cycle detection in an undirected graph using dfs and height array - c++

Question

My job is to complete the isCyclic() function in following program. I can handle this job with visited array and passing parent to dfs() function but I am trying another solution, So I use a height array to keep track of distance of nodes in DFS tree for determining parents and cycle. this height array initial by zero. If distance of two node be exactly one these two node are parent child.
But I cannot understand why my solution doesn't work. can someone tell me why output of this code is not correct?
thanks for your help.
An example of graph and height value of nodes:
/*
.1
/ \
.2 .2
/ \
.3 .3
*/
#include<bits/stdc++.h>
using namespace std;
class Graph
{
int V;
list<int> *adj;
public :
Graph(int V);
void addEdge(int v,int w);
bool isCyclic();
};
vector<int> g[100001];
Graph::Graph(int V)
{
this->V = V;
adj = new list<int>[V];
}
void Graph::addEdge(int v,int w)
{
adj[v].push_back(w);
adj[w].push_back(v);
}
int main()
{
int T;
cin>>T;
while(T--)
{
int _size,N;
cin>>_size>>N;
Graph *g = new Graph(_size);
for(int i=0;i<N;i++)
{
int u,v;
cin>>u>>v;
g->addEdge(u,v);
}
cout<<g->isCyclic()<<endl;
}
}
/*Please note that it's Function problem i.e.
you need to write your solution in the form of Function(s) only.
Driver Code to call/invoke your function is mentioned above.*/
/*The structure of the class is as follows
which contains an integer V denoting the no
of vertices and a list of adjacency vertices.
class Graph
{
int V;
list<int> *adj;
public :
Graph(int V);
void addEdge(int v,int w);
bool isCyclic();
};*/
/*You are required to complete this method*/
bool dfs(int v, int hi, list<int> *adj, int *h) {
h[v] = hi;
list<int>::iterator it;
for(it = adj[v].begin(); it != adj[v].end(); it++) {
int u = *it;
//cycle detect
if (h[u]>0 && hi - h[u] > 1)
return true;
if (h[u]==0 && dfs(u, hi+1, adj, h))
return true;
}
return false;
}
/*You are required to complete this method*/
bool Graph :: isCyclic()
{
//Your code here
int h[V];
for(int i = 0; i < V; i++) h[i] = 0;
for(int i = 0; i< V; i++)
if ( h[i] == 0 && dfs(i, 1, adj, h) ) return true;
return false;
}
A input that make my answer incorrect:
Input:
85 59
0 34 32 54 6 16 45 44 82 52 57 15 20 60 52 44 75 77 48 18 53 75 14 40 39 46 24 26 32 0 39 74 34 29 43 41 45 45 0 42 54 14 58 75 31 67 34 63 16 39 81 69 29 52 67 26 14 6 52 3 48 49 77 83 78 78 81 38 38 38 38 8 53 53 40 84 77 31 63 9 70 16 78 57 69 60 83 83 23 7 43 72 56 35 27 6 70 23 2 24 61 40 74 71 50 29 28 42 60 48 51 2 64 2 59 48 19 57
Its Correct output is:
1
And Your Code's output is:
0