Uva 11324 The Largest Clique【强连通 DAG动规 spfa】

白书上的例题

做一遍tarjan后，缩点，每一个scc节点的权为它的结点数，做一次DAG上的动规，求出路径上的最大点权和，就可以了

 #include<cstdio>
 #include<cstring>
 #include<iostream>
 #include<algorithm>
 #include<stack>
 #include<vector>
 using namespace std;

 const int maxn = ;
 int n,m;
 int first[maxn];
 int sc[maxn],scn[maxn],low[maxn],pre[maxn];
 int scnt,ecnt,dfs_clock;
 int dp[maxn];

 int first1[maxn];
 int ecnt1;

 struct Edge{
     int v,next;
 }e[maxn*];

 Edge e1[maxn*];

 stack<int> S;

 void init(){
     ecnt = ecnt1 = ;
     memset(first,-,sizeof(first));
     memset(first1,-,sizeof(first1));
     memset(dp,,sizeof(dp));
 }

 void addedges(int u,int v){
     e[ecnt].v = v;
     e[ecnt].next = first[u];
     first[u] = ecnt++;
 }

 void addedges1(int u,int v){
     e1[ecnt1].v = v;
     e1[ecnt1].next = first1[u];
     first1[u] = ecnt1++;
 }

 void dfs(int u){
     low[u] = pre[u] = ++dfs_clock;
     S.push(u);
     for(int i = first[u];~i;i = e[i].next){
         int v = e[i].v;
         if(!pre[v]){
             dfs(v);
             low[u] = min(low[u],low[v]);
         }
         else if(!sc[v]) low[u] = min(low[u],pre[v]);
     }
     if(pre[u] == low[u]){
         scnt++;
         for(;;){
             int x = S.top();S.pop();
             sc[x] = scnt;
             scn[scnt]++;
             if(x == u) break;
         }
     }
 }

 void find_scc(){
     while(!S.empty()) S.pop();
     scnt = dfs_clock = ;
     memset(low,,sizeof(low));memset(pre,,sizeof(pre));
     memset(sc,,sizeof(sc));memset(scn,,sizeof(scn));

     for(int i = ;i <= n;i++) if(!pre[i]) dfs(i);
 }

 int solve(int p){
     if(dp[p]) return dp[p];
     for(int i = first1[p];~i;i = e1[i].next){
         int v = e1[i].v;
         dp[p] = max(dp[p],solve(v));
     }
     return dp[p] = dp[p] + scn[p];
 }

 int main(){
     int T;
     scanf("%d",&T);
     while(T--){
         init();
         scanf("%d %d",&n,&m);
         for(int i = ;i < m;i++ ){
             int u,v;
             scanf("%d %d",&u,&v);
             addedges(u,v);
         }
         find_scc();

         for(int u = ;u <= n;u++){
             for(int i = first[u];~i;i = e[i].next){
                 int v = e[i].v;
                 if(sc[u] != sc[v]) addedges1(sc[u],sc[v]);
             }
         }

         int ans = ;
         for(int i = ;i <= scnt;i++) ans = max(ans,solve(i));
         printf("%d\n",ans);
     }
     return ;
 }

还有另一种做法是，建立一个超级源点，与入度为0的scc节点连接，做一次spfa,求出路径上的最大点权和

 #include<cstdio>
 #include<cstring>
 #include<iostream>
 #include<algorithm>
 #include<stack>
 #include<vector>
 #include<queue>
 using namespace std;

 const int maxn = ;
 const int INF = ;
 int n,m;
 int first[maxn];
 int sc[maxn],scn[maxn],low[maxn],pre[maxn];
 int scnt,ecnt,dfs_clock;
 int dp[maxn];

 int du[maxn];
 int dis[maxn];
 int inq[maxn];

 int first1[maxn];
 int ecnt1;

 struct Edge{
     int v,next;
 }e[maxn*];

 Edge e1[maxn*];

 stack<int> S;
 vector<int> g[maxn];
 int val[maxn];

 void init(){
     ecnt = ecnt1 = ;
     memset(first,-,sizeof(first));
     memset(val,,sizeof(val));
     memset(du,,sizeof(du));
 }

 void addedges(int u,int v){
     e[ecnt].v = v;
     e[ecnt].next = first[u];
     first[u] = ecnt++;
 }

 void dfs(int u){
     low[u] = pre[u] = ++dfs_clock;
     S.push(u);
     for(int i = first[u];~i;i = e[i].next){
         int v = e[i].v;
         if(!pre[v]){
             dfs(v);
             low[u] = min(low[u],low[v]);
         }
         else if(!sc[v]) low[u] = min(low[u],pre[v]);
     }
     if(pre[u] == low[u]){
         scnt++;
         for(;;){
             int x = S.top();S.pop();
             sc[x] = scnt;
             val[scnt]++;
             if(x == u) break;
         }
     }
 }

 void find_scc(){
     while(!S.empty()) S.pop();
     scnt = dfs_clock = ;
     memset(low,,sizeof(low));memset(pre,,sizeof(pre));
     memset(sc,,sizeof(sc));memset(scn,,sizeof(scn));

     for(int i = ;i <= n;i++) if(!pre[i]) dfs(i);
 }

 int spfa(){
     memset(inq, , sizeof(inq));
     queue<int>q;
     g[].clear();
     q.push();
     dis[] = ; val[] = ;
     for(int i = ; i <= scnt; i++){if(du[i] == )g[].push_back(i); dis[i] = -INF;}
     int ans = ;
     while(!q.empty()){
         int u = q.front(); q.pop(); inq[u] = ;
         for(int i = ; i < g[u].size(); i++){
             int v = g[u][i];
             if(dis[v] < dis[u] + val[v]){
                 dis[v] = dis[u] + val[v];
                 ans = max(ans, dis[v]);
                 if(inq[v] == )inq[v] = , q.push(v);
             }
         }
     }
     return ans;
 }  

 int main(){
     int T;
     scanf("%d",&T);
     while(T--){
         init();
         scanf("%d %d",&n,&m);
         for(int i = ;i < m;i++ ){
             int u,v;
             scanf("%d %d",&u,&v);
             addedges(u,v);
         }
         find_scc();
         for(int i = ;i <= scnt;i++) g[i].clear();

         for(int u = ;u <= n;u++){
             for(int i = first[u];~i;i = e[i].next){
                 int v = e[i].v;
                 if(sc[u] != sc[v]) g[sc[u]].push_back(sc[v]),du[sc[v]]++;
             }
         }
         printf("%d\n",spfa());
     }
     return ;
 }