對于給定有向圖，先進行拓撲處理，然后求出最長路徑。

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//尋找圖的關鍵路徑 
#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <queue>
using namespace std;
 
//最大邊數，最大點數 
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;
	}
} ;
 
 
// 求圖的拓撲序 
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;
}
 
//求圖的關鍵路徑 
 
 
//輸出圖的關鍵路徑
int criPath[Max_N]; 
void findPrecusorNode(Graph &G, int vertex, int number)
{
	criPath[number] = vertex;
	//當前節點沒有前驅節點，已經找到了一條關鍵路徑 
	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;
				//更新前驅節點 
				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("關鍵路徑長度為：%d\n",Max_cost);			
	for (int i=0; i<G.number; i++)
		if (lastVis[i] == Max_cost)
		{
			// 輸出關鍵路徑
			findPrecusorNode(g,i,0); 
		}
}
int main()
{
	Graph G;
	//給定10個節點
	
	int n;
	puts("請輸入點的數目:");
	scanf("%d",&n); 
	G.initGraph(n);
	puts("請輸入邊的數目:");
	int m,x,y,w;;
	scanf("%d",&m);
	printf("節點編號0 ~ %d\n",n-1); 
	puts("請輸入邊：（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("圖中存在環，故不存在關鍵路徑"); 
	return 0;
}