C++基于优先队列基础的prime算法

算法过程：

提示：优先队列基于最小二叉堆实现，最小生成树集合基于双向链表实现，链表单元是一个结构体，包含两个元素，分别是节点的number和节点的weight，另外设置一个一维数组表示该相对应的节点是否被纳入最小生成树集合。

1.将一个图的顶点分为两部分，一部分是最小生成树中的结点（A集合），另一部分是未处理的结点（B集合）。

2.首先选择一个结点，将这个结点加入A中，然后，对集合A中的顶点遍历，找出A中顶点关联的所有边的权值，将这些权值依次入队，然后从最小优先队列中选取最小的那个（设为v），将此顶点从B中删除，加入集合A中。

3.递归重复步骤2，直到B集合中的结点为空，结束此过程。

4.A集合中的结点就是由Prime算法得到的最小生成树的结点，依照步骤2的结点连接这些顶点，得到的就是这个图的最小生成树。

以下是代码部分：

1、从两个txt文件中依次读取节点和节点之间的路径权重，txt文件的格式是：第一行为节点总数，从第二行开始，第一个int型为一个节点number，第二个int型为另一个节点number，之后的float型为连接节点1和节点2之间的路径权重。

2、输出文件格式和输入文件一样。

#include <algorithm>#include <cstdio>#include <iostream>#include <string>#include <cstring>#include <climits>#include<cmath>#include <ctime>#include <fstream>#include <vector>#include <sys/stat.h>#include<algorithm>using namespace std;#define int_max 1000000#define maxnum 100000float sum;int nodeNum, edgeNum;FILE *fp;FILE *newfp;string fileName, fileName2, newFileName, newFileName2 ;int getNumberOfNodes(){int verticeNum;fp=fopen(fileName.c_str(),"rt+");if(fp==NULL) cout<<"no file "<<endl;    fscanf(fp,"%d\n",&verticeNum);    fclose(fp);    cout<<" the node number is "<<verticeNum<<endl;    return verticeNum;}int getNumberOfEdges(){char flag;int edgeNum,count;fp=fopen(fileName.c_str(),"rt+");while(!feof(fp)){flag=fgetc(fp);if(flag=='\n') count++ ;}edgeNum=count;fclose(fp);cout<<" the edge number is "<<edgeNum<<endl;return edgeNum;}typedef struct linkedList{float weg;int nodenum;struct linkedList *next;}linkedList;typedef struct Node{float weg;int nodenum;}Node;typedef struct Heap{Node allnode[maxnum+1];int size;}Heap;linkedList path;Node nodeinHeap;Heap heap;int visited[maxnum+1];void enterheap(int nodenum,float weg){    int i, index;    for(i = 1;i <= heap.size;i ++){        if(heap.allnode[i].nodenum == nodenum){            if(heap.allnode[i].weg > weg){            heap.allnode[i].weg = weg;                for(index = i;heap.allnode[index / 2].weg > weg;index /= 2){                heap.allnode[index].nodenum = heap.allnode[index / 2].nodenum;                heap.allnode[index].weg = heap.allnode[index / 2].weg;                }                heap.allnode[index].nodenum = nodenum;                heap.allnode[index].weg = weg;            }            return ;        }    }    heap.size++;    for(i = heap.size;heap.allnode[i / 2].weg > weg;i /= 2){    heap.allnode[i].nodenum = heap.allnode[i / 2].nodenum;        heap.allnode[i].weg = heap.allnode[i / 2].weg;    }    heap.allnode[i].nodenum = nodenum;    heap.allnode[i].weg = weg;}int extractmin(){return heap.allnode[1].nodenum;//0 or 1?}int sortHeap(){int i, child;heap.allnode[1].nodenum = heap.allnode[heap.size].nodenum;heap.allnode[1].weg = heap.allnode[heap.size].weg;//size-1?heap.size--;for(int i =1;i*2<=heap.size;i=child){child = 2 * i;if(child != heap.size && heap.allnode[child + 1].weg < heap.allnode[child].weg){child++;}if(heap.allnode[child].weg < heap.allnode[i].weg){float wegstore = heap.allnode[i].weg;int nodestore = heap.allnode[i].nodenum;heap.allnode[i].nodenum = heap.allnode[child].nodenum;    heap.allnode[i].weg = heap.allnode[child].weg;    heap.allnode[child].nodenum = nodestore;    heap.allnode[child].weg = wegstore;}else{break;}}return 0;}void buildLinkedList(linkedList *edgeRelation,int beginNode, int endNode,float weg){linkedList *former = &edgeRelation[beginNode];linkedList *nextNode = (linkedList*)malloc(sizeof(linkedList));nextNode->nodenum = endNode;nextNode->weg = weg;nextNode->next = NULL;while(former->next&&former->nodenum!=endNode){former = former->next;}if(former->nodenum ==endNode){if(former->weg>weg){former->weg = weg;}}else{former->next = nextNode;}}int primalg(linkedList *edgeRelation,int wholenode){heap.size = 0;heap.allnode[0].weg = -1;edgeRelation[1].weg = 0;int nodenum;linkedList *conedge;enterheap(1,0);int updateNode = 0;float updateWeg;//int count=0;while(heap.size!=0){nodenum = extractmin();sortHeap();visited[nodenum] = 1;conedge = edgeRelation[nodenum].next;while(conedge){if(visited[conedge->nodenum]==0){//cout<<"enter no visit"<<endl;if(conedge->weg<edgeRelation[conedge->nodenum].weg){edgeRelation[conedge->nodenum].weg = conedge->weg;edgeRelation[conedge->nodenum].nodenum = nodenum;updateNode = conedge->nodenum;updateWeg = edgeRelation[conedge->nodenum].weg;}enterheap(conedge->nodenum, edgeRelation[conedge->nodenum].weg);}conedge = conedge->next;}}return 0;}int main() {cout<<"====================================="<<endl;for (int j = 0; j <= 1; j++) {if (j == 0) {fileName = "sparse_100000.txt";newFileName = "sparseMSF.txt";cout<<"This test is for sparse graph."<<endl;}if (j == 1) {fileName = "dense_100000.txt";newFileName = "denseMSF.txt";cout<<"This test is for dense graph."<<endl;}nodeNum = getNumberOfNodes();edgeNum = getNumberOfEdges();fp = fopen(fileName.c_str(), "rt+");//create the output fileFILE *newfp = fopen(newFileName.c_str(), "wt+");fscanf(fp, "%d\n", &nodeNum);linkedList *linklist = (linkedList*) malloc(sizeof(linkedList) * (nodeNum + 1));for (int i = 1; i <= nodeNum; i++) {linklist[i].nodenum = i;linklist[i].weg = int_max;linklist[i].next = NULL;visited[i] = 0;}float weight;int a, b;for (int i = 1; i <= nodeNum; i++) {fscanf(fp, "%d%d%f\n", &a, &b, &weight);buildLinkedList(linklist, a, b, weight);buildLinkedList(linklist, b, a, weight);}fclose(fp);primalg(linklist, nodeNum);double sum2 = 0;for (int i = 1; i <= nodeNum; i++) {if (linklist[i].weg == int_max) {continue;} else {sum2 += linklist[i].weg;//output the result to filefprintf(newfp, "%d", linklist[i].nodenum);fputs(" ", newfp);fprintf(newfp, "%d", linklist[i].next->nodenum);fputs(" ", newfp);fprintf(newfp, "%f\n", linklist[i].next->weg);}}cout << "The sum weight is " << sum2 << endl;cout<<"====================================="<<endl;}return 0;}