12. 二叉堆（binary heap）

fatal.h

#include <stdio.h>
#include <stdlib.h>

#define Error(Str)        FatalError(Str)
#define FatalError(Str)   fprintf(stderr, "%s\n", Str), exit(1)

binheap.h

typedef int ElementType;

#ifndef _BinHeap_H
#define _BinHeap_H

struct HeapStruct;
typedef struct HeapStruct *PriorityQueue;

PriorityQueue Initialize(int MaxElements);
void Destroy(PriorityQueue H);
void MakeEmpty(PriorityQueue H);
void Insert(ElementType X, PriorityQueue H);
ElementType DeleteMin(PriorityQueue H);
ElementType FindMin(PriorityQueue H);
int IsEmpty(PriorityQueue H);
int IsFull(PriorityQueue H);
void Print(PriorityQueue H);

#endif

binheap.c

#include "binheap.h"
#include "fatal.h"
#include <stdlib.h>

#define MinPQSize (10)
#define MinData (-32767)

struct HeapStruct
{
    int Capacity;
    int Size;
    ElementType *Elements;
};

PriorityQueue Initialize(int MaxElements)
{
    PriorityQueue H;

    if (MaxElements < MinPQSize)
        Error("Priority queue size is too small");

    H = malloc(sizeof(struct HeapStruct));
    if (H == NULL)
        FatalError("Out of space!!!");

    /* Allocate the array plus one extra for sentinel */
    H->Elements = malloc((MaxElements + 1) * sizeof(ElementType));
    if (H->Elements == NULL)
        FatalError("Out of space!!!");

    H->Capacity = MaxElements;
    H->Size = 0;
    H->Elements[0] = MinData;

    return H;
}

void MakeEmpty(PriorityQueue H)
{
    H->Size = 0;
}

/* H->Element[ 0 ] is a sentinel */
void Insert(ElementType X, PriorityQueue H)
{
    int i;

    if (IsFull(H))
    {
        Error("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;
}

ElementType DeleteMin(PriorityQueue H)
{
    int i, Child;
    ElementType MinElement, LastElement;

    if (IsEmpty(H))
    {
        Error("Priority queue is empty");
        return H->Elements[0];
    }
    MinElement = H->Elements[1];
    LastElement = H->Elements[H->Size--];

    for (i = 1; i * 2 <= H->Size; i = Child)
    {
        /* Find smaller child */
        Child = i * 2;
        if (Child != H->Size && H->Elements[Child + 1] < H->Elements[Child])
            Child++;

        /* Percolate one level */
        if (LastElement > H->Elements[Child])
            H->Elements[i] = H->Elements[Child];
        else
            break;
    }
    H->Elements[i] = LastElement;
    return MinElement;
}

ElementType FindMin(PriorityQueue H)
{
    if (!IsEmpty(H))
        return H->Elements[1];
    Error("Priority Queue is Empty");
    return H->Elements[0];
}

int IsEmpty(PriorityQueue H)
{
    return H->Size == 0;
}

int IsFull(PriorityQueue H)
{
    return H->Size == H->Capacity;
}

void Destroy(PriorityQueue H)
{
    free(H->Elements);
    free(H);
}

void Print(PriorityQueue H)
{
    int i, j;
    
    for (i = 1, j = 1; i <= H->Size; i++)
    {
        if (i == j)
        {
            j *= 2;
            printf("\n");
        }
        printf("%d ", H->Elements[i]);
    }
    printf("\n\n");
}

testheap.c

#include "binheap.h"
#include <stdio.h>

#define MaxSize (33)

int main()
{
    PriorityQueue H;
    int i, j;

    H = Initialize(MaxSize);
    for (i = 0, j = MaxSize / 2; i < MaxSize; i++, j = (j + 71) % MaxSize)
    {
        Insert(j, H);
        printf("Insert %d:", j);
        Print(H);
    }

    j = 0;
    while (!IsEmpty(H))
    {
        if (DeleteMin(H) != j++)
            printf("Error in DeleteMin, %d", j);
        printf("DeleteMin %d:", j - 1);
        Print(H);
    }

    printf("Done...\n");
    return 0;
}