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//算法6.13 关键路径算法
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#include <iostream>
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using namespace std;
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#define MVNum 100 //最大顶点数
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#define BDNum MVNum * (MVNum - 1) //最大边数
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#define OK 1
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#define ERROR 0
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typedef char VerTexType;
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//- - - - -图的邻接表存储表示- - - - -
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typedef struct ArcNode{ //边结点
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int adjvex; //该边所指向的顶点的位置
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int weight; //权值
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struct ArcNode *nextarc; //指向下一条边的指针
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}ArcNode;
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typedef struct VNode{
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VerTexType data; //顶点信息
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ArcNode *firstarc; //指向第一条依附该顶点的边的指针
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}VNode, AdjList[MVNum]; //AdjList表示邻接表类型
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typedef struct{
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AdjList vertices; //邻接表
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AdjList converse_vertices; //逆邻接表
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int vexnum, arcnum; //图的当前顶点数和边数
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}ALGraph;
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//- - - - - - - - - - - - - - - -
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//- - - - -顺序栈的定义- - - - -
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typedef struct{
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int *base;
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int *top;
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int stacksize;
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}spStack;
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//- - - - - - - - - - - - - - - -
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int indegree[MVNum]; //数组indegree存放个顶点的入度
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int ve[BDNum]; //事件vi的最早发生时间
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int vl[BDNum]; //事件vi的最迟发生时间
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int topo[MVNum]; //记录拓扑序列的顶点序号
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spStack S;
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//----------------栈的操作--------------------
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void InitStack(spStack &S){
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//栈的初始化
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S.base = new int[MVNum];
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if(!S.base)
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exit(1);
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S.top = S.base;
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S.stacksize = MVNum;
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}//InitStack
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void Push(spStack &S , int i){
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//入栈
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if(S.top - S.base == S.stacksize)
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return;
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*S.top++ = i;
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}//Push
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void Pop(spStack &S , int &i){
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//出栈
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if(S.top == S.base)
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return;
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i = *--S.top;
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}//Pop
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bool StackEmpty(spStack S){
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//判断栈是否为空
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if(S.top == S.base)
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return true;
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return false;
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}//StackEmpty
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//---------------------------------------
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int LocateVex(ALGraph G , VerTexType v){
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//确定点v在G中的位置
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for(int i = 0; i < G.vexnum; ++i)
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if(G.vertices[i].data == v)
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return i;
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return -1;
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}//LocateVex
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int CreateUDG(ALGraph &G){
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//创建有向图G的邻接表、逆邻接表
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int i , k;
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cout <<"请输入总顶点数，总边数，以空格隔开:";
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cin >> G.vexnum >> G.arcnum; //输入总顶点数，总边数
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cout << endl;
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cout << "输入点的名称，如a" << endl;
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for(i = 0; i < G.vexnum; ++i){ //输入各点，构造表头结点表
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cout << "请输入第" << (i+1) << "个点的名称:";
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cin >> G.vertices[i].data; //输入顶点值
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G.converse_vertices[i].data = G.vertices[i].data;
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//初始化表头结点的指针域为NULL
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G.vertices[i].firstarc=NULL;
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G.converse_vertices[i].firstarc=NULL;
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}//for
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cout << endl;
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cout << "输入边依附的顶点及其权值，如a b 3" << endl;
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for(k = 0; k < G.arcnum;++k){ //输入各边，构造邻接表
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VerTexType v1 , v2;
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int i , j , w;
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cout << "请输入第" << (k + 1) << "条边依附的顶点及其权值:";
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cin >> v1 >> v2 >> w; //输入一条边依附的两个顶点
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i = LocateVex(G, v1); j = LocateVex(G, v2);
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//确定v1和v2在G中位置，即顶点在G.vertices中的序号
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ArcNode *p1=new ArcNode; //生成一个新的边结点*p1
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p1->adjvex=j; //邻接点序号为j
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p1->nextarc = G.vertices[i].firstarc; G.vertices[i].firstarc=p1;
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p1->weight = w;
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//将新结点*p1插入顶点vi的边表头部
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ArcNode *p2=new ArcNode; //生成一个新的边结点*p1
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p2->adjvex=i; //逆邻接点序号为i
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p2->nextarc = G.converse_vertices[j].firstarc; G.converse_vertices[j].firstarc=p2;
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p2->weight = w;
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//将新结点*p1插入顶点vi的边表头部
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}//for
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return OK;
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}//CreateUDG
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void FindInDegree(ALGraph G){
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//求出各顶点的入度存入数组indegree中
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int i , count;
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for(i = 0 ; i < G.vexnum ; i++){
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count = 0;
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ArcNode *p = G.converse_vertices[i].firstarc;
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if(p){
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while(p){
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p = p->nextarc;
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count++;
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}
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}//if
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indegree[i] = count;
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}//for
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}//FindInDegree
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int TopologicalOrder(ALGraph G , int topo[]){
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//有向图G采用邻接表存储结构
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//若G无回路，则生成G的一个拓扑序列topo[]并返回OK，否则ERROR
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int i , m;
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FindInDegree(G); //求出各顶点的入度存入数组indegree中
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InitStack(S); //栈S初始化为空
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for(i = 0; i < G.vexnum; ++i)
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if(!indegree[i]) Push(S, i); //入度为0者进栈
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m = 0; //对输出顶点计数，初始为0
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while(!StackEmpty(S)){ //栈S非空
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Pop(S, i); //将栈顶顶点vi出栈
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topo[m]=i; //将vi保存在拓扑序列数组topo中
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++m; //对输出顶点计数
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ArcNode *p = G.vertices[i].firstarc; //p指向vi的第一个邻接点
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while(p){
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int k = p->adjvex; //vk为vi的邻接点
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--indegree[k]; //vi的每个邻接点的入度减1
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if(indegree[k] ==0) Push(S, k); //若入度减为0，则入栈
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p = p->nextarc; //p指向顶点vi下一个邻接结点
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}//while
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}//while
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if(m < G.vexnum) return ERROR; //该有向图有回路
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else return OK;
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}//TopologicalOrder
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int CriticalPath(ALGraph G){
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//G为邻接表存储的有向网，输出G的各项关键活动
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int n , i , k , j , e , l;
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if (!TopologicalOrder(G, topo)) return ERROR;
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//调用拓扑排序算法，使拓扑序列保存在topo中，若调用失败，则存在有向环，返回ERROR
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n = G.vexnum; //n为顶点个数
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for(i = 0; i < n; i++) //给每个事件的最早发生时间置初值0
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ve[i] = 0;
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/*――――――――――按拓扑次序求每个事件的最早发生时间－――――－―――――*/
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for(i = 0;i < n; i++){
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k = topo[i]; //取得拓扑序列中的顶点序号k
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ArcNode *p = G.vertices[k].firstarc; //p指向k的第一个邻接顶点
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while(p != NULL){ //依次更新k的所有邻接顶点的最早发生时间
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j = p->adjvex; //j为邻接顶点的序号
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if(ve[j] < ve[k] + p->weight) //更新顶点j的最早发生时间ve[j]
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ve[j] = ve[k] + p->weight;
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p = p->nextarc; //p指向k的下一个邻接顶点
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} //while
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} //for
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for(i=0;i<n;i++) //给每个事件的最迟发生时间置初值ve[n-1]
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vl[i]=ve[n-1];
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/*――――――――――按逆拓扑次序求每个事件的最迟发生时间－――――－―――――*/
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for(i = n - 1;i >= 0; i--){
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k = topo[i]; //取得拓扑序列中的顶点序号k
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ArcNode *p = G.vertices[k].firstarc; //p指向k的第一个邻接顶点
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while(p != NULL){ //根据k的邻接点，更新k的最迟发生时间
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j = p->adjvex; //j为邻接顶点的序号
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if(vl[k] > vl[j] - p->weight) //更新顶点k的最迟发生时间vl[k]
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vl[k] = vl[j] - p->weight;
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p = p->nextarc; //p指向k的下一个邻接顶点
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}//while
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}//for
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/*――――――――――――判断每一活动是否为关键活动－――――――－―――――*/
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cout << endl;
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cout << "关键活动路径为:";
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for(i = 0;i < n; i++){ //每次循环针对vi为活动开始点的所有活动
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ArcNode *p = G.vertices[i].firstarc; //p指向i的第一个邻接顶点
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while(p != NULL) {
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j = p->adjvex; //j为i的邻接顶点的序号
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e = ve[i]; //计算活动<vi, vj>的最早开始时间
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l = vl[j] - p->weight; //计算活动<vi, vj>的最迟开始时间
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if(e == l) //若为关键活动，则输出<vi, vj>
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cout << G.vertices[i].data << "-->" << G.vertices[j].data << " ";
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p = p->nextarc; //p指向i的下一个邻接顶点
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} //while
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} //for
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return OK;
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}//CriticalPath
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int main(){
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cout << "************算法6.13 关键路径算法**************" << endl << endl;
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ALGraph G;
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CreateUDG(G);
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int *topo = new int [G.vexnum];
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cout << endl;
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cout << "有向图创建完成!" << endl << endl;
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if(!CriticalPath(G))
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cout << "网中存在环，无法进行拓扑排序！" <<endl << endl;
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cout << endl;
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return OK;
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}//main
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