图论——Dijkstra+prim算法涉及到的优先队列（二叉堆）

【0】README

0.1）为什么有这篇文章？因为 Dijkstra算法的优先队列实现 涉及到了一种新的数据结构，即优先队列（二叉堆）的操作需要更改以适应这种新的数据结构，我们暂且吧它定义为Distance， 而不是单纯的int类型；
0.2）本文源代码均为原创， int类型的优先队列（二叉堆）的操作实现，参见http://blog.csdn.net/PacosonSWJTU/article/details/49498255， （并比较他们的打印结果，很有必要）

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【1】因为 Dijkstra算法的优先队列实现， 需要用到二叉堆的相关操作，但是操作的元素类型（ElementType 不是 单纯的int类型）， 而是如下：

struct Distance
{
 int vertexIndex; //当前顶点下标
 int distance; //初始顶点到当前顶点的distance
};

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【2】看个荔枝

2.1）需要特别说明的是： indexOfVertexInHeap 数组记录的是顶点vertex在 heap中的位置， 如 indexOfVertexInHeap [1] = 4；表明heap的第4个位置记录这 编号为1的vertex;
2.2）优先队列的insert和deleteMin 的执行演示（请将我的手动演示结果同我的代码打印结果做对比，经过对比，你发现它们的效果是一致的，恰好说明了我的代码的可行性）：

Attention）

• A1）其实本文中的二叉堆优先队列的实现源代码和 int类型的优先队列源代码类似，只不过它们操作的数据类型不一样罢了，当然， 这只需要简单的修改即可；
• A2）打印结果在文末，可以看到，ElementType采用int 和 Distance的打印效果一样，这正证明了我们采用Distance结构体对源码的修改是无误的，相比于单纯的int 类型，只不过Distance又多了一个 顶点下标vertexIndex成员变量而已；

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【3】source code + printing results

3.1）download source code：
https://github.com/pacosonTang/dataStructure-algorithmAnalysis/tree/master/chapter9/binaryHeap_dijkstra_prim
3.2）source code at a glance：（for complete code , please click the given link above）

1st file：distance.h

#include 

#define Error(str) printf("\n error: %s \n",str)   

struct Distance;
typedef struct Distance *Distance;
struct Distance
{
    int vertexIndex;
    int distance;
};

Distance makeEmptyDistance();

2nd file：distance.c

#include "distance.h"
#include 

// allocate the memory for Distance struct
Distance makeEmptyDistance()
{
    Distance element;

    element = (Distance)malloc(sizeof(struct Distance));
    if(!element)
    {
        Error("out of space ,from func makeEmptyDistance");
        return NULL;
    }       

    return element;
}

3rd file：binaryheap.h

#include 
#include 
#include "distance.h"

#define ElementType Distance

#define Error(str) printf("\n error: %s \n",str)   

struct BinaryHeap;
typedef struct BinaryHeap *BinaryHeap;

void swap(ElementType x, ElementType y);
BinaryHeap initBinaryHeap(int capacity);
void insert(ElementType value, BinaryHeap bh, int*);
ElementType deleteMin(BinaryHeap, int*);
int isFull(BinaryHeap bh);
int isEmpty(BinaryHeap bh);
void percolateUp(int index, BinaryHeap bh);
void percolateDownFromOne(int index, BinaryHeap bh, int*);
void printBinaryHeap(BinaryHeap bh);
void printBinaryHeapFromZero(BinaryHeap bh);

struct BinaryHeap 
{
    int capacity;
    int size;   
    ElementType *elements;      
};

4th file：binaryheap.c

#include "binaryheap.h"
#include 

#define MaxInt (int)pow(2, 16)
//judge whether the BinaryHeap is full or not , also 1 or 0 
int isFull(BinaryHeap bh)
{
    return bh->size == bh->capacity - 1; 
}

//judge whether the BinaryHeap is empty or not , also 1 or 0 
int isEmpty(BinaryHeap bh)
{
    return bh->size == 0;
}

// get the left child of node under index with startup 1
int leftChildFromOne(int index)
{
    return index * 2;
}

void printBinaryHeap(BinaryHeap bh)
{
    int i;
    ElementType *temp;
    
    if(!bh)
        Error("printing execution failure, for binary heap is null, from func printBinaryHeap");    

    temp = bh->elements;
    for(i = 1; i < bh->capacity; i++)
    {
        printf("\n\t heap[%d] = ", i);
        if(i <= bh->size)
            printf("vertex[%d] + distance[%d]", bh->elements[i]->vertexIndex+1, bh->elements[i]->distance);     
        else
            printf("NULL");
    }
    printf("\n");   
}  

//print the binary heap who starts from index 0
void printBinaryHeapFromZero(BinaryHeap bh)
{
    int i;
    ElementType *temp;
    
    if(!bh)
        Error("printing execution failure, for binary heap is null, from func printBinaryHeap");    

    temp = bh->elements;
    for(i = 0; i < bh->capacity; i++)
    {
        printf("\n\t index[%d] = ", i);
        if(i < bh->size)
            printf("%d", bh->elements[i]->distance);
        else
            printf("NULL");
    }
    printf("\n");
}  

void swap(ElementType x, ElementType y)
{
    struct Distance temp;
    
    temp = *x;
    *x = *y;
    *y = temp;  
}

ElementType deleteMin(BinaryHeap bh, int* heapIndexRecord)
{   
    ElementType minimum;
    ElementType *data;  
    
    if(isEmpty(bh))
    {
        Error("failed deleting minimum , for the BinaryHeap is empty, from func deleteMin !");
        return NULL;    
    }

    data = bh->elements;     
    minimum = data[1];
    
    swap(data[1], data[bh->size]);      
    bh->size-- ; // size-- occurs prior to percolateDownFromOne 
    percolateDownFromOne(1, bh, heapIndexRecord) ;  
    return minimum;
} 

// percolating down the element when its value is greater than children (minimal heap)
 //Attention: all of bh->elements starts from index 1
 void percolateDownFromOne(int index, BinaryHeap bh, int* heapIndexRecord)
 {  
    ElementType *data;
    int size;
    struct Distance temp;
    int child;

    data = bh->elements;
    size = bh->size;    

    for(temp = *data[index]; leftChildFromOne(index) <= size; index = child)
    {
        child = leftChildFromOne(index);
        if(child < size && data[child]->distance > data[child+1]->distance)
            child++;
        if(temp.distance > data[child]->distance)
        {           
            *data[index] = *data[child];            
            heapIndexRecord[bh->elements[index]->vertexIndex] = index; //update the heapIndexRecord
        }
        else
            break;
    }   
    *data[index] = temp;    
    heapIndexRecord[bh->elements[index]->vertexIndex] = index; //update the heapIndexRecord
 }

// Attention, the index of the heap starts from 1
// return the index the element inserted into the binary heap
void insert(ElementType value, BinaryHeap bh, int* heapIndexRecord)
{
    int i;
    
    if(isFull(bh))
    {
        Error("failed insertion , for the BinaryHeap is full, from func insert!");
        return ;    
    }   
    if(!isEmpty(bh))
        for(i = ++bh->size; bh->elements[i/2]->distance > value->distance; i /= 2)                  
        {
            //copyElement(bh->elements[i/2], bh->elements[i]);       
            *bh->elements[i] = *bh->elements[i/2];
            heapIndexRecord[bh->elements[i]->vertexIndex] = i; //update the heapIndexRecord
        }
    else
        i = ++bh->size;     
    *bh->elements[i] = *value;
    heapIndexRecord[bh->elements[i]->vertexIndex] = i; //update the heapIndexRecord
}

BinaryHeap initBinaryHeap(int capacity)
{
    BinaryHeap bh;
    ElementType *temp;
    int i;

    bh = (BinaryHeap)malloc(sizeof(struct BinaryHeap));
    if(!bh) {
        Error("out of space, from func initBinaryHeap");        
        return NULL;
    }  
    bh->capacity = capacity;
    bh->size = 0;

    temp = (ElementType*)malloc(capacity * sizeof(Distance));
    if(!temp) {
        Error("out of space, from func initBinaryHeap");        
        return NULL;
    } 
    bh->elements = temp;
    
    for(i=0; i < capacity; i++)
    {
        temp[i] = (ElementType)malloc(sizeof(struct Distance));
        if(!temp[i]) {
            Error("out of space, from func initBinaryHeap");        
            return NULL;
        }       
    }

    return bh;
}

// allocate the memory for storing index of  vertex in heap and let every element -1
int *makeEmptyArray(int size)
{
    int *array;
    int i;

    array = (int*)malloc(size * sizeof(int));
    if(!array)
    {
        Error("out of space ,from func makeEmptyArray");
        return NULL;
    }       
    for(i=0; idistance = data[i];
        tempDisStruct->vertexIndex = i;
        insert(tempDisStruct, bh, indexOfVertexInHeap);
    }   
    printBinaryHeap(bh);
    printIndexOfVertexInHeap(bh->size, indexOfVertexInHeap);

    printf("\n\t=== test for inserting the binary heap with element {100, 20, 90} in turn ===\n");
    
    tempDisStruct->distance = 100;
    tempDisStruct->vertexIndex = size;
    insert(tempDisStruct, bh, indexOfVertexInHeap); 
    printBinaryHeap(bh);

    tempDisStruct->distance = 20;
    tempDisStruct->vertexIndex = size+1;
    insert(tempDisStruct, bh, indexOfVertexInHeap); 
    printBinaryHeap(bh);

    tempDisStruct->distance = 90;
    tempDisStruct->vertexIndex = size+2;
    insert(tempDisStruct, bh, indexOfVertexInHeap); 
    printBinaryHeap(bh);

    printIndexOfVertexInHeap(bh->size, indexOfVertexInHeap);

    printf("\n\t=== test for inserting the binary heap with 5 ===\n");  
    tempDisStruct->distance = 5;
    tempDisStruct->vertexIndex = size+3;
    insert(tempDisStruct, bh, indexOfVertexInHeap); 
    printBinaryHeap(bh);

    printf("\n\t=== test for 3 deletings towards the minimum in binary heap ===\n");
    deleteMin(bh, indexOfVertexInHeap); 
    printBinaryHeap(bh);
    deleteMin(bh, indexOfVertexInHeap);     
    printBinaryHeap(bh);
    deleteMin(bh, indexOfVertexInHeap); 
    printBinaryHeap(bh);
}

3.3）printing results：

转载于:https://www.cnblogs.com/pacoson/p/4976629.html