所有节点最短路径的Johnson实现

本文主要是介绍所有节点最短路径的Johnson实现，希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！

一、数据集形式

这里写图片描述
其中：6105（节点个数） 7035（边数）
0（id） 1609（起始边） 1622（终边） 57.403187（权重）

二、数据集

数据集下载链接

三、实现代码

// Dijkstra.cpp : Defines the entry point for the console application.
//#include "stdafx.h"
#include "time.h"
#include <fstream>
#include<iostream>
#include <stack>
#include <queue>
#include<algorithm>
using namespace std;
int nodeNumber;
int edgeNumber;#define PATH "E://dataset//MapSet//MinCreateTree//Testnew.txt"//#define PATH "E://dataset//MapSet//MinCreateTree//Ol.txt"
//#define PATH "E://dataset//MapSet//MinCreateTree//TGRoad.txt"
//#define PATH "E://dataset//MapSet//MinCreateTree//California.txt"
class CWeightSort {
public:int value;double weight;CWeightSort *before;CWeightSort *next;
};
class CTreeNode
{
public:CTreeNode(){}~CTreeNode() {}int value;double  weight;CTreeNode *next;
};
class CTree
{
public:CTree() {weight = 65535;smallWeigth = NULL;}~CTree() {}int value;CTreeNode *next;CTree *before;double weight;CWeightSort *smallWeigth;bool state;
};
CTree * S;
CTree* createTree(char* filename)
{CTree *tree;ifstream ReadFile;int temp;ReadFile.open(filename, ios::in);//ios::in 表示以只读的方式读取文件ReadFile >> nodeNumber;//第一个字符是数组长度ReadFile >> edgeNumber;tree = new CTree[nodeNumber];S = new CTree;S->weight = 0;S->value = 0;S->next = NULL;S->before = NULL;CTreeNode *nt;//为树赋初值for (int i = 0; i < nodeNumber; i++){nt = new CTreeNode;nt->value = i;nt->weight = 0;nt->next = S->next;S->next = nt;tree[i].next = NULL;tree[i].value = i;tree[i].before = NULL;}while (!ReadFile.eof())            //按空格读取，遇到空白符结束{nt = new CTreeNode();       //读出的数据新建一个节点ReadFile >> temp;ReadFile >> temp;ReadFile >> (nt->value);ReadFile >> (nt->weight);nt->next = tree[temp].next;tree[temp].next = nt;}return tree;
}
//Bellman算法
queue<CTree *> myQ;
void Bellman(CTree *t, CTree *tree)
{CTreeNode *p = t->next;while (p != NULL){//链接的节点已经完成，不做任何改变if (t->weight != 65535 && tree[p->value].weight>t->weight + p->weight){//cout << tree[p->value].value << " ";tree[p->value].weight = t->weight + p->weight;tree[p->value].before = t;//Bellman(tree, p->value);myQ.push(&tree[p->value]);}p = p->next;}
}
void Bell(CTree *S,CTree *tree)
{myQ.push(S);while (!myQ.empty()){Bellman(myQ.front(), tree);myQ.pop();}
}
double **Johnson; 
//Dijkstra 算法
class CQueue {                                  //一个保持队形的队列结构
public:CQueue() {que = new CWeightSort();que->next = NULL;}void Add(CWeightSort *nq) {//将新节点按顺序插入到队列上CWeightSort *q = que;while (q->next != NULL){if (nq->weight < q->next->weight){q->next->before = nq;nq->next = q->next;nq->before = q;q->next = nq;break;}q = q->next;}if (q->next == NULL){nq->next = q->next;nq->before = q;q->next = nq;}}CWeightSort * del(CWeightSort *nq){nq->before->next = nq->next;if (nq->next != NULL)nq->next->before = nq->before;return nq;}bool empty(){if (que->next == NULL)return true;return false;}CWeightSort *que;
};
void initDijkstra(CTree *tree, int in)
{for (int i = 0; i < nodeNumber; i++){tree[i].state=true;tree[i].before = NULL; //delete tree[i].smallWeigth;tree[i].smallWeigth = NULL;}tree[in].smallWeigth = new CWeightSort;tree[in].smallWeigth->weight = 0;
}
CTree* Dijkstra(CTree *tree,int in)
{initDijkstra(tree, in);CQueue myQue;CWeightSort *myi = new CWeightSort;myi->value = in;myi->before = NULL;myQue.Add(myi);CWeightSort *nt = NULL;while (!myQue.empty()){nt = myQue.del(myQue.que->next);Johnson[in][nt->value] = nt->weight + tree[nt->value].weight - tree[in].weight;//如果在这里设置数组可以得到所有值，但占用空间太大//cout << nt->value << "(" << nt->weight << ")" << " ";//标记这个节点为已经访问状态tree[nt->value].state = false;CTreeNode *p = tree[nt->value].next;while (p != NULL){//链接的节点已经完成，不做任何改变if (tree[p->value].state){//链接的节点，没有更小的值if (tree[p->value].smallWeigth == NULL){CWeightSort *node = new CWeightSort;node->value = p->value;node->weight = tree[nt->value].smallWeigth->weight + p->weight;tree[p->value].smallWeigth = node;tree[p->value].before = &tree[nt->value];myQue.Add(node);}//链接的节点，存在更小的值else if (tree[p->value].smallWeigth->weight>tree[nt->value].smallWeigth->weight + p->weight){CWeightSort *node = myQue.del(tree[p->value].smallWeigth);node->value = p->value;node->weight = tree[nt->value].smallWeigth->weight + p->weight;tree[p->value].smallWeigth = node;tree[p->value].before = &tree[nt->value];myQue.Add(node);}}p = p->next;}}return &tree[nt->value];
}
int main()
{//构建图CTree *tree = createTree(PATH);double useTime;clock_t start, finish;start = clock();//修改图中的weightBell(S,tree);//对图边的权重进行改变for (int i = 0; i < nodeNumber; i++){CTreeNode *p = tree[i].next;while (p!=NULL){p->weight = p->weight + tree[0].weight - tree[p->value].weight;p = p->next;}}//对于每个节点进行DijkstraJohnson = new double *[nodeNumber];for (int i = 0; i < nodeNumber ; i++){Johnson[i] = new double[nodeNumber];memset(Johnson[i], 65535, sizeof(double)*nodeNumber);}for (int i = 0; i < nodeNumber; i++){CTree *q = Dijkstra(tree, i);}finish = clock();useTime = (double)(finish - start) / CLOCKS_PER_SEC * 1000;printf("%f 毫秒\n", useTime);system("pause");return 0;
}