POJ 2455 Secret Milking Machine (二分 + 最大流)

题目大意：

给出一张无向图，找出T条从1..N的路径，互不重复，求走过的所有边中的最大值最小是多少。

算法讨论：

首先最大值最小就提醒我们用二分，每次二分一个最大值，然后重新构图，把那些边权符合要求的边加入新图，在新图上跑网络流。

这题有许多注意的地方：

1、因为是无向图，所以我们在加正向边和反向边的时候，流量都是1，而不是正向边是1，反向边是0。

2、题目中说这样的路径可能不止t条，所以我们在最后二分判定的时候不能写 == t，而是要 >= t。

3、这题很容易T ，表示我T了N遍，弱菜啊。

Codes：

 #include <cstring>
 #include <cstdlib>
 #include <iostream>
 #include <algorithm>
 #include <cstdio>
 #include <vector>
 #include <queue>

 using namespace std;

 struct Edge{
     int from, to, cap, flow;
     Edge(int _from = , int _to = , int _cap = , int _flow = ):
         from(_from), to(_to), cap(_cap), flow(_flow) {}
 }E[ + ];

 struct Dinic{
     static const int N =  + ;
     static const int M =  + ;
     static const int oo = 0x3f3f3f3f;

     int n, m, s, t;
     vector <Edge> edges;
     vector <int> G[N];
     int dis[N], cur[N];
     bool vi[N];

     void Clear(){
         for(int i = ; i <= n; ++ i) G[i].clear();
         edges.clear();
     }

     void Add(int from, int to, int cap, int flow){
         edges.push_back((Edge){from, to, cap, });
         edges.push_back((Edge){to, from, cap, });
         int m = edges.size();
         G[from].push_back(m - );
         G[to].push_back(m - );
     }

     bool bfs(){
         for(int i = ; i <= n; ++ i) vi[i] = false;
         dis[s] = ; vi[s] = true;
         queue <int> q; q.push(s);

         while(!q.empty()){
             int x = q.front(); q.pop();
             for(int i = ; i < G[x].size(); ++ i){
                 Edge &e = edges[G[x][i]];
                 if(!vi[e.to] && e.cap > e.flow){
                     vi[e.to] = true;
                     dis[e.to] = dis[x] + ;
                     q.push(e.to);
                 }
             }
         }
         return vi[t];
     }

     int dfs(int x, int a){
         if(x == t || a == ) return a;
         int flw = , f;
         for(int &i = cur[x]; i < G[x].size(); ++ i){
             Edge &e = edges[G[x][i]];
             if(dis[x] +  == dis[e.to] && (f = dfs(e.to, min(a, e.cap - e.flow))) > ){
                 e.flow += f; edges[G[x][i]^].flow -= f;
                 a -= f; flw += f;
                 if(!a) break;
             }
         }
         return flw;
     }

     int Maxflow(int s, int t){
         this->s = s;this-> t = t;
         int flw = ;
         while(bfs()){
             memset(cur, , sizeof cur);
             flw += dfs(s, oo);
         }
         return flw;
     }

 }Net;

 int ns, ps, ts;
 int l = 0x3f3f3f3f, r, mid;

 bool check(int mv){
     for(int i = ; i < ps; ++ i){
         if(E[i].cap <= mv){
             Net.Add(E[i].from, E[i].to, , );
         }
     }
     return Net.Maxflow(, Net.n) >= ts;
 }

 int Solve(){
     int ans;

     while(l <= r){
         Net.Clear();
         mid = l + (r - l) / ;
         if(check(mid)){
             ans = mid; r = mid - ;
         }
         else l = mid + ;
     }

     return ans;
 }

 int main(){
     int x, y, z;

     scanf("%d%d%d", &ns, &ps, &ts);
     Net.n = ns;
     for(int i = ; i < ps; ++ i){
         scanf("%d%d%d", &x, &y, &z);
         E[i] = (Edge){x, y, z, };
         l = min(l, z); r = max(r, z);
     }

     printf("%d\n", Solve());
     return ;
 }

POJ 2455

让人更加不能理解的是，为什么我换了上面的邻接表的形式，用STL容器来存邻接表就AC，用数组来存就T成狗。

下面是我狂T的代码，良心网友们给查查错误呗。

 #include <cstdio>
     #include <iostream>
     #include <cstring>
     #include <cstdlib>
     #include <algorithm>
     #include <queue>

     using namespace std;

     int ns, ps, ts, te;
     int l=0x3f3f3f3f, r, Mid;

     struct Edge{
         int from, to, dt;
     }e[ + ];

     struct Dinic{
       static const int maxn =  + ;
       static const int maxm =  + ;
       static const int oo = 0x3f3f3f3f;

       int n,m,s,t;
       int tot;
       int first[maxn],next[maxm];
       int u[maxm],v[maxm],cap[maxm],flow[maxm];
       int cur[maxn],dis[maxn];
       bool vi[maxn];

       Dinic(){tot=;memset(first,-,sizeof first);}
       void Clear(){tot = ;memset(first,-,sizeof first);}
       void Add(int from,int to,int cp,int flw){
           u[tot] = from;v[tot] = to;cap[tot] = cp;flow[tot] = ;
           next[tot] = first[u[tot]];
           first[u[tot]] = tot;
           ++ tot;
       }
       bool bfs(){
           memset(vi,false,sizeof vi);
           queue <int> q;
           dis[s] = ;vi[s] = true;
           q.push(s);

           while(!q.empty()){
           int now = q.front();q.pop();
           for(int i = first[now];i != -;i = next[i]){
               if(!vi[v[i]] && cap[i] > flow[i]){
               vi[v[i]] = true;
               dis[v[i]] = dis[now] + ;
               q.push(v[i]);
             }
           }
         }
         return vi[t];
       }
       int dfs(int x,int a){
           if(x == t || a == ) return a;
           int flw=,f;
           int &i = cur[x];
           for(i = first[x];i != -;i = next[i]){
             if(dis[x] +  == dis[v[i]] && (f = dfs(v[i],min(a,cap[i]-flow[i]))) > ){
               flow[i] += f;flow[i^] -= f;
             a -= f;flw += f;
             if(a == ) break;
           }
         }
         return flw;
       }
       int MaxFlow(int s,int t){
           this->s = s;this->t = t;
           int flw=;
           while(bfs()){
             memset(cur,,sizeof cur);
           flw += dfs(s,oo);
         }
         return flw;
       }
     }Net;

     bool check(int mid){
         Net.Clear();
         for(int i = ; i <= ps; ++ i){
             if(e[i].dt <= mid){
                 Net.Add(e[i].from, e[i].to, , );
                 Net.Add(e[i].to, e[i].from, , );
             }
         }
         return Net.MaxFlow(, Net.n) >= ts;
     }
     int Solve(){
         int ans;
         while(l <= r){
             Mid = l + (r - l) / ;
             if(check(Mid)){
                 ans = Mid; r = Mid - ;
             }
             else l = Mid + ;
         }
         return ans;
     }
     int main(){
         int x, y, z;
         scanf("%d%d%d", &ns, &ps, &ts);
         Net.n = ns;te = ;
         for(int i = ; i <= ps; ++ i){
             scanf("%d%d%d", &x, &y, &z);
             ++ te;
             e[te].from = x;e[te].to = y;e[te].dt = z;
             l = min(l, z); r = max(z, r);
         }
         printf("%d\n", Solve());
         return ;
     }

POJ 2455 T 版