DFS algorithm to detect cycles in graph - algorithm

Question

#include <iostream>
#include <vector>
#include <stack>
using namespace std;
class Graph{
public:
vector<int> adjList[10001];
void addEdge(int u,int v){
adjList[u].push_back(v);
adjList[v].push_back(u);
}
};
bool dfs(Graph graph, int n){
vector<int> neighbors;
int curr,parent;
bool visited[10001] = {0};
stack<int> s;
//Depth First Search
s.push(1);
parent = 0;
while(!s.empty()){
curr = s.top();
neighbors = graph.adjList[curr];
s.pop();
//If current is unvisited
if(visited[curr] == false){
for(int j=0; j<neighbors.size(); j++){
//If node connected to itself, then cycle exists
if(neighbors[j] == curr){
return false;;
}
else if(visited[neighbors[j]] == false){
s.push(neighbors[j]);
}
//If the neighbor is already visited, and it is not a parent, then cycle is detected
else if(visited[neighbors[j]] == true && neighbors[j] != parent){
return false;
}
}
//Mark as visited
visited[curr] = true;
parent = curr;
}
}
//Checking if graph is fully connected
for(int i=1; i<=n; i++){
if(visited[i] == false){
return false;
}
}
//Only if there are no cycles, and it's fully connected, it's a tree
return true;
}
int main() {
int m,n,u,v;
cin>>n>>m;
Graph graph = Graph();
//Build the graph
for(int edge=0; edge<m; edge++){
cin>>u>>v;
graph.addEdge(u,v);
}
if(dfs(graph,n)){
cout<<"YES"<<endl;
}
else{
cout<<"NO"<<endl;
}
return 0;
}
I am trying to determine if a given graph is a tree.
I perform DFS and look for cycles, if a cycle is detected, then the given graph is not a tree.
Then I check if all nodes have been visited, if any node is not visited, then given graph is not a tree
The first line of input is:
n m
Then m lines follow, which represent the edges connecting two nodes
n is number of nodes
m is number of edges
example input:
3 2
1 2
2 3
This is a SPOJ question http://www.spoj.com/problems/PT07Y/ and I am getting Wrong Answer. But the DFS seems to be correct according to me.

Answer 1

So I checked your code against some simple test cases in comments, and it seems that for
7 6
3 1
3 2
2 4
2 5
1 6
1 7
you should get YES as answer, while your program gives NO.
This is how neighbours looks like in this case:
1: 3 6 7
2: 3 4 5
3: 1 2
4: 2
5: 2
6: 1
7: 1
So when you visit 1 you push 3,6,7 on the stack. Your parent is set as 1. This is all going good.
You pop 7 from the stack, you don't push anything on the stack and cycle check clears out, so as you exit while loop you set visited[7] as true and set you parent to 7 (!!!!!).
Here is you can see this is not going well, since once you popped 6 from the stack you have 7 saved as parent. And it should be 1. This makes cycle check fail on neighbor[0] != parent.
I'd suggest adding keeping parent in mapped array and detect cycles by applying union-merge.