LOJ-1300 - Odd Personality
///============================================================================///
/// ///
/// IT'S ME ///
/// BISHAL GAUTAM ///
/// CSE,JAHANGIRNAGAR UNIVERSITY,DHAKA ///
/// "Follow Excellence..Success will chase U" ///
/// ///
///============================================================================///
#include<bits/stdc++.h>
#define PI acos(-1.0)
#define X first
#define Y second
#define mpp make_pair
#define nl printf("\n")
#define SZ(x) (int)(x.size())
#define pb(x) push_back(x)
#define pii pair<int,int>
#define pll pair<ll,ll>
#define pdd pair<double,double>
///==Scanning====///
#define S(a) scanf("%d",&a)
#define P(a) printf("%d",a)
#define SL(a) scanf("%lld",&a)
#define S2(a,b) scanf("%d%d",&a,&b)
#define S3(a,b,c) scanf("%d%d%d",&a,&b,&c)
#define SL2(a,b) scanf("%lld%lld",&a,&b)
#define SL3(a,b,c) scanf("%lld%lld%lld",&a,&b,&c)
///==Arr,Vec Functions==///
#define all(v) v.begin(),v.end()
#define CLR(a) memset(a,0,sizeof(a))
#define SET(a) memset(a,-1,sizeof(a))
#define CPY(a,b) memcpy(a,b,sizeof(a))
#define MAX(a) (*max_element(all(a)))
#define MIN(a) (*min_element(all(a)))
#define fv(i,v) for(int i=0;i<(int)v.size();i++)
#define fr(i,a,n) for(int i=a;i<=n;i++)
#define rf(i,n,a) for(int i=n;i>=a;i--)
///===Some Useful====///
#define OnBit(a) __builtin_popcountll((ll)a)
#define LB(v,k) lower_bound(v.begin(),v.end(),k)
#define _cin ios_base::sync_with_stdio(0),cin.tie(0)
#define dbg(x) cerr<<__LINE__<< ":: "<<#x<<"= "<<x<<endl
#define UNIK(v) sort(all(v)),v.resize( unique(all(v)) -v.begin() );
#define fi(n) for(__typeof(n.begin()) it=n.begin();it!=n.end();it++)
#define IO freopen("A.in","r",stdin),freopen("Out.out","w",stdout)
using namespace std;
///===TypeDefs=====///
typedef long long ll;
typedef unsigned long long ull;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vll;
typedef vector<pii> vii;
///===Number Theory===///
//template< class T > inline T SQR(T a) { return ((a)*(a)); }
//template< class T > inline T gcd(T a,T b) {a=abs(a);b=abs(b); if(!b) return a; return gcd(b,a%b);}
//template< class T > inline T lcm(T a,T b) {a=abs(a);b=abs(b); return (a/_gcd(a,b))*b;}
//template<typename T> T POW(T b,T p) {T r=1; while(p){if(p&1)r=(r*b);b=(b*b);p>>=1;}return r;}
//template<typename T> T BigMod(T b,T p,T m) {T r=1; while(p){if(p&1)r=(r*b)%m;b=(b*b)%m;p>>=1;}return r;}
//template<typename T> T ModInverse(T n,T m) { return BigMod(n,m-2,m); }
//
/////==GeoMetry=========///
//double DEG(double x) { return (180.0*x)/(PI);}
//double RAD(double x) { return (x*(double)PI)/(180.0);}
//template<typename T> double DIS(T a,T b){ return sqrt((double)( SQR(a.X-b.X)+ SQR(a.Y-b.Y))); }
//template<typename T> T ANGLE(T a,T b){ return atan( double(a.Y-b.Y) / double(a.X-b.X));}
//template<typename T> int isLeft(T a,T b,T c) { return (c.X-a.X)*(b.Y-a.Y)-(b.X-a.X)*(c.Y-a.Y); }
//
/////===IO-Related===///
//template< class T > void prnt(T v) { fv(i,v) {if(!i)cout<<v[i];else cout<<" "<<v[i];} cout<<endl; }
//template< class T > void BIN(T n) { if(!n){nl;return;}BIN(n/2);cout<<(n%2); }
//template<typename T> T in(){ char ch; T n = 0; bool ng = false; while (1) { ch = getchar(); if (ch == '-') { ng = true; ch = getchar(); break;} if (ch>='0' && ch<='9') break; } while (1) { n = n*10 + (ch - '0'); ch = getchar(); if (ch<'0' || ch>'9') break; } return (ng?-n:n); }
///====Some-Stuff===///
/// atoi( str.c_str() ); // char string to int
/// sprintf(str,"%d",num);// num to char string
///int month[]={-1,31,28,31,30,31,30,31,31,30,31,30,31}; //Not Leap Year
///int dx[]={1,0,-1,0};int dy[]={0,1,0,-1}; //4 Direction
///int dx[]={1,1,0,-1,-1,-1,0,1};int dy[]={0,1,1,1,0,-1,-1,-1};//8 Direction
///int dx[]={2,1,-1,-2,-2,-1,1,2};int dy[]={1,2,2,1,-1,-2,-2,-1};//Knight Direction
/**************************************************************************************
* ///////////////////////////////////////////////////////////////////////////////////*
*************************************************************************************/
///==========CONSTANTS==============///
/// Digit 0123456789*#@%&^$"- ///
#define MX 10005
#define MXX 12500005
#define inf 2000000000
#define MD 1000000007LL
#define eps 1e-9
///================================///
vector<int>G[MX+2];
int tmm=0,St[MX+2],vis[MX+2],low[MX+2];
set< pii >Brg;
void Dfs(int u,int p) {
St[u]=++tmm;
low[u]=tmm;
vis[u]=1;
for(int i=0; i<SZ(G[u]); i++) {
int v=G[u][i];
if( v==p )continue;
if( !vis[v] ) {
Dfs(v,u);
if( low[v]>St[u] ) {
Brg.insert( mpp( min(u,v),max(u,v) ) );
}
low[u]=min( low[u],low[v] );
}
else low[u]=min( low[u],St[v] );
}
}
int Bicolor_Bfs(int x){
queue<int>Q;
Q.push(x);
vis[ x ]=1;
int cnt=1,f=1;
while( !Q.empty() ){
int u=Q.front(); Q.pop();
for(int i=0;i<SZ(G[u]);i++){
int v=G[u][i];
pii tp=mpp( min(u,v),max(u,v) );
if( Brg.count(tp) ) continue;
if( !vis[v] ){
cnt++;
vis[v]=3-vis[u]; /// 2 or 1;
Q.push(v);
}
else if( vis[v]==vis[u] ){
f=0; ///Not bicolorable;
}
}
}
if(!f) return cnt;
else return 0;
}
int main() {
int tc,cs=1,i,j,k,n,m,x,y,z;
S(tc);
while(tc--) {
S2(n,m);
fr(i,0,n)G[i].clear();
fr(i,1,m) {
S2(x,y);
G[x].pb(y);
G[y].pb(x);
}
CLR(St);
CLR(vis);
tmm=0;
Brg.clear();
///First find & Remove all bridges
fr(i,0,n-1) {
if(!vis[i]) {
Dfs(i,-1);
}
}
///Now run Dfs to find different components & check bicolorability;
///Note: Graph which is not bicolorable contains odd length CYCLE !!
CLR(vis);
int ans=0;
fr(i,0,n-1){
if( !vis[i] ){
int tmp=Bicolor_Bfs(i);
/// If not bicolorable return size of comp else 0;
ans+=tmp;
}
}
printf("Case %d: %d\n",cs++,ans);
}
return 0;
}
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