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‎Graph/Articulation points.cpp

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#include<bits/stdc++.h>
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#include<ext/pb_ds/assoc_container.hpp>
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#include<ext/pb_ds/tree_policy.hpp>
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#define FIO ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
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#define Fileio freopen("output.txt","w",stdout);freopen("input.txt","r",stdin);
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#define all(v) v.begin(),v.end()
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#define rall(v) v.rbegin(),v.rend()
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#define MEM(a,x) memset(a,x,sizeof(a))
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#define SZ(v) v.size()
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#define nl "\n"
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#define bug cout<<"bug"<<nl;
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#define pi acos(-1.0)
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#define ll long long
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#define pb push_back
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#define mp make_pair
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#define pii pair< int,int >
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#define pll pair< ll,ll >
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#define vii vector< int >
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#define vll vector< ll >
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#define vpi vector< pii >
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#define vpl vector<pll>
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#define MX 100005
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#define EPS 1e-12
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#define ss second
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#define ff first
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using namespace std;
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using namespace __gnu_pbds;
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template<typename T>
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using ordered_set=tree<T,null_type,less<T>,rb_tree_tag,tree_order_statistics_node_update>;
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template<typename T>
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using ordered_multiset=tree<T, null_type, less_equal<T>, rb_tree_tag,tree_order_statistics_node_update>;
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inline ll powr(int a,int b){ll res=1;while(b){if(b&1) res*=a;a*=a;b/=2;}return res;}
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int cases=1;
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#ifdef ppqq
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#define debug(...) __f(#__VA_ARGS__, __VA_ARGS__)
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template < typename Arg1 >
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void __f(const char* name, Arg1&& arg1){
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cerr << name << " is " << arg1 << std::endl;
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}
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template < typename Arg1, typename... Args>
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void __f(const char* names, Arg1&& arg1, Args&&... args){
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const char* comma = strchr(names+1, ',');
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cerr.write(names, comma - names) << " is " << arg1 <<" ";
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__f(comma+1, args...);
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}
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#else
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#define debug(...)
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#endif
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///******************************************START******************************************
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int n,m,timer;
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vector<int> adj[100005],in_time,low;
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vector<bool> vis,cut_ver;
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void dfs(int u,int p)
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{
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int child=0;
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in_time[u]=low[u]=timer++;
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vis[u]=true;
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for(auto it: adj[u])
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{
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if(it==p) continue;
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if(vis[it])
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low[u]=min(in_time[it],low[u]);
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else
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{
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dfs(it,u);
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low[u]=min(low[u],low[it]);
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if(low[it]>=in_time[u] && p!=-1)
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cut_ver[u]=true;
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child++;
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}
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}
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if(p==-1 && child>1) cut_ver[u]=true;
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}
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void findArticulationPoints()
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{
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in_time.assign(n+2,0);
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low.assign(n+2,0);
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vis.assign(n+2,false);
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cut_ver.assign(n+2,0);
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timer=1;
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for(int i=1;i<=n;i++)
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if(!vis[i]) dfs(i,-1);
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for(int i=1;i<=n;i++)
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if(cut_ver[i]) cout<<i<<" ";
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}
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int main()
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{
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FIO;
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cin>>n>>m;
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for(int i=0,x,y;i<m;i++)
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{
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cin>>x>>y;
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adj[x].push_back(y);
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adj[y].push_back(x);
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}
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findArticulationPoints();
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}

‎Graph/Finding Bridge.cpp

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#include<bits/stdc++.h>
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#include<ext/pb_ds/assoc_container.hpp>
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#include<ext/pb_ds/tree_policy.hpp>
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#define FIO ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
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#define Fileio freopen("output.txt","w",stdout);freopen("input.txt","r",stdin);
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#define all(v) v.begin(),v.end()
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#define rall(v) v.rbegin(),v.rend()
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#define MEM(a,x) memset(a,x,sizeof(a))
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#define SZ(v) v.size()
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#define nl "\n"
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#define bug cout<<"bug"<<nl;
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#define pi acos(-1.0)
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#define ll long long
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#define pb push_back
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#define mp make_pair
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#define pii pair< int,int >
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#define pll pair< ll,ll >
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#define vii vector< int >
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#define vll vector< ll >
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#define vpi vector< pii >
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#define vpl vector<pll>
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#define MX 100005
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#define EPS 1e-12
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#define ss second
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#define ff first
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using namespace std;
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using namespace __gnu_pbds;
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template<typename T>
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using ordered_set=tree<T,null_type,less<T>,rb_tree_tag,tree_order_statistics_node_update>;
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template<typename T>
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using ordered_multiset=tree<T, null_type, less_equal<T>, rb_tree_tag,tree_order_statistics_node_update>;
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inline ll powr(int a,int b){ll res=1;while(b){if(b&1) res*=a;a*=a;b/=2;}return res;}
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int cases=1;
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#ifdef ppqq
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#define debug(...) __f(#__VA_ARGS__, __VA_ARGS__)
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template < typename Arg1 >
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void __f(const char* name, Arg1&& arg1){
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cerr << name << " is " << arg1 << std::endl;
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}
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template < typename Arg1, typename... Args>
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void __f(const char* names, Arg1&& arg1, Args&&... args){
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const char* comma = strchr(names+1, ',');
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cerr.write(names, comma - names) << " is " << arg1 <<" ";
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__f(comma+1, args...);
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}
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#else
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#define debug(...)
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#endif
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///******************************************START******************************************
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int n,m,timer;
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vector<int> adj[100005],in_time,low;
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vector<pair<int,int>> bridge;
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vector<bool> vis,cut_ver;
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void dfs(int u,int p)
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{
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in_time[u]=low[u]=timer++;
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vis[u]=true;
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for(auto it: adj[u])
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{
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if(it==p) continue;
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if(vis[it])
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low[u]=min(in_time[it],low[u]);
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else
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{
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dfs(it,u);
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low[u]=min(low[u],low[it]);
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if(low[it]>in_time[u])
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bridge.push_back({u,it});
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}
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}
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}
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void findBridges()
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{
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in_time.assign(n+2,0);
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low.assign(n+2,0);
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vis.assign(n+2,false);
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cut_ver.assign(n+2,0);
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timer=1;
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for(int i=1;i<=n;i++)
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if(!vis[i]) dfs(i,-1);
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for(auto it: bridge) cout<<it.first<<" "<<it.second<<"\n";
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}
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int main()
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{
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FIO;
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cin>>n>>m;
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for(int i=0,x,y;i<m;i++)
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{
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cin>>x>>y;
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adj[x].pb(y);
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adj[y].pb(x);
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}
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findBridges();
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}

‎Graph/Strongly Connected Component.cpp

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#include<bits/stdc++.h>
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#include<ext/pb_ds/assoc_container.hpp>
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#include<ext/pb_ds/tree_policy.hpp>
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#define FIO ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
5+
#define Fileio freopen("output.txt","w",stdout);freopen("input.txt","r",stdin);
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#define all(v) v.begin(),v.end()
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#define rall(v) v.rbegin(),v.rend()
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#define MEM(a,x) memset(a,x,sizeof(a))
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#define SZ(v) v.size()
10+
#define nl "\n"
11+
#define bug cout<<"bug"<<nl;
12+
#define pi acos(-1.0)
13+
#define ll long long
14+
#define pb push_back
15+
#define mp make_pair
16+
#define pii pair< int,int >
17+
#define pll pair< ll,ll >
18+
#define vii vector< int >
19+
#define vll vector< ll >
20+
#define vpi vector< pii >
21+
#define vpl vector<pll>
22+
#define MX 100005
23+
#define EPS 1e-12
24+
#define ss second
25+
#define ff first
26+
using namespace std;
27+
using namespace __gnu_pbds;
28+
29+
template<typename T>
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using ordered_set=tree<T,null_type,less<T>,rb_tree_tag,tree_order_statistics_node_update>;
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template<typename T>
32+
using ordered_multiset=tree<T, null_type, less_equal<T>, rb_tree_tag,tree_order_statistics_node_update>;
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34+
inline ll powr(int a,int b){ll res=1;while(b){if(b&1) res*=a;a*=a;b/=2;}return res;}
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int cases=1;
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#ifdef ppqq
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#define debug(...) __f(#__VA_ARGS__, __VA_ARGS__)
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template < typename Arg1 >
40+
void __f(const char* name, Arg1&& arg1){
41+
cerr << name << " is " << arg1 << std::endl;
42+
}
43+
template < typename Arg1, typename... Args>
44+
void __f(const char* names, Arg1&& arg1, Args&&... args){
45+
const char* comma = strchr(names+1, ',');
46+
cerr.write(names, comma - names) << " is " << arg1 <<" ";
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__f(comma+1, args...);
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}
49+
#else
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#define debug(...)
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#endif
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///******************************************START******************************************
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///test: https://www.hackerearth.com/practice/algorithms/graphs/strongly-connected-components/tutorial/
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int n,m,cnt;
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vector<int> adj[100005],rev[100005];
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bool vis[100005];
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stack<int> st;
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void dfs1(int u)
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{
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vis[u]=true;
64+
for(auto it: adj[u])
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if(!vis[it]) dfs1(it);
66+
st.push(u);
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}
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void dfs2(int u)
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{
70+
cnt++;
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vis[u]=true;
72+
for(auto it: rev[u]){
73+
if(!vis[it]) dfs2(it);
74+
}
75+
}
76+
void SCC()
77+
{
78+
for(int i=1;i<=n;i++)
79+
if(!vis[i]) dfs1(i);
80+
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for(int i=1;i<=n;i++) vis[i]=false;
82+
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int odd=0,even=0;
84+
85+
while(!st.empty())
86+
{
87+
int u=st.top();
88+
st.pop();
89+
if(!vis[u])
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{
91+
cnt=0;
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dfs2(u);
93+
if(cnt%2) odd+=cnt;
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else even+=cnt;
95+
}
96+
}
97+
cout<<odd-even;
98+
}
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int main()
100+
{
101+
FIO;
102+
cin>>n>>m;
103+
for(int i=0,x,y;i<m;i++)
104+
{
105+
cin>>x>>y;
106+
adj[x].push_back(y);
107+
rev[y].push_back(x);
108+
}
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SCC();
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}

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