强联通分量+缩点

强联通分量,一个有向图中的某一个子图,满足该子图中任意一点,都可以到达该子图中任意点.
计算的方法叫tarjan算法,也就是一个dfs方法,每次对未被访问过的一个点开始,因为如果该点是在一个强联通分量内(当然,假设不止是他一个人),那么该强联通分量肯定是一个”大于环的结构”.那肯定可以dfs下去,关键的地方来了,每个被他所到达的点,如果已经被找到过(特指在寻找该分量时被找到过,而不是此前已经被划入某分量中)或者还未被访问过(全新的),那么需要访问他,并回溯他的low,该low,记录一个点,能够访问到的所有点中最小的dfn值,那么也就是说,一个分量内,所有点除最初点,都会触碰到最初点,降低自己的low值,那么,这样就可以找到最初点了.由此,一个分量也被确定.
缩点是容易的.
hdu 5934

/* Farewell. */#include <iostream>#include <vector>#include <cstdio>#include <stack>#include <cstring>#include <algorithm>#include <queue>#include <map>#include <string>#include <cmath>#include <bitset>#include <iomanip>#include <set>using namespace std;#define lson l,m,rt<<1#define rson m+1,r,rt<<1|1#define MP make_pair#define MT make_tuple#define PB push_backtypedef long long  LL;typedef unsigned long long ULL;typedef pair<int,int > pii;typedef pair<LL,LL> pll;typedef pair<double,double > pdd;typedef pair<double,int > pdi;const int INF = 0x7fffffff;const LL INFF = 0x7f7f7f7fffffffff;#define debug(x) std::cerr << #x << " = " << (x) << std::endlconst int MAXM = 5e3+17;const int MOD = 998244353;const int MAXN = 1e3+17;struct bomb{    LL x,y,r,c;    bomb(LL a,LL b,LL p,LL d):x(a),y(b),r(p),c(d){}    bomb(){}}all[MAXN];vector<int > G[MAXN];int DFN[MAXN],Low[MAXN],in[MAXN],instack[MAXN],num,idx;  stack<int> S;  int belong[MAXN];vector<int > GC[MAXN];LL ct[MAXN];void tarjan(int u)  {      int v;    DFN[u] = Low[u] = ++idx;      instack[u] = 1;      S.push(u);      for(int i=0; i<G[u].size(); i++)      {          v = G[u][i];          if(!DFN[v])          {              tarjan(v);              Low[u] = min(Low[u], Low[v]);          }          else if(instack[v])              Low[u] = min(Low[u], DFN[v]);      }      if(DFN[u] == Low[u])      {          num++;          do          {              v = S.top();              S.pop();              instack[v] = 0;            belong[v] = num;          }while(v != u);      }}  void scc(int n)  {      for(int i=0; i<n; i++)          if(!DFN[i])              tarjan(i);  }  int main(int argc, char const *argv[]){    #ifndef ONLINE_JUDGEfreopen("in.txt","r",stdin);freopen("out.txt","w",stdout);#endif    int t,x=1;    cin>>t;    while(t--)    {        printf("Case #%d: ",x++ );        while(!S.empty()) S.pop();        memset(in,0,sizeof(in));        memset(DFN,0,sizeof(DFN));        memset(Low,0,sizeof(Low));        memset(instack,0,sizeof(instack));        memset(belong,-1,sizeof(belong));        num = -1;        idx = 0;        int n,nc = -1;                cin>>n;        for (int i = 0; i < n; ++i)        {            G[i].clear();            GC[i].clear();            ct[i] = INFF;        }        for (int i = 0; i < n; ++i)        {            LL a,b,c,d;            scanf("%lld%lld%lld%lld",&a,&b,&c,&d);            all[i] = bomb(a,b,c,d);        }        for (int i = 0; i < n; ++i)        {            LL x = all[i].x,y = all[i].y;            for (int j = 0; j < n; ++j)            {                if(j==i) continue;                LL tx = all[j].x,ty = all[j].y;                LL dis = abs(tx-x)*abs(tx-x)+abs(ty-y)*abs(ty-y);                if(dis<=all[i].r*all[i].r)                    G[i].push_back(j);            }        }        scc(n);        for(int i = 0;i < n;++i)        {            debug(i);            debug(belong[i]);        }        for (int i = 0; i < n; ++i)        {            int ic = belong[i];            nc = max(ic,nc);            ct[ic] = min(ct[ic],all[i].c);            for (int j = 0; j < G[i].size(); ++j)                if(ic != belong[G[i][j]])                {                    GC[ic].push_back(belong[G[i][j]]);                    ++in[belong[G[i][j]]];                }        }        LL ans = 0;        for (int i = 0; i <= nc; ++i)            if(in[i]==0)                ans += ct[i];        cout<<ans<<endl;    }    return 0;}