Problems in evaluating subgraphs of a graph - c++

Question

Here is the question link.
Given an undirected graph. Density of a graph is |E|⁄|V|. Your task is to choose non-empty set of vertices V such that subgraph induced on V has maximal density and print this density. But if maximal density is strictly greater than 1, just print ">1".
Maximum number of vertices: 105
Maximum number of edges: 105
I just made a simple solution, but in this solution I can keep track of the whole graph, but how do I get the value of density for smaller subGraphs?
#include<iostream>
#include<vector>
using namespace std;
vector<int> adj[1000002]; // adjacency lists adj for storing graph edges
int node=0; // initializing for node value(vertices)
bool visited[100001]={false}; // keeps track of visited nodes(vertices)
int edge=-1;
int ans=-1;
int n; // keeps optimum value of no. of nodes
int e; // keeps optimum value of no. of edges
void dfs(int s)
{
node++;
edge++;
if(edge>0)
{
float dummy=(float)edge/(float)node;
if(dummy>ans)
{ans=dummy;
e=edge;
n=node;
}
}
visited[s]=true;
int t;
for(int i=0;i!=adj[s].size();i++)
{ t=adj[s][i];
if(visited[t]==false)
{
dfs(t);
}
}
}
int main()
{
long long v,ed,i,j,x,y;
cin>>v>>ed;
for(long long k=0;k<ed;k++)
{
cin>>x>>y;
adj[x].push_back(y);
adj[y].push_back(x);
}
if(ed>v)
cout<<">1"<<endl;
else{
for(i=1;i<=v;i++)
{
if(visited[i]==false)
{
node=0;
edge=-1;
dfs(i);
//cout<<e<<"/"<<n<<endl;
}
}
cout<<e<<"/"<<n<<endl;}
}

Answer 1

Follow these steps to get better result:
1.Do a dfs on each component to get the answer.
2.Avoid the floating point calculation you are doing and try all integer calculation.
3.No reason to use long long here with that range
Change the code to something like this should work:
#include<iostream>
#include<vector>
using namespace std;
vector<int> adj[1000002]; // adjacency lists adj for storing graph edges
int node=0; // initializing for node value(vertices)
bool visited[100001]={false}; // keeps track of visited nodes(vertices)
int edge=0;
void dfs(int s)
{
node++;
visited[s]=true;
int t;
edge+=adj[s].size();
for(int i=0;i!=adj[s].size();i++)
{
t=adj[s][i];
if(visited[t]==false)
{
dfs(t);
}
}
}
int main()
{
int v,ed,i,j,x,y;
cin>>v>>ed;
for(int k=0;k<ed;k++)
{
cin>>x>>y;
adj[x].push_back(y);
adj[y].push_back(x);
}
int mark[3]; mark[0]=mark[1]=mark[2]=0;
int mx_node=0;
for(i=1;i<=v;i++)
{
if(visited[i]==false)
{
node=0;
edge=0;
dfs(i);
edge/=2;
if(node>edge){
mark[0]=1;
mx_node=mx_node<node?node:mx_node;
}
else if(node==edge) mark[1]=1;
else mark[2]=1;
}
}
if(mark[2]) printf(">1\n");
else if(mark[1]) printf("1\n");
else printf("%d/%d\n",mx_node-1,mx_node);
}