	
    for(j=i; (2*j+1) <= H->Size && H->Elements[j]>Min(H->Elements[2*j],H->Elements[2*j+1]);)
    {
        if(H->Elements[2*j]<H->Elements[2*j+1])
        {
            Swap(&H->Elements[j], &H->Elements[2*j]);
            j *= 2;
        }
        else
        {
            Swap(&H->Elements[j], &H->Elements[2*j+1]);
            j = 2*j+1;
        }
    }            
}
priorityQueue buildHeap(int a[], int n)
{
    int i, j;
    priorityQueue H;
    H = (priorityQueue)malloc(sizeof(priorityQueue));
    if(H == NULL)
        printf("Out of space!!!");
    H->Elements = (int *)malloc((n+1)*sizeof(int));
    if(H->Elements == NULL)
        printf("Out of space!!!");

    H->Capacity = n;
    H->Size = n;
    H->Elements[0] = -1;
    for(i=1; i<=n; i++)
	H->Elements[i] = a[i-1];

    for(j=n/2; j>0; j--)
	percolateDown(j, H);
	
    return H;
}
int Min(int a, int b)
{
    return ((a < b)? a : b);
}
void printQueue(priorityQueue H)
{
    int i;
    if(isEmpty(H))
        printf("H is NULL");
    for(i=1; i<=H->Size; i++)
        printf("%d ", H->Elements[i]);
}
void main()
{
    int input[15] = {10,12,1,14,6,5,8,15,3,9,7,4,11,13,2};
    printQueue(buildHeap(input, 15));
}