I wrote a code segment to determine the longest path in a graph. Following is the code. But I don't know how to get the computational complexity in it because of the recursive method in the middle. Since finding the longest path is an NP complete problem I assume it's something like O(n!)
or O(2^n)
, but how can I actually determine it?
public static int longestPath(int A) {
int k;
int dist2=0;
int max=0;
visited[A] = true;
for (k = 1; k <= V; ++k) {
if(!visited[k]){
dist2= length[A][k]+longestPath(k);
if(dist2>max){
max=dist2;
}
}
}
visited[A]=false;
return(max);
}