c语言实现
/*AOE-网的关键路径*/
# include<stdio.h>
# include<malloc.h>
# define MAX_VERTEX_NUM 20
# define TRUE 1
# define FALSE 0
/*AOE-网的邻接表表示法*/
typedef char VertexData;
//弧结点结构
typedef struct ArcNode {
int adjvex; //该弧指向顶点的位置
struct ArcNode* nextarc; //指向下一条弧的指针
int activity; //弧表示的活动
int weight; //权值
}ArcNode;
//表头结点结构
typedef struct VertexNode {
VertexData data; //顶点数据
ArcNode* firstarc; //指向该顶点的第一条弧的指针
}VertexNode;
//邻接表结构
typedef struct {
VertexNode vertex[MAX_VERTEX_NUM];
int vexnum, arcnum; //图的顶点数和弧数
}AdjList;
/*求顶点位置*/
int LocateVertex(AdjList* G, VertexData v) {
int k;
for (k = 0; k < G->vexnum; k++) {
if (G->vertex[k].data == v)
break;
}
return k;
}
/*创建AOE-网的邻接表*/
int CreateAdjList(AdjList* G) {
int i, j, k, activity, weight;
VertexData v1, v2;
ArcNode* p;
printf("输入图的顶点数和弧数:"); //输入图的顶点数和弧数
scanf("%d%d", &G->vexnum, &G->arcnum);
printf("输入图的顶点:");
for (i = 0; i < G->vexnum; i++) { //输入图的顶点,初始化顶点结点
scanf(" %c", &(G->vertex[i].data));
G->vertex[i].firstarc = NULL;
}
for (k = 0; k < G->arcnum; k++) {
printf("输入第%d条弧的两个顶点、弧表示的活动及权值:", k + 1);
scanf(" %c %c %d %d", &v1, &v2, &activity, &weight); //输入一条弧的两个顶点、弧表示的活动及权值
i = LocateVertex(G, v1);
j = LocateVertex(G, v2);
p = (ArcNode*)malloc(sizeof(ArcNode)); //申请新弧结点
p->activity = activity;
p->weight = weight;
p->adjvex = j;
p->nextarc = G->vertex[i].firstarc;
G->vertex[i].firstarc = p;
}
}
/*顺序栈的存储结构*/
typedef struct {
int elem[MAX_VERTEX_NUM]; //用于存放栈中元素的一维数组
int top; //存放栈顶元素的下标,top为-1表示空栈
}SeqStack;
/*初始化顺序栈*/
void InitStack(SeqStack* S) {
S->top = -1;
}
/*判空*/
int IsEmpty(SeqStack* S) {
if (S->top == -1) //栈为空
return TRUE;
else
return FALSE;
}
/*顺序栈进栈*/
int Push(SeqStack* S, int x) {
if (S->top == MAX_VERTEX_NUM - 1) //栈已满
return FALSE;
S->top++;
S->elem[S->top] = x; //x进栈
return TRUE;
}
/*顺序栈出栈*/
int Pop(SeqStack* S) {
if (S->top == -1) //栈为空
return FALSE;
S->top--;
return TRUE;
}
int indegree[MAX_VERTEX_NUM]; //存放各顶点入度数
int ve[MAX_VERTEX_NUM]; //各顶点的最早发生时间
/*求各顶点入度算法*/
void FindID(AdjList G) {
int i;
ArcNode* p;
for (i = 0; i < G.vexnum; i++)
indegree[i] = 0;
for (i = 0; i < G.vexnum; i++) {
p = G.vertex[i].firstarc;
while (p != NULL) {
indegree[p->adjvex]++;
p = p->nextarc;
}
}
}
/*拓扑排序,求逆拓扑序列及事件最早发生时间ve(i)*/
int TopoSort(AdjList G, SeqStack* T) { //栈T用于生成逆拓扑序列
int i, k, count = 0;
SeqStack S; //栈S用于存放入度为0的顶点
ArcNode* p;
FindID(G); //求各顶点入度
InitStack(T); //初始化栈T
InitStack(&S); //初始化栈S
for (i = 0; i < G.vexnum; i++) {
if (indegree[i] == 0)
Push(&S, i); //将入度为0的顶点入栈S
}
for (i = 0; i < G.vexnum; i++)
ve[i] = 0; //初始化最早发生时间
while (!IsEmpty(&S)) {
i = S.elem[S.top];
Pop(&S);
count++;
Push(T, i); //按拓扑顺序进入栈T
p = G.vertex[i].firstarc;
while (p != NULL) {
k = p->adjvex;
indegree[k]--; //i号顶点的每个邻接点的入度减1
if (indegree[k] == 0)
Push(&S, k); //若入度减为0则入栈
if (ve[i] + p->weight > ve[k]) //按拓扑顺序计算事件最早发生时间
ve[k] = ve[i] + p->weight;
p = p->nextarc;
}
}
printf("\n事件最早发生时间为:"); //输出事件的最早发生时间
for (i = 0; i < G.vexnum; i++)
printf("%d ", ve[i]);
if (count < G.vexnum) {
printf("该图存在回路!\n");
return FALSE;
}
else
return TRUE;
}
/*关键路径算法*/
void CriticalPath(AdjList G, SeqStack* T) {
ArcNode* p;
int i, j, k, dut, ei, li;
char tag;
int vl[MAX_VERTEX_NUM]; //每个顶点的最迟发生时间
TopoSort(G, T); //① 求事件最早发生时间和逆拓扑序列栈T
for (i = 0; i < G.vexnum; i++)
vl[i] = ve[G.vexnum - 1]; //将各事件的最晚发生时间初始化为汇点的最早发生时间
while (!IsEmpty(T)) { //② 按逆拓扑顺序求各顶点的最晚发生时间vl值
j = T->elem[T->top];
Pop(T);
p = G.vertex[j].firstarc;
while (p != NULL) {
k = p->adjvex;
dut = p->weight;
if (vl[k] - dut < vl[j])
vl[j] = vl[k] - dut;
p = p->nextarc;
}
}
printf("\n事件最晚发生时间为:"); //输出事件的最晚发生时间
for (i = 0; i < G.vexnum; i++)
printf("%d ", vl[i]);
printf("\n关键活动及对应的弧为:\n");
for (j = 0; j < G.vexnum; j++) { //③ 求各活动的最早开始时间ei和最晚开始时间li
p = G.vertex[j].firstarc;
while (p != NULL) {
k = p->adjvex;
dut = p->weight;
ei = ve[j];
li = vl[k] - dut;
if (ei == li) //④ 输出关键活动及对应的路径
printf("a%d v%c->v%c\n", p->activity, G.vertex[j].data, G.vertex[k].data);
p = p->nextarc;
}
}
}
int main() {
AdjList G;
SeqStack T;
CreateAdjList(&G);
CriticalPath(G, &T);
return 0;
}
AOE网:关键路径和关键活动
https://download.csdn.net/download/dark_walker/12032098
https://blog.csdn.net/CocoWu892/article/details/82822300
//寻找图的关键路径
#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <queue>
using namespace std;
//最大边数,最大点数
const int Max_M=100100;
const int Max_N=50100;
struct Graph
{
int nodeNumber,Link[Max_N],number;
struct node
{
int vertex,weight,next;
} edge[Max_M];
void initGraph(int n=0)
{
number=n;
nodeNumber=0;
memset(Link,-1,sizeof(Link));
}
void addEdge(int vertex_x,int vertex_y,int weight)
{
edge[nodeNumber].vertex = vertex_y;
edge[nodeNumber].weight = weight;
edge[nodeNumber].next = Link[vertex_x];
Link[vertex_x] = nodeNumber;
nodeNumber++;
}
void eraseLink(int vertex)
{
Link[vertex] = -1;
}
} ;
// 求图的拓扑序
int topoOrder[Max_N],inDegree[Max_N];
bool topo(Graph &G, int *topoOrder)
{
memset(inDegree,0,sizeof(inDegree));
for (int i=0;i<G.number;i++)
{
for (int p=G.Link[i];p!=-1;p=G.edge[p].next)
inDegree[G.edge[p].vertex]++;
}
queue<int> que;
for (int i=0;i<G.number;i++)
if (inDegree[i] == 0)
que.push(i);
int cnt=0;
while (!que.empty())
{
int vertex = que.front();
topoOrder[cnt++] = vertex;
que.pop();
for (int p=G.Link[vertex];p!=-1;p=G.edge[p].next)
{
if (--inDegree[G.edge[p].vertex] == 0)
que.push( G.edge[p].vertex );
}
}
return cnt == G.number;
}
//求图的关键路径
//输出图的关键路径
int criPath[Max_N];
void findPrecusorNode(Graph &G, int vertex, int number)
{
criPath[number] = vertex;
//当前节点没有前驱节点,已经找到了一条关键路径
if (G.Link[vertex] == -1)
{
for (int i=number; i>0 ;i--)
printf("%d ",criPath[i]);
printf("%d\n",criPath[0]);
}
else
{
for (int p=G.Link[vertex]; p != -1; p=G.edge[p].next)
findPrecusorNode(G, G.edge[p].vertex, number+1);
}
}
int lastVis[Max_N];
Graph g;
void getCriticalPath(Graph &G, int *topoOrder)
{
memset(lastVis,0,sizeof(lastVis));
g.initGraph(G.number);
for (int i=0; i<G.number; i++)
{
for (int p=G.Link[i]; p != -1; p=G.edge[p].next)
{
if ( lastVis[ G.edge[p].vertex ] < lastVis[i] + G.edge[p].weight )
{
lastVis[ G.edge[p].vertex ] = lastVis[i] + G.edge[p].weight;
//更新前驱节点
g.eraseLink( G.edge[p].vertex);
g.addEdge(G.edge[p].vertex, i, G.edge[p].weight);
}
else
if ( lastVis[ G.edge[p].vertex ] == lastVis[i] + G.edge[p].weight )
g.addEdge(G.edge[p].vertex, i, G.edge[p].weight);
}
}
int Max_cost=0;
for (int i=0; i<G.number; i++)
Max_cost=max(Max_cost, lastVis[i]);
printf("关键路径长度为:%d\n",Max_cost);
for (int i=0; i<G.number; i++)
if (lastVis[i] == Max_cost)
{
// 输出关键路径
findPrecusorNode(g,i,0);
}
}
int main()
{
Graph G;
//给定10个节点
int n;
puts("请输入点的数目:");
scanf("%d",&n);
G.initGraph(n);
puts("请输入边的数目:");
int m,x,y,w;;
scanf("%d",&m);
printf("节点编号0 ~ %d\n",n-1);
puts("请输入边:(按格式 vertex_x vertex_y weight) ");
for (int i=1; i<=m; i++)
{
scanf("%d%d%d",&x,&y,&w);
G.addEdge(x,y,w);
}
if (topo(G, topoOrder))
getCriticalPath(G,topoOrder);
else
puts("图中存在环,故不存在关键路径");
return 0;
}