Johnson算法「建议收藏」

Jetbrains全家桶1年46，售后保障稳定

C++版:

/************************************************************ 
Johnson.h: Johnson算法，存储为邻接表， 
Date: 2014/1/5 
Author: searchop 
************************************************************/  
#ifndef ALGRAPH_H  
#define ALGRAPH_H  
#include   
#include   
#include   
#include   
#include   
#include   
using namespace std;  
//邻接表的结构  
struct ArcNode          //表结点  
{  
int source;        //图中该弧的源节点  
int adjvex;        //该弧所指向的顶点的位置  
ArcNode *nextarc;  //指向下一条弧的指针  
int weight;         //每条边的权重  
};  
template   
struct VertexNode           //头结点  
{  
VertexType data;    //顶点信息  
ArcNode *firstarc;  //指向第一条依附于该顶点的弧的指针  
int key;            //Prim:保存连接该顶点和树中结点的所有边中最小边的权重;   
//BellmanFord:记录从源结点到该结点的最短路径权重的上界  
VertexNode *p;      //指向在树中的父节点  
int indegree;       //记录每个顶点的入度  
};  
const int SIZE = 6;  
//图的操作  
template   
class ALGraph  
{  
public:  
typedef VertexNode VNode;  
ALGraph(int verNum) : vexnum(verNum), arcnum(0)  
{  
for (int i = 0; i < MAX_VERTEX_NUM; i++)  
{  
vertices[i].firstarc = NULL;  
vertices[i].key = INT_MAX/2;  
vertices[i].p = NULL;  
vertices[i].indegree = 0;  
}  
}  
//构造算法导论410页图（带权有向图）  
void createWDG()  
{  
cout << "构造算法导论410页图（带权有向图）..." << endl;  
int i;  
for (i = 1; i < vexnum; i++)  
vertices[i].data = 'a' + i - 1;       
insertArc(1, 2, 3);  
insertArc(1, 3, 8);  
insertArc(1, 5, -4);  
insertArc(2, 4, 1);  
insertArc(2, 5, 7);  
insertArc(3, 2, 4);  
insertArc(4, 3, -5);  
insertArc(4, 1, 2);  
insertArc(5, 4, 6);  
}  
void createG()  
{  
cout << "构造图G'...." << endl;  
vertices[0].data = 's';  
insertArc(0, 1, 0);  
insertArc(0, 2, 0);  
insertArc(0, 3, 0);  
insertArc(0, 4, 0);  
insertArc(0, 5, 0);  
}  
//Johnson算法，先使用BellmanFord算法，使所有的边的权重变为非负值，  
//然后运用dijkstra算法求出结点对的最短路径  
int **Johnson()  
{  
createG();          //构造G’  
displayGraph();  
if (!BellmanFord(1))  
cout << "the input graph contains a negative-weight cycle" << endl;  
else  
{  
int h[SIZE];  
int i, j, k;  
//将数组h[]的值设为运行BellmanFord后取得的值，h[i]为结点s到其他点的最短路径  
for (i = 0; i < vexnum; i++)  
h[i] = vertices[i].key;  
//遍历所有的边，将边的权值重新赋值,即将所有的边的权值改为负值  
for (i = 0; i < vexnum; i++)  
{  
ArcNode *arc = vertices[i].firstarc;  
for (; arc != NULL; arc = arc->nextarc)  
arc->weight = arc->weight + h[arc->source] - h[arc->adjvex];  
}     
以下为代码：  
cout << "改变权重后的图为：" << endl;                                                                                                                     displayGraph();  
int **d = new int *[SIZE];  
for (j = 0; j < SIZE; j++)  
d[j] = new int[SIZE];  
//对每个结点运行dijkstra算法，求出每个点到其他点的最短路径，保存在key中  
for (k = 1; k < SIZE; k++)  
{  
Dijkstra(k+1);  
for (i = 1; i < SIZE; i++)  
d[k][i] = vertices[i].key + h[i] - h[k];  
}  
cout << "最后计算出的结点对的最短距离：" << endl;  
displayTwoDimArray(d);  
return d;  
}  
}  
//输出一个二维数组  
void displayTwoDimArray(int **p)  
{  
for (int i = 0; i < SIZE; i++)  
{  
for (int j = 0; j < SIZE; j++)  
cout << p[i][j] << " ";  
cout << endl;  
}  
cout << "~~~~~~~~~~~~~~~" << endl;  
}  
//打印邻接链表  
virtual void displayGraph()  
{  
for (int i = 0; i < vexnum; i++)  
{  
cout << "第" << i+1 << "个顶点是：" << vertices[i].data  
<< " 顶点的入度为：" << vertices[i].indegree << " 邻接表为: ";  
ArcNode *arcNode = vertices[i].firstarc;  
while (arcNode != NULL)  
{  
cout << " -> " << vertices[arcNode->adjvex].data  
<< "(" << arcNode->weight << ")";  
arcNode = arcNode->nextarc;  
}  
cout << endl;  
}  
cout << "*******************************************************" << endl;  
}  
//PVnode排序准则  
class PVNodeCompare  
{  
public:  
bool operator() (VNode *pvnode1, VNode *pvnode2)  
{  
return pvnode1->key > pvnode2->key;  
}  
};  
//对每个结点的最短路径估计和前驱结点进行初始化，最短路径初始化为INT_MAX, p初始化为NULL  
//并将源节点的key初始化为0  
void InitalizeSingleSource(int index)  
{  
for (int i = 0; i < MAX_VERTEX_NUM; i++)  
{  
vertices[i].key = INT_MAX>>2;  
vertices[i].p = NULL;  
}  
vertices[index].key = 0;  
}  
//对边（u, v）进行松弛，将目前s到v的最短路径v.key与s到u的最短路径加上w(u, v)的值进行比较  
//如果比后面的值还大，则进行更新，将v.key缩短，并且将p置为u  
void relax(ArcNode *arc)  
{  
//竟然溢出了！！  
if (vertices[arc->adjvex].key > vertices[arc->source].key + arc->weight)  
{  
vertices[arc->adjvex].key = vertices[arc->source].key + arc->weight;  
vertices[arc->adjvex].p = &vertices[arc->source];  
}  
}  
//BellmanFord, index为实际第几个点  
bool BellmanFord(int index)  
{  
InitalizeSingleSource(index-1);  
for (int i = 1; i < vexnum; i++)     //循环共进行vexnum-1次  
{  
//遍历所有的边，并对每个边进行一次松弛  
for (int j = 0; j < vexnum; j++)  
{  
for (ArcNode *arc = vertices[j].firstarc; arc != NULL; arc = arc->nextarc)  
relax(arc);  
}  
}  
//再次遍历所有的边，检查图中是否存在权重为负值的环路，如果存在，则返回false  
for (int j = 0; j < vexnum; j++)  
{  
for (ArcNode *arc = vertices[0].firstarc; arc != NULL; arc = arc->nextarc)  
{  
if (vertices[arc->adjvex].key > vertices[arc->source].key + arc->weight)  
return false;  
}  
}  
cout << "BellmanFord求出的单源最短路径：" << endl;  
for (int i = 1; i < vexnum; i++)  
{  
printPath(index-1, i);  
}  
cout << "**************************************************" << endl;  
return true;  
}  
void Dijkstra(int index)  
{  
InitalizeSingleSource(index-1);  
vector snode;       //保存已经找到最短路径的结点  
vector que;       //保存结点的指针的数组，用这个数组执行堆的算法  
//将结点指针进队列，形成以key为关键值的最小堆  
for (int i = 0; i < vexnum; i++)  
que.push_back(&(vertices[i]));  
//使que按照pvnodecompare准则构成一个最小堆  
make_heap(que.begin(), que.end(), PVNodeCompare());     
while (que.empty() == false)  
{  
//将队列中拥有最小key的结点出队  
VNode *node = que.front();  
pop_heap(que.begin(), que.end(), PVNodeCompare());   //从堆中删除最小的结点，只是放到了vector的最后  
que.pop_back();      //将vector中的这个结点彻底删除，因为后面还要再排序一次，以免影响后面的堆排序，pop算法。  
snode.push_back(*node);  
for (ArcNode *arc = node->firstarc; arc != NULL; arc = arc->nextarc)  
relax(arc);  
make_heap(que.begin(), que.end(), PVNodeCompare());  
}  
cout << "Dijkstra求出的单源最短路径：" << endl;  
for (int i = 1; i < vexnum; i++)  
{  
if (i != index-1)  
printPath(index-1, i);  
}  
cout << "**************************************************" << endl;  
}  
protected:  
//插入一个表结点  
void insertArc(int vHead, int vTail, int weight)  
{  
//构造一个表结点  
ArcNode *newArcNode = new ArcNode;  
newArcNode->source = vHead;  
newArcNode->adjvex = vTail;  
newArcNode->nextarc = NULL;  
newArcNode->weight = weight;  
//arcNode 是vertics[vHead]的邻接表  
ArcNode *arcNode = vertices[vHead].firstarc;  
if (arcNode == NULL)  
vertices[vHead].firstarc = newArcNode;  
else  
{  
while (arcNode->nextarc != NULL)  
{  
arcNode = arcNode->nextarc;        
}  
arcNode->nextarc = newArcNode;  
}  
arcnum++;  
vertices[vTail].indegree++;         //对弧的尾结点的入度加1  
}  
//打印源节点到i的最短路径  
void printPath(int i, int j)  
{  
cout << "从源节点 " << vertices[i].data << " 到目的结点 "  
<< vertices[j].data << " 的最短路径是：" /*<< endl*/;  
__printPath(&vertices[i], &vertices[j]);  
cout << " 权重为：" << vertices[j].key << endl;  
}  
void __printPath(VNode* source, VNode* dest)  
{  
if (source == dest)  
cout << source->data << "->";  
else if (dest->p == NULL)  
cout << " no path！" << endl;  
else  
{  
__printPath(source, dest->p);  
cout << dest->data << "->";  
}  
}  
private:  
//const数据成员必须在构造函数里初始化  
static const int MAX_VERTEX_NUM = 20;  //最大顶点个数  
VNode vertices[MAX_VERTEX_NUM];      //存放结点的数组  
int vexnum;             //图的当前顶点数  
int arcnum;             //图的弧数  
};  

转载于:https://my.oschina.net/piorcn/blog/824353

版权声明：本文内容由互联网用户自发贡献，该文观点仅代表作者本人。本站仅提供信息存储空间服务，不拥有所有权，不承担相关法律责任。如发现本站有涉嫌侵权/违法违规的内容， 请发送邮件至 举报，一经查实，本站将立刻删除。

发布者：全栈程序员栈长，转载请注明出处：https://javaforall.cn/200706.html原文链接：https://javaforall.cn

原文地址：https://cloud.tencent.com/developer/article/2150122