Question: find the longest simple path from s to t in a directed graph.

To determine the longest simple path in a directed graph is Np-complete, 
so the basic idea of solving this kind of problem is to use Exhaustive search.
//graph[SIZE] is a linked-list representation of  a directed graph, in which every element is graph[i] is 
//a neighbour of i;
list<int> graph[SIZE];
//weight[SIZE][SIZE] is a matrix representation, storeing the distance from i to j in weight[i][j];
//s is source, t is destination;
int s, t;
//longestDistance is a static varible to keep track of the longest distance from s to t;
int longestDistance=0;
//color[i] is used to mark whether i is visited or not;
bool color[SIZE]={false}; 
color[s]=true;
Exhaustive_search(s, 0);
void Exhaustive_search(int node, int distance){
	list<int>::iterator iter;
	int neibour;
	for(iter=graph[node].begin(); iter!=graph[node].end(); iter++){
		neighbout=*iter;
		if(color[neighbour]==false){
			color[neighbour]=true;
			if(neighbour==t){
				if(longestDistance<distance+weight[node][neighbour])
					longestDistance=distance+weight[node][neighbout];
			}
			else
				Exhausitive_search(neibour, distance+weight[node][neighbour]);
			color[neighbour]=false;
		}
	}
}

The time complexity is O(N!); 
The space complexity is O(N+E);
(N is the number of node of the graph, E is the number of edges of the graph)