关键路径（AOE）---《数据结构》严蔚敏

// exam1.cpp : 定义控制台应用程序的入口点。
//

#include "stdafx.h"
#include <iostream>
#include <stack>
using namespace std;

#define MAXVEX 20

typedef struct ArcNode
{
	int adjvex;
	int weight;
	struct ArcNode* nextarc;
}ArcNode;

typedef struct HeadNode
{
	int data;
	ArcNode* firstarc;
}HeadNode;

typedef struct ALGraph
{
	int arcnum;
	int vexnum;
	int* ve;
	int* vl;
	HeadNode vex[MAXVEX];
}ALGraph;

void InitALGraph(ALGraph& G)
{
	cout<<"please enter the number of the vertex:"<<endl;
	cin>>G.vexnum;

	G.arcnum=0;
	for(int i=1;i<G.vexnum+1;i++)
	{
		G.vex[i].data=i;
		G.vex[i].firstarc=NULL;
	}

	cout<<"please enter the Arc..."<<endl;
	cout<<"head tail weight"<<endl;
	int adj1,adj2,w;
	while(cin>>adj1>>adj2>>w)
	{
		G.arcnum++;
		ArcNode* arc;
		arc=G.vex[adj1].firstarc;
		if(arc==NULL)
		{
			G.vex[adj1].firstarc=(ArcNode*)malloc(sizeof(ArcNode));
			arc=G.vex[adj1].firstarc;
			arc->adjvex=adj2;
			arc->weight=w;
			arc->nextarc=NULL;
		}
		else
		{
			while(arc->nextarc)
			{
				arc=arc->nextarc;
			}
			arc->nextarc=(ArcNode*)malloc(sizeof(ArcNode));
			arc->nextarc->adjvex=adj2;
			arc->nextarc->weight=w;
			arc->nextarc->nextarc=NULL;
		}
	}

	for(int i=1;i<G.vexnum+1;i++)
	{
		cout<<"vextex"<<i<<"'s adjacent vertices are:";
		ArcNode* arc;
		arc=G.vex[i].firstarc;
		while(arc!=NULL)
		{
			cout<<arc->adjvex<<"-"<<arc->weight<<" ";
			arc=arc->nextarc;
		}
		cout<<endl;
	}
}

void CalIndegree(ALGraph G,int* indegree)
{
	for(int i=1;i<G.vexnum+1;i++)
	{
		ArcNode* arc;
		arc=G.vex[i].firstarc;
		while(arc!=NULL)
		{
			indegree[arc->adjvex]++;
			arc=arc->nextarc;
		}
	}
}

int TopologicalOrder(ALGraph &G,stack<int> &TNode)
{
	int *indegree=(int*)malloc(sizeof(int)*(G.vexnum+1));
	memset(indegree,0,sizeof(int)*(G.vexnum+1));
	G.ve=(int*)malloc(sizeof(int)*(G.vexnum+1));
	memset(G.ve,0,sizeof(int)*(G.vexnum+1));

	CalIndegree(G,indegree);
	stack<int> s;

	for(int i=1;i<G.vexnum+1;i++)
	{
		if(indegree[i]==0)
		{
			s.push(i);
		}
	}

	cout<<"The topological sort of the graph is"<<endl;
	int count=0;
	while(!s.empty())
	{
		int i=s.top();
		TNode.push(i);
		s.pop();
		cout<<i<<" ";
		count++;

		ArcNode* arc;
		arc=G.vex[i].firstarc;
		while(arc!=NULL)
		{
			if(G.ve[i]+arc->weight>G.ve[arc->adjvex])
			{
				G.ve[arc->adjvex]=G.ve[i]+arc->weight;
			}

			if(--indegree[arc->adjvex]==0)
			{
				s.push(arc->adjvex);
			}
			arc=arc->nextarc;
		}
	}

	cout<<endl;
	if(count==G.vexnum)
	{
		cout<<"No loop in the graph..."<<endl;
	}
	else
	{
		cout<<"There are a loop in the graph..."<<endl;
		return 0;
	}

	cout<<"The early staring time is:"<<endl;
	for(int i=1;i<G.vexnum+1;i++)
	{
		cout<<G.ve[i]<<" ";
	}
	cout<<endl;

	return 1;
}

void CriticalPath(ALGraph G)
{
	G.vl=(int*)malloc(sizeof(int)*(G.vexnum+1));
	memset(G.vl,0,sizeof(int)*(G.vexnum+1));
	stack<int> s;

	if(TopologicalOrder(G,s))
	{
		for(int i=1;i<G.vexnum+1;i++)
		{
			G.vl[i]=G.ve[G.vexnum];
		}
		while(!s.empty())
		{
			int i=s.top();
			s.pop();

			ArcNode* arc;
			arc=G.vex[i].firstarc;

			while(arc!=NULL)
			{
				int k=arc->adjvex;
				if(G.vl[k]-arc->weight<G.vl[i])
				{
					G.vl[i]=G.vl[k]-arc->weight;
				}
				arc=arc->nextarc;
			}
		}
	}
	else
	{
		return;
	}

	cout<<"The laster starting time is:"<<endl;
	for(int i=1;i<G.vexnum+1;i++)
	{
		cout<<G.vl[i]<<" ";
	}
	cout<<endl;

	cout<<"The critical path of the graph is:"<<endl;
	for(int i=1;i<G.vexnum+1;i++)
	{
		ArcNode* arc;
		arc=G.vex[i].firstarc;
		while(arc!=NULL)
		{
			int k=arc->adjvex;
			if(G.ve[i]==G.vl[k]-arc->weight)
			{
				cout<<G.vex[i].data<<"->"<<G.vex[k].data<<endl;
			}
			arc=arc->nextarc;
		}
	}

	return;
}

int main(void)
{
	ALGraph G;
	InitALGraph(G);	

	CriticalPath(G);

	system("pause");
	return 0;
}