DFS Sample Code

0

#include <bits/stdc++.h>

using namespace std;

vector<int>v[100];
bool visited[100];

int node,edge;

void DFS(int n)
{
    visited[n]=true;
    cout<<n<<" ";
    int temp;
    for(int i=0; i<v[n].size(); i++)
    {
        temp=v[n][i];
        if(!visited[temp])
            DFS(temp);
    }
}


int main()
{
    cin>>node>>edge;
    for(int i=0; i<edge; i++)
    {
        int x,y;
        cin>>x>>y;
        v[x].push_back(y);
        v[y].push_back(x);
    }

    int src,dst;
    cin>>src>>dst;
    memset(visited,0,sizeof visited);
    cout<<"DFS traverse order is = ";
    DFS(src);
    cout<<endl;
    if(visited[dst])
        cout<<dst<<" is reachable from "<<src<<endl;
    else
        cout<<dst<<" is not reachable from "<<src<<endl;
    return 0;
}


USACO: The Castle

0

Problem Link : http://train.usaco.org/usacoprob2?a=qBACVBxoOsW&S=castle


/*
PROG: castle
LANG: C++
*/

#include <bits/stdc++.h>

#define pii             pair <int,int>
#define sc              scanf
#define pf              printf
#define Pi              2*acos(0.0)
#define ms(a,b)         memset(a, b, sizeof(a))
#define pb(a)           push_back(a)
#define MP              make_pair
#define db              double
#define ll              long long
#define EPS             10E-10
#define ff              first
#define ss              second
#define sqr(x)          (x)*(x)
#define D(x)            cout<<#x " = "<<(x)<<endl
#define VI              vector <int>
#define DBG             pf("Hi\n")
#define MOD             100007
#define MAX             10000
#define CIN             ios_base::sync_with_stdio(0); cin.tie(0)
#define SZ(a)           (int)a.size()
#define sf(a)           scanf("%d",&a)
#define sfl(a)          scanf("%lld",&a)
#define sff(a,b)        scanf("%d %d",&a,&b)
#define sffl(a,b)       scanf("%lld %lld",&a,&b)
#define sfff(a,b,c)     scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c)    scanf("%lld %lld %lld",&a,&b,&c)
#define loop(i,n)       for(int i=0;i<n;i++)
#define REP(i,a,b)      for(int i=a;i<=b;i++)
#define TEST_CASE(t)    for(int z=1;z<=t;z++)
#define PRINT_CASE      printf("Case %d: ",z)
#define all(a)          a.begin(),a.end()
#define intlim          2147483648
#define inf             1000000
#define ull             unsigned long long

using namespace std;


/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
bool check(int N,int pos)
{
    return (bool)(N & (1<<pos));
}
/*------------------------------------------------*/

int graph[52][52];
int dp[2505];
int visited[52][52];

int r,c,s,extend=0;

int dfs(int i, int j, int x)
{
//    if(visited[i][j]) return 0;
    visited[i][j]=x;
    int d=0;
    if(!check(graph[i][j],0) && !visited[i][j-1]) d+=1+dfs(i,j-1,x);
    if(!check(graph[i][j],2) && !visited[i][j+1]) d+=1+dfs(i,j+1,x);
    if(!check(graph[i][j],1) && !visited[i-1][j]) d+=1+dfs(i-1,j,x);
    if(!check(graph[i][j],3) && !visited[i+1][j]) d+=1+dfs(i+1,j,x);
    return d;
}

int n,m;

void func(int i, int j,int x)
{
    int t=visited[i][j];
    int d=0;
    if(check(graph[i][j],0) && t!=visited[i][j-1] && j-1>=1)
    {
        d=dp[t]+dp[visited[i][j-1]];
        if(d>extend)
        {
            extend=d;
            r=i,c=j;
            s=0;
        }
        else if(d==extend)
        {
            if(j<c)
            {
                r=i,c=j;
                s=0;
            }
            else if(j==c)
            {
                if(i>r)
                {
                    r=i,j=c;
                    s=0;
                }
            }
        }
    }

    if(check(graph[i][j],2) && t!=visited[i][j+1] && j+1<=m)
    {
        d=dp[t]+dp[visited[i][j+1]];
        if(d>extend)
        {
            extend=d;
            r=i,c=j;
            s=2;
        }
        else if(d==extend)
        {
            if(j<c)
            {
                r=i,c=j;
                s=2;
            }
            else if(j==c)
            {
                if(i>r)
                {
                    r=i,j=c;
                    s=2;
                }
                else if(i==r)
                {
                    if(s!=1)
                    {
                        r=i,j=c;
                        s=2;
                    }
                }
            }
        }
    }

    // if(check(graph[i][j],2) && !visited[i][j+1]) d+=1+dfs(i,j+1,x);
    //if(check(graph[i][j],1) && !visited[i-1][j]) d+=1+dfs(i-1,j,x);
    if(check(graph[i][j],1) && t!=visited[i-1][j] && i-1>=1)
    {
        d=dp[t]+dp[visited[i-1][j]];
        if(d>extend)
        {
            extend=d;
            r=i,c=j;
            s=1;
        }
        else if(d==extend)
        {
            if(j<c)
            {
                r=i,c=j;
                s=1;
            }
            else if(j==c)
            {
                if(i>r)
                {
                    r=i,j=c;
                    s=1;
                }
                else if(i==r)
                {
                    r=i,j=c;
                    s=1;
                }
            }
        }
    }
    //if(check(graph[i][j],3) && !visited[i+1][j]) d+=1+dfs(i+1,j,x);

    if(check(graph[i][j],3) && t!=visited[i+1][j] && i+1<=n)
    {
        d=dp[t]+dp[visited[i+1][j]];
        if(d>extend)
        {
            extend=d;
            r=i,c=j;
            s=3;
        }
        else if(d==extend)
        {
            if(j<c)
            {
                r=i,c=j;
                s=3;
            }
            else if(j==c)
            {
                if(i>r)
                {
                    r=i,j=c;
                    s=3;
                }
            }
        }
    }
}

int main()
{
    freopen("castle.in","r",stdin);
    freopen("castle.out","w",stdout);
    cin>>n>>m;
    swap(n,m);
    REP(i,1,n) REP(j,1,m) cin>>graph[i][j];

    int k=0;
    int ans=-1;
    REP(i,1,n) REP(j,1,m)
    {
        if(!visited[i][j])
        {
            k++;
            dp[k]=dfs(i,j,k)+1;
            ans=max(ans,dp[k]);
        }
    }

    cout<<k<<endl<<ans<<endl;
    REP(i,1,n) REP(j,1,m)
    {
        func(i,j,visited[i][j]);
//        cout<<i<<" "<<j<<" "<<extend<<" "<<s<<endl;
    }
    cout<<extend<<endl;
    cout<<r<<" "<<c;
    if(s==2)pf(" E\n");
    else
        pf(" N\n");
    return 0;
}

USACO: Superprime Rib

0

Problem Link : http://train.usaco.org/usacoprob2?a=tffkkLavmsp&S=sprime


/*
PROG: sprime
LANG: C++
*/

#include <bits/stdc++.h>

#define pii             pair <int,int>
#define sc              scanf
#define pf              printf
#define Pi              2*acos(0.0)
#define ms(a,b)         memset(a, b, sizeof(a))
#define pb(a)           push_back(a)
#define MP              make_pair
#define db              double
#define ll              long long
#define EPS             10E-10
#define ff              first
#define ss              second
#define sqr(x)          (x)*(x)
#define D(x)            cout<<#x " = "<<(x)<<endl
#define VI              vector <int>
#define DBG             pf("Hi\n")
#define MOD             100007
#define MAX             10000
#define CIN             ios_base::sync_with_stdio(0); cin.tie(0)
#define SZ(a)           (int)a.size()
#define sf(a)           scanf("%d",&a)
#define sfl(a)          scanf("%lld",&a)
#define sff(a,b)        scanf("%d %d",&a,&b)
#define sffl(a,b)       scanf("%lld %lld",&a,&b)
#define sfff(a,b,c)     scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c)    scanf("%lld %lld %lld",&a,&b,&c)
#define loop(i,n)       for(int i=0;i<n;i++)
#define REP(i,a,b)      for(int i=a;i<b;i++)
#define TEST_CASE(t)    for(int z=1;z<=t;z++)
#define PRINT_CASE      printf("Case %d: ",z)
#define all(a)          a.begin(),a.end()
#define intlim          2147483648
#define inf             1000000
#define ull             unsigned long long

using namespace std;


/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
//bool check(int N,int pos){return (bool)(N & (1<<pos));}
/*------------------------------------------------*/

vector<ll>v;
int n;

bool isprime(ll n)
{
    if(n==2) return 1;
    if(!(n & 1)) return 0;

    for(int i=3; i*i<=n; i+=2)
        if(n%i==0) return 0;
    return 1;
}

void dfs(ll u,int m)
{
    if(!isprime(u)) return;
    if(m==n)
    {
        v.pb(u);
        return;
    }
    for(int i=1; i<=9; i+=2)
    {
        int x=u*10+i;
        dfs(x,m+1);
    }
}

int main()
{
    freopen("sprime.in","r",stdin);
    freopen("sprime.out","w",stdout);
    cin>>n;
    for(int i=2; i<=9; i++)
        dfs(i,1);
    sort(all(v));
    loop(i,SZ(v)) cout<<v[i]<<endl;
    return 0;
}

Light OJ : 1168 – Wishing Snake

0

Problem Link : http://www.lightoj.com/volume_showproblem.php?problem=1168

Algorithm :

1. Make a graph from input data and Determine the SCC of the graph.
2. Make a new Graph from SCC. Consider Each SCC as a node of this graph.
3. If any Node of SCC_graph have more than 1 out degree and It is not possible to traverse all node from the SCC which contain’s the node 0 of the input graph then Print “NO”.
4. Otherwise Print “YES”;


/*
         +-+ +-+ +-+
         |R| |.| |S|
         +-+ +-+ +-+
 */

#include <bits/stdc++.h>

#define pii             pair <int,int>
#define sc              scanf
#define pf              printf
#define Pi              2*acos(0.0)
#define ms(a,b)         memset(a, b, sizeof(a))
#define pb(a)           push_back(a)
#define MP              make_pair
#define db              double
#define ll              long long
#define EPS             10E-10
#define ff              first
#define ss              second
#define sqr(x)          (x)*(x)
#define D(x)            cout<<#x " = "<<(x)<<endl
#define VI              vector <int>
#define DBG             pf("Hi\n")
#define MOD             100007
#define MAX             1005
#define CIN             ios_base::sync_with_stdio(0); cin.tie(0)
#define SZ(a)           (int)a.size()
#define sf(a)           scanf("%d",&a)
#define sff(a,b)        scanf("%d%d",&a,&b)
#define sfff(a,b,c)     scanf("%d%d%d",&a,&b,&c)
#define loop(i,n)       for(int i=0;i<n;i++)
#define REP(i,a,b)      for(int i=a;i<b;i++)
#define TEST_CASE(t)    for(int z=1;z<=t;z++)
#define PRINT_CASE      printf("Case %d: ",z)
#define all(a)          a.begin(),a.end()
#define intlim          2147483648
#define inf             1000000
#define ull             unsigned long long

using namespace std;


const int fx[]={+1,-1,+0,+0};
const int fy[]={+0,+0,+1,-1};

vector<int>graph[MAX],rev_graph[MAX],scc_graph[MAX];
int visited[MAX];
int node[MAX],scc_num[MAX],node_num,scc;
stack<int>st;
bool test,scc_vis[MAX];

void allclear()
{
    loop(i,node_num+2)
    {
        visited[i]=0;
        graph[i].clear();
        rev_graph[i].clear();
        scc_num[i]=0;
    }
    loop(i,scc+2)
    {
        scc_graph[i].clear();
        scc_vis[i]=0;
    }
    node_num=0;
    scc=0;
}

void dfs1(int u)
{
    visited[u]++;
    loop(i,SZ(graph[u]))
    {
        int v=graph[u][i];
        if(visited[v]==0)
            dfs1(v);
    }
    st.push(u);
}

void dfs2(int u)
{
    visited[u]++;
    scc_num[u]=scc;
    loop(i,SZ(rev_graph[u]))
    {
        int v=rev_graph[u][i];
        if(visited[v]!=2)
            dfs2(v);
    }
}

void dfs3(int u)
{
    scc_vis[u]=1;
    if(SZ(scc_graph[u])>1)
        {test=0;return;}
    loop(i,SZ(scc_graph[u]))
    dfs3(scc_graph[u][i]);
}

int main()
{
    ///freopen("in.txt","r",stdin);
    ///freopen("out.txt","w",stdout);

    int t;
    sf(t);
    TEST_CASE(t)
    {
        ms(node,-1);
        int n,m,u,v;
        node_num=0;
        node[0]=node_num;
        sf(n);
        loop(i,n)
        {
            sf(m);
            loop(j,m)
            {
                sff(u,v);
                if(node[u]==-1) node[u]=++node_num;
                if(node[v]==-1) node[v]=++node_num;
                graph[node[u]].pb(node[v]);
                rev_graph[node[v]].pb(node[u]);
            }
        }

        loop(i,node_num)
        {
            if(visited[i]==0)
                dfs1(i);
        }

        scc=0;
        while(!st.empty())
        {
            u=st.top();
            st.pop();
            if(visited[u]!=2)
            {
                scc++;
                dfs2(u);
            }
        }

        loop(i,node_num)
        {
            loop(j,SZ(graph[i]))
            {
                u=graph[i][j];
                if(scc_num[i]!=scc_num[u])
                    scc_graph[scc_num[i]].pb(scc_num[u]);
            }
        }

        test=1;
        dfs3(scc_num[0]);
        if(test)
        {
            REP(i,1,scc+1)
            {
                if(!scc_vis[i])
                    test=0;
            }
        }
        PRINT_CASE;
        if(test)
            pf("YES\n");
        else
            pf("NO\n");
        allclear();

    }
    return 0;
}


Light OJ : 1417 – Forwarding Emails

0

Problem Link : http://www.lightoj.com/volume_showproblem.php?problem=1417


/*
         +-+ +-+ +-+
         |R| |.| |S|
         +-+ +-+ +-+
 */
 
#include <bits/stdc++.h>
 
#define pii             pair <int,int>
#define sc              scanf
#define pf              printf
#define Pi              2*acos(0.0)
#define ms(a,b)         memset(a, b, sizeof(a))
#define pb(a)           push_back(a)
#define MP              make_pair
#define db              double
#define ll              long long
#define EPS             10E-10
#define ff              first
#define ss              second
#define sqr(x)          (x)*(x)
#define D(x)            cout<<#x " = "<<(x)<<endl
#define VI              vector <int>
#define DBG             pf("Hi\n")
#define MOD             100007
#define MAX             50005
#define CIN             ios_base::sync_with_stdio(0); cin.tie(0)
#define SZ(a)           (int)a.size()
#define sf(a)           scanf("%d",&a)
#define sff(a,b)        scanf("%d%d",&a,&b)
#define sfff(a,b,c)     scanf("%d%d%d",&a,&b,&c)
#define loop(i,n)       for(int i=0;i<n;i++)
#define REP(i,a,b)      for(int i=a;i<b;i++)
#define TEST_CASE(t)    for(int z=1;z<=t;z++)
#define PRINT_CASE      printf("Case %d: ",z)
#define all(a)          a.begin(),a.end()
#define intlim          2147483648
#define inf             1000000
#define ull             unsigned long long
 
using namespace std;
 
int n,dfsnum,dis[MAX];
vector<int> graph[MAX],rev_graph[MAX];
bool mp[MAX],mp1[MAX],mp2[MAX];
 
void allclear()
{
    loop(i,n+2)
    {
        graph[i].clear();
        rev_graph[i].clear();
        dis[i]=0;
        mp[i]=mp1[i]=mp2[i]=0;
    }
    dfsnum=0;
}
 
void dfs1(int u)
{
    mp[u]=1;
    dfsnum++;
    loop(i,SZ(graph[u]))
    {
        int v=graph[u][i];
        if(!mp[v])
            dfs1(v);
    }
    dis[u]=++dfsnum;
}
 
void dfs2(int u)
{
    mp1[u]=1;
    loop(i,SZ(rev_graph[u]))
    {
        int v=rev_graph[u][i];
        if(!mp1[v])
            dfs2(v);
    }
}
 
void dfs3(int u)
{
    mp2[u]=1;
    dfsnum++;
    loop(i,SZ(graph[u]))
    {
        int v=graph[u][i];
        if(!mp2[v])
            dfs3(v);
    }
}
 
void dfs4(int u)
{
    mp2[u]=0;
    loop(i,SZ(graph[u]))
    {
        int v=graph[u][i];
        if(mp2[v])
            dfs4(v);
    }
}
 
int main()
{
    ///freopen("in.txt","r",stdin);
    ///freopen("out.txt","w",stdout);
 
    int t;
    sf(t);
    TEST_CASE(t)
    {
        sf(n);
        allclear();
        int a,b;
        loop(i,n)
        {
            sff(a,b);
            graph[a].pb(b);
            rev_graph[b].pb(a);
        }
        REP(i,1,n+1)
        {
            if(!mp[i])
                dfs1(i);
        }
 
        vector<pii>top_sort;
        REP(i,1,n+1)
        {
            top_sort.pb(MP(dis[i],i));
        }
 
 
        sort(top_sort.rbegin(),top_sort.rend());
        vector<int>scc;
 
        loop(i,SZ(top_sort))
        {
            int u=top_sort[i].ss;
            if(!mp1[u])
            {
                scc.pb(u);
                dfs2(u);
            }
        }
 
        top_sort.clear();
        loop(i,SZ(scc))
        {
            int u=scc[i];
            if(!mp2[u])
            {
                dfsnum=0;
                dfs3(u);
                top_sort.pb(MP(dfsnum,u));
                dfs4(u); // this DFS is clearing only visited node.
            }
        }
 
        sort(top_sort.rbegin(),top_sort.rend());
        PRINT_CASE;
        if(SZ(top_sort)==1)
            pf("%d\n",top_sort[0].ss);
        else
        {
            loop(i,SZ(top_sort)-1)
            {
                if(top_sort[i].ff!=top_sort[i+1].ff) // This is for determine the smallest one.
                {
                    pf("%d\n",top_sort[i].ss);
                    break;
                }
            }
        }
    }
    return 0;
}

Light OJ 1108 – Instant View of Big Bang

0

Problem Link : http://www.lightoj.com/volume_showproblem.php?problem=1108

Algorithm:

1. Make a graph by reverse the edge direction.
2. Run Bellman Ford in reverse Graph and check if there exist a negative weight cycle. Reversing edge doesn’t affect in cycle because if we reverse the edge direction then cycle remain unchanged.
3. If exist a negative cycle then run a DFS on the reverse graph for finding the nodes which are reachable from negative cycle and store them in a vector and after sorting the vector print them.
4. If there is no negative cycle then print impossible.


/*
         +-+ +-+ +-+
         |R| |.| |S|
         +-+ +-+ +-+
 */

#include <bits/stdc++.h>

#define pii             pair <int,int>
#define sc              scanf
#define pf              printf
#define Pi              2*acos(0.0)
#define ms(a,b)         memset(a, b, sizeof(a))
#define pb(a)           push_back(a)
#define MP              make_pair
#define db              double
#define ll              long long
#define EPS             10E-10
#define ff              first
#define ss              second
#define sqr(x)          (x)*(x)
#define D(x)            cout<<#x " = "<<(x)<<endl
#define VI              vector <int>
#define DBG             pf("Hi\n")
#define MOD             100007
#define MAX             1005
#define CIN             ios_base::sync_with_stdio(0); cin.tie(0)
#define SZ(a)           (int)a.size()
#define sf(a)           scanf("%d",&a)
#define sff(a,b)        scanf("%d%d",&a,&b)
#define sfff(a,b,c)     scanf("%d%d%d",&a,&b,&c)
#define loop(i,n)       for(int i=0;i<n;i++)
#define REP(i,a,b)      for(int i=a;i<b;i++)
#define TEST_CASE(t)    for(int z=1;z<=t;z++)
#define PRINT_CASE      printf("Case %d: ",z)
#define all(a)          a.begin(),a.end()
#define intlim          2147483648
#define inf             1000000
#define ull             unsigned long long

using namespace std;

struct data
{
    int u,v,w;
    data(int x, int y, int z)
    {
        u=x,v=y,w=z;
    }
};

int n,m,total_edge;
vector<data> graph;
vector<int>ans,reverse_graph[MAX];
map<int,bool>mp;
int d[MAX];
bool visited[MAX];

void dfs(int u)
{
    mp[u]=1;
    ans.pb(u);
    loop(i,SZ(reverse_graph[u]))
    {
        int v=reverse_graph[u][i];
        if(!mp[v])
            dfs(v);
    }
}

bool bellmanford()
{
    for(int i=1;i<n;i++)
    {
        loop(i,m)
        {
            int u=graph[i].u;
            int v=graph[i].v;
            if(d[u]+graph[i].w<d[v])
            {
                d[v]=d[u]+graph[i].w;
            }
        }
    }

    bool negative_cycle=0;

    loop(i,m)
        {
            int u=graph[i].u;
            int v=graph[i].v;
            if(d[u]+graph[i].w<d[v])
            {
                negative_cycle=1;
                d[v]=d[u]+graph[i].w;
                if(!mp[u])
                    dfs(u);
            }
        }
        return negative_cycle;
}

void allclear()
{
    graph.clear();
    ans.clear();
    mp.clear();

    loop(i,n+2)
        {d[i]=inf;reverse_graph[i].clear();}
}

int main()
{
    ///freopen("in.txt","r",stdin);
    ///freopen("out.txt","w",stdout);
    int t;
    sf(t);
    TEST_CASE(t)
    {
        int u,v,w;
        sff(n,m);
        allclear();
        loop(i,m)
        {
            sfff(u,v,w);
            graph.pb(data(v,u,w));//reversing graph
            reverse_graph[v].pb(u);
        }
        
        PRINT_CASE;
        if(bellmanford())
        {
            sort(all(ans));
            pf("%d",ans[0]);
            REP(i,1,SZ(ans))
            pf(" %d",ans[i]);
            pf("\n");
        }
        else
            pf("impossible\n");
    }
    return 0;
}


Light OJ 1034 – Hit the Light Switches

0

Problem Link : http://www.lightoj.com/volume_showproblem.php?problem=1034


/*
         +-+ +-+ +-+
         |R| |.| |S|
         +-+ +-+ +-+
 */

#include <bits/stdc++.h>

#define pii             pair <int,int>
#define sc              scanf
#define pf              printf
#define Pi              2*acos(0.0)
#define ms(a,b)         memset(a, b, sizeof(a))
#define pb(a)           push_back(a)
#define MP              make_pair
#define db              double
#define ll              long long
#define EPS             10E-10
#define ff              first
#define ss              second
#define sqr(x)          (x)*(x)
#define D(x)            cout<<#x " = "<<(x)<<endl
#define VI              vector <int>
#define DBG             pf("Hi\n")
#define MOD             100007
#define MAX             10005
#define CIN             ios_base::sync_with_stdio(0); cin.tie(0)
#define SZ(a)           (int)a.size()
#define sf(a)           scanf("%d",&a)
#define sff(a,b)        scanf("%d%d",&a,&b)
#define sfff(a,b,c)     scanf("%d%d%d",&a,&b,&c)
#define loop(i,n)       for(int i=0;i<n;i++)
#define REP(i,a,b)      for(int i=a;i<b;i++)
#define TEST_CASE(t)    for(int z=1;z<=t;z++)
#define PRINT_CASE      printf("Case %d: ",z)
#define all(a)          a.begin(),a.end()
#define intlim          2147483648
#define inf             1000000
#define ull             unsigned long long

using namespace std;

int n,m;
vector<int>graph[MAX],topsort;
bool visited[MAX],test;

void allclear()
{
    loop(i,n+2)
    {
        graph[i].clear();
        visited[i]=0;
    }
    topsort.clear();
}

void dfs(int u)
{
    visited[u]=1;
    loop(i,SZ(graph[u]))
    {
        int v=graph[u][i];
        if(!visited[v])
            dfs(v);
    }
    if(test)
        topsort.pb(u);
}

int main()
{
    ///freopen("in.txt","r",stdin);
    ///freopen("out.txt","w",stdout);
    int t,a,b;
    sf(t);
    TEST_CASE(t)
    {
        sff(n,m);
        loop(i,m)
        {
            sff(a,b);
            graph[a].pb(b);
        }
        test=1;
        int ans=0;
        REP(i,1,n+1)
        {
            if(!visited[i])
                dfs(i);
        }

        test=0;
        loop(i,n+2) visited[i]=0;
        for(int i=SZ(topsort)-1; i>=0; i--)
        {
            int u=topsort[i];
            if(!visited[u])
            {
                dfs(u);
                ans++;
            }
        }
        PRINT_CASE;
        pf("%d\n",ans);
        allclear();
    }
    return 0;
}


Another solution of this problem using Strongly Connected components(SCC) is here…


/*
         +-+ +-+ +-+
         |R| |.| |S|
         +-+ +-+ +-+
 */

#include <bits/stdc++.h>

#define pii             pair <int,int>
#define sc              scanf
#define pf              printf
#define Pi              2*acos(0.0)
#define ms(a,b)         memset(a, b, sizeof(a))
#define pb(a)           push_back(a)
#define MP              make_pair
#define db              double
#define ll              long long
#define EPS             10E-10
#define ff              first
#define ss              second
#define sqr(x)          (x)*(x)
#define D(x)            cout<<#x " = "<<(x)<<endl
#define VI              vector <int>
#define DBG             pf("Hi\n")
#define MOD             100007
#define MAX             10005
#define CIN             ios_base::sync_with_stdio(0); cin.tie(0)
#define SZ(a)           (int)a.size()
#define sf(a)           scanf("%d",&a)
#define sff(a,b)        scanf("%d%d",&a,&b)
#define sfff(a,b,c)     scanf("%d%d%d",&a,&b,&c)
#define loop(i,n)       for(int i=0;i<n;i++)
#define REP(i,a,b)      for(int i=a;i<b;i++)
#define TEST_CASE(t)    for(int z=1;z<=t;z++)
#define PRINT_CASE      printf("Case %d: ",z)
#define all(a)          a.begin(),a.end()
#define intlim          2147483648
#define inf             1000000
#define ull             unsigned long long

using namespace std;

int n,m;
vector<int>graph[MAX],reverse_graph[MAX],scc;
vector<pii>v;
int indegree[MAX],topsort[MAX],finish;
bool visited[MAX];

void allclear()
{
    loop(i,n+2)
    {
        graph[i].clear();
        reverse_graph[i].clear();
        indegree[i]=0;
        visited[i]=0;
        topsort[i];
    }
    scc.clear();
    v.clear();
    finish=0;
}

void dfs1(int u)
{
    finish++;
    visited[u]=1;
    loop(i,SZ(graph[u]))
    {
        int v=graph[u][i];
        if(!visited[v])
            dfs1(v);
    }
    topsort[u]=++finish;
}

void dfs2(int u)
{
    visited[u]=1;
    loop(i,SZ(reverse_graph[u]))
    {
        int v=reverse_graph[u][i];
        if(!visited[v])
            dfs2(v);
    }
}

void dfs3(int u)
{
    visited[u]=1;
    loop(i,SZ(graph[u]))
    {
        int v=graph[u][i];
        if(!visited[v])
            dfs3(v);
    }
}
int main()
{
    ///freopen("in.txt","r",stdin);
    ///freopen("out.txt","w",stdout);
    int t,a,b;
    sf(t);
    TEST_CASE(t)
    {
        sff(n,m);
        loop(i,m)
        {
            sff(a,b);
            graph[a].pb(b);
            reverse_graph[b].pb(a);
            indegree[b]++;
        }

        int ans=0;
        REP(i,1,n+1)
        {
            if(!visited[i])
                dfs1(i);
        }

        REP(i,1,n+1)
        {
            v.pb(MP(topsort[i],i));
        }
        sort(all(v));
        loop(i,n+2)
        visited[i]=0;

        for(int i=SZ(v)-1; i>=0; i--)
        {
            int u=v[i].ss;
            if(!visited[u])
            {
                scc.pb(u);
                dfs2(u);
            }
        }

        loop(i,n+2)
        visited[i]=0;

        loop(i,SZ(scc))
        {
            if(!visited[scc[i]])
            {
                ans++;
                dfs3(scc[i]);
            }
        }
        PRINT_CASE;
        pf("%d\n",ans);
        allclear();
    }
    return 0;
}