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euler
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‎Graph/Euler Tour(Directed).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 200005
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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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//Ref : https://github.com/sayedgkm/CodeLibrary/blob/master/Graph/Euler_circuit(directed).cpp
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vector<int> adj[MX],rev[MX];
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int inDeg[MX],outDeg[MX];
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bool vis[MX],vis2[MX];
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vector<int> tour;
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void findTour(int u)
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{
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while(adj[u].size())
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{
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int v=adj[u].back();
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adj[u].pop_back();
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findTour(v);
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}
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tour.push_back(u);
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}
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void dfs(int u)
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{
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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(vis[it]) continue;
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dfs(it);
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}
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}
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void dfs2(int u)
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{
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vis2[u]=true;
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for(auto it: rev[u])
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{
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if(!vis2[it]) dfs2(it);
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}
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}
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bool connected(int u,int n)
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{
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dfs(u);
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dfs2(u);
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for(int i=1;i<=n;i++) if(!vis[i] && !vis2[i] && (inDeg[i] || outDeg[i])) return false;
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return true;
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}
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bool isEulerCycle(int n)
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{
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int st=-1;
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for(int i=1;i<=n;i++)
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{
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if(inDeg[i]!=outDeg[i]) return false;
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if(outDeg[i]) st=i;
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}
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if(st==-1) return true;
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///if the graph is already connected no need to check it just return true
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if(connected(st,n)) return true;
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return false;
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}
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bool isEulerPath(int n)
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{
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int st=-1,odd=0;
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for(int i=1;i<=n;i++)
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{
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if(inDeg[i]!=outDeg[i])
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{
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if(abs(inDeg[i]-outDeg[i])>1) return false;
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odd++;
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}
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if(outDeg[i]) st=i;
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}
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if(st==-1) return true;
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///if the graph is already connected no need to check it just return true
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if(connected(st,n) && odd==2) return true;
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return false;
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}
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void EulerCycle(int n)
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{
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if(isEulerCycle(n))
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{
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int st=1;
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for(int i=1;i<=n;i++) if(outDeg[i]) st=i;
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findTour(st);
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reverse(all(tour));
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for(auto it: tour) cout<<it<<" ";
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}
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else cout<<"IMPOSSIBLE\n";
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}
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void EulerPath(int n)
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{
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if(isEulerPath(n))
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{
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int st=1;
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for(int i=1;i<=n;i++) if(inDeg[i]!=outDeg[i]) st=i;
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findTour(st);
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reverse(all(tour));
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for(auto it: tour) cout<<it<<" ";
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}
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else cout<<"IMPOSSIBLE\n";
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}
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int main()
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{
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FIO;
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int n,m;
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cin>>n>>m;
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for(int i=0;i<m;i++)
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{
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int u,v;
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cin>>u>>v;
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adj[u].push_back(v);
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rev[v].push_back(u);
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inDeg[v]++;
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outDeg[u]++;
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}
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EulerPath(n);
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}

‎Graph/Euler Tour.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 >
17+
#define pll pair< ll,ll >
18+
#define vii vector< int >
19+
#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 200005
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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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//Ref : https://github.com/sayedgkm/CodeLibrary/blob/master/Graph/Euler_circuit.cpp
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multiset<int> adj[MX];
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int deg[MX];
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bool vis[MX];
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vector<int> tour;
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void findTour(int u)
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{
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while(adj[u].size())
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{
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int v=*adj[u].begin();
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adj[u].erase(adj[u].find(v));
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adj[v].erase(adj[v].find(u));
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findTour(v);
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}
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tour.push_back(u);
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}
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void dfs(int u)
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{
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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(vis[it]) continue;
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dfs(it);
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}
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}
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bool connected(int u,int n)
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{
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dfs(u);
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for(int i=1;i<=n;i++) if(!vis[i] && deg[i]) return false;
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return true;
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}
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bool isEulerCycle(int n)
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{
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int st=-1;
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for(int i=1;i<=n;i++)
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{
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if(deg[i]%2) return false;
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if(deg[i]) st=i;
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}
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if(st==-1) return true;
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///if the graph is already connected no need to check it just return true
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if(connected(st,n)) return true;
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return false;
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}
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bool isEulerPath(int n)
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{
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int st=-1,odd=0;
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for(int i=1;i<=n;i++)
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{
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if(deg[i]%2) odd++;
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if(deg[i]) st=i;
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}
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if(st==-1) return true;
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///if the graph is already connected no need to check it just return true
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if(connected(st,n) && odd==2) return true;
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return false;
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}
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void EulerCycle(int n)
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{
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if(isEulerCycle(n))
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{
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int st=1;
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for(int i=1;i<=n;i++) if(deg[i]) st=i;
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findTour(st);
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reverse(all(tour));
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for(auto it: tour) cout<<it<<" ";
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}
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else cout<<"IMPOSSIBLE\n";
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}
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void EulerPath(int n)
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{
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if(isEulerPath(n))
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{
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int st=1;
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for(int i=1;i<=n;i++) if(deg[i]%2) st=i;
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findTour(st);
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reverse(all(tour));
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for(auto it: tour) cout<<it<<" ";
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}
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else cout<<"IMPOSSIBLE\n";
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}
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int main()
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{
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FIO;
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int n,m;
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cin>>n>>m;
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for(int i=0;i<m;i++)
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{
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int u,v;
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cin>>u>>v;
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adj[u].insert(v);
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adj[v].insert(u);
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deg[u]++;
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deg[v]++;
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}
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}

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