POJ 2396 有源有汇有上下界可行流问题

题意：给一个矩阵，给出每行每列之和，附加一些条件，如第i行第j列数必需大于（小于）多少。
思路题解：矩阵模型，模拟网络流，行、列标号为结点，构图，附加s,t，s连行标（容量上下限每行之和（必需以这个
值全部送过去），每个列标连向t（容量上下限每列之和）），其他每个行到列都有边（有限制的按限制
来，无限制的自己添加）。由于s->网络->t，若有解，总流量f必为
矩阵所有数之和，故添加边t-S,容量上下线为矩阵和sum，这样保证了每个点出入流相等，满足流量平衡，
转化为无源无汇有上下线可行流问题，在建立超级源点汇点ss,tt，按无源无汇法做一遍ss->tt最大流，
判断可行即可。可行输出方案。PS，若题目改为求有源有汇有限制最大流问题，可以在残量网络再走一次
s->t（原图源汇）最大流（solo可行的后悔边啥~）
此题，有源有汇有限制可行流问题，主要是建图，就是一个字烦！其一：0的时候要所有，行列为0要
讨论，其二，>,<,=符号的判定，讨论下，其三，重边，这个不是链前星锁解决那个重边，而是重边
是“且”的关系，如，先给上限，再来一边给下限！坑爹啊这是要！无法，hash判重吧，重了，再修改原来的
边，要搞清楚反向边（建图时跑第一次（第一次判断有无解）前）流量始终为0（提供后悔的，和之后没有

半毛钱关系）！至于算法，不再是问题，dinic跑的。

#include<iostream>  //47ms，1A
#include<cstdio>
#include<queue>
#include<vector>
using namespace std;
int n,m;const int inf=0x3f3f3f3f;
int suminf[300];int sumouf[300];
int e[20000][5]; int head[300];int level[300];int vis[300];
int hash[250][300];int ans[250][300];
int nume=0;
bool bfs()          //dinic“d,bfs”，不用说了
{
    for(int i=0;i<n+m+4;i++)
       level[i]=vis[i]=0;
    vis[n+m+2]=1;
    queue<int>q;q.push(n+m+2);
    while(!q.empty())
    {
        int cur=q.front();q.pop();
        for(int i=head[cur];i!=-1;i=e[i][1])
        {
            int v=e[i][0];
            if(!vis[v]&&e[i][2]>0)
            {
                level[v]=level[cur]+1;
                vis[v]=1;
                if(v==m+n+3)return 1;
                q.push(v);
            }
        }
    }
    return vis[n+m+3];
}
int dfs(int u,int minf)
{
    if(u==n+m+3||minf==0){return minf;}
    int sumf=0,f;
    for(int i=head[u];i!=-1&&minf;i=e[i][1])
        {
            int v=e[i][0];
            if(level[v]==level[u]+1&&e[i][2]>0)
            {
                f=dfs(v,minf<e[i][2]?minf:e[i][2]);
               if(f==0)continue;
                e[i][2]-=f;e[i^1][2]+=f;
                minf-=f;sumf+=f;
            }
        }
        return sumf;
}
void dinic()
{
    int sumflow=0;
    while(bfs())
    {
        sumflow+=dfs(n+m+2,inf);
    }
}
bool check()           //无源无汇的，出发点ss（超级源点）的边有一条不满流就无解，原因简单必需保证流量平衡（为之提供下限）
{
    for(int i=head[n+m+2];i!=-1;i=e[i][1])
    {
        if(e[i][2]!=0)return 0;
    }
    return 1;
}
int main()
{
    int N;
    scanf("%d",&N);
    while(N--)   //N组输入
    {
        scanf("
%d%d",&n,&m);   //忽略空行
         nume=0;
         int sum=0,temp;
         bool mark=0;
       for(int i=0;i<=n+m+5;i++)
         {
             head[i]=-1;
             suminf[i]=sumouf[i]=0;
         }
         for(int i=0;i<=n;i++)
           for(int j=n+1;j<=n+m+1;j++)
              ans[i][j]=hash[i][j]=0;
        for(int i=1;i<=n;i++)                  //有源有汇的源点s
        {
            scanf("%d",&temp);sum+=temp;
            e[nume][0]=i;e[nume][1]=head[0];head[0]=nume;
            e[nume][2]=0;e[nume][3]=temp;e[nume++][4]=temp;
            suminf[i]+=temp;sumouf[0]+=temp;
            e[nume][0]=0;e[nume][1]=head[i];head[i]=nume;
            e[nume++][2]=0;
        }
        for(int i=n+1;i<=m+n;i++)         //汇点t
        {
            scanf("%d",&temp);
            e[nume][0]=n+1+m;e[nume][1]=head[i];head[i]=nume;
            e[nume][2]=0;e[nume][3]=temp;e[nume++][4]=temp;
            suminf[n+m+1]+=temp;sumouf[i]+=temp;
            e[nume][0]=i;e[nume][1]=head[n+m+1];head[n+m+1]=nume;
            e[nume++][2]=0;
        }
            e[nume][0]=0;e[nume][1]=head[n+m+1];head[n+m+1]=nume;  //添加t->s
            e[nume][2]=0;e[nume][3]=sum;e[nume++][4]=sum;
             suminf[0]+=sum;sumouf[n+m+1]+=sum;
            e[nume][0]=n+m+1;e[nume][1]=head[0];head[0]=nume;
            e[nume++][2]=0;
        int ca;scanf("%d",&ca); int row,col,lim;char cc;
         for(int i=0;i<ca;i++)                          //按条件建图
         {
             scanf("%d%d %c %d",&row,&col,&cc,&lim);
             if(col!=0&&row==0)
             {
                 if(cc=='=')
                  for(int i=1;i<=n;i++)
                   {
                     if(hash[i][n+col])        //判重，下面一致
                     {
                         int pp;
                         for( pp=head[i];e[pp][0]!=n+col;pp=e[pp][1])
                         ;
                         suminf[n+col]-=e[pp][3]; sumouf[i]-=e[pp][3];
                         if(lim>e[pp][3])e[pp][3]=lim;
                         if(lim<e[pp][4])e[pp][4]=lim;
                         if(e[pp][3]>e[pp][4])mark=1;
                         e[pp][2]=e[pp][4]-e[pp][3];
                         suminf[n+col]+=e[pp][3]; sumouf[i]+=e[pp][3];
                     }
                     else
                     {
                     e[nume][0]=n+col;e[nume][1]=head[i];head[i]=nume;
                     e[nume][2]=0;e[nume][3]=lim;e[nume++][4]=lim;

                     suminf[n+col]+=lim; sumouf[i]+=lim;hash[i][n+col]=1;
                     e[nume][0]=i;e[nume][1]=head[n+col];head[n+col]=nume;
                     e[nume++][2]=0;
                     }
                   }
                 else if(cc=='>')
                 {
                     for(int i=1;i<=n;i++)
                   {
                       if(hash[i][n+col])
                     {    int pp;
                         for( pp=head[i];e[pp][0]!=n+col;pp=e[pp][1])
                         ;
                         suminf[n+col]-=e[pp][3]; sumouf[i]-=e[pp][3];
                         if(lim+1>e[pp][3])e[pp][3]=lim+1;
                         if(inf<e[pp][4])e[pp][4]=inf;
                         if(e[pp][3]>e[pp][4])mark=1;
                         e[pp][2]=e[pp][4]-e[pp][3];
                         suminf[n+col]+=e[pp][3]; sumouf[i]+=e[pp][3];
                     }
                     else
                    {

                     e[nume][0]=n+col;e[nume][1]=head[i];head[i]=nume;
                     e[nume][2]=inf-lim-1;e[nume][3]=lim+1;e[nume++][4]=inf;
                     suminf[n+col]+=lim+1; sumouf[i]+=lim+1;hash[i][n+col]=1;
                     e[nume][0]=i;e[nume][1]=head[n+col];head[n+col]=nume;
                     e[nume++][2]=0;
                    }
                   }
                 }
                 else if(cc=='<')
                 {
                     for(int i=1;i<=n;i++)
                    if(hash[i][n+col])
                     {  int pp;
                         for(pp=head[i];e[pp][0]!=n+col;pp=e[pp][1])
                         ;
                         suminf[n+col]-=e[pp][3]; sumouf[i]-=e[pp][3];
                         if(0>e[pp][3])e[pp][3]=0;
                         if(lim-1<e[pp][4])e[pp][4]=lim-1;
                         if(e[pp][3]>e[pp][4])mark=1;
                         e[pp][2]=e[pp][4]-e[pp][3];
                         suminf[n+col]+=e[pp][3]; sumouf[i]+=e[pp][3];
                     }
                     else
                    {
                     e[nume][0]=n+col;e[nume][1]=head[i];head[i]=nume;
                     e[nume][2]=lim-1;e[nume][3]=0;e[nume++][4]=lim-1;hash[i][n+col]=1;
                     //inf[n+rol]+=lim; sumouf[i]+=lim;
                     e[nume][0]=i;e[nume][1]=head[n+col];head[n+col]=nume;
                     e[nume++][2]=0;
                    }
                   }

             }
             else if(row!=0&&col==0)
             {
                  if(cc=='>')
                 {
                     for(int i=n+1;i<=n+m;i++)
                   {   if(hash[row][i])
                     {   int pp;
                         for( pp=head[row];e[pp][0]!=i;pp=e[pp][1])
                         ;
                         suminf[i]-=e[pp][3]; sumouf[row]-=e[pp][3];
                         if(lim+1>e[pp][3])e[pp][3]=lim+1;
                         if(inf<e[pp][4])e[pp][4]=inf;
                         if(e[pp][3]>e[pp][4])mark=1;
                         e[pp][2]=e[pp][4]-e[pp][3];
                         suminf[i]+=e[pp][3]; sumouf[row]+=e[pp][3];
                     }
                     else
                       {
                     e[nume][0]=i;e[nume][1]=head[row];head[row]=nume;
                     e[nume][2]=inf-lim-1;e[nume][3]=lim+1;e[nume++][4]=inf;
                     suminf[i]+=lim+1; sumouf[row]+=lim+1;hash[row][i]=1;
                     e[nume][0]=row;e[nume][1]=head[i];head[i]=nume;
                     e[nume++][2]=0;
                       }
                   }
                 }
                 else if(cc=='=')
                  for(int i=n+1;i<=n+m;i++)
                   {
                          if(hash[row][i])
                     {    int pp;
                         for(pp=head[row];e[pp][0]!=i;pp=e[pp][1])
                         ;
                         suminf[i]-=e[pp][3]; sumouf[row]-=e[pp][3];
                         if(lim>e[pp][3])e[pp][3]=lim;
                         if(lim<e[pp][4])e[pp][4]=lim;
                         if(e[pp][3]>e[pp][4])mark=1;
                         e[pp][2]=e[pp][4]-e[pp][3];
                         suminf[i]+=e[pp][3]; sumouf[row]+=e[pp][3];
                     }
                     else
                    {

                     e[nume][0]=i;e[nume][1]=head[row];head[row]=nume;
                     e[nume][2]=0;e[nume][3]=lim;e[nume++][4]=lim;
                     suminf[i]+=lim; sumouf[row]+=lim;hash[row][i]=1;
                     e[nume][0]=row;e[nume][1]=head[i];head[i]=nume;
                     e[nume++][2]=0;
                    }
                   }
                  else if(cc=='<')
                  for(int i=n+1;i<=n+m;i++)
                   {
                        if(hash[row][i])
                     {   int pp;
                         for( pp=head[row];e[pp][0]!=i;pp=e[pp][1])
                         ;
                         suminf[i]-=e[pp][3]; sumouf[row]-=e[pp][3];
                         if(0>e[pp][3])e[pp][3]=0;
                         if(lim-1<e[pp][4])e[pp][4]=lim-1;
                         if(e[pp][3]>e[pp][4])mark=1;
                         e[pp][2]=e[pp][4]-e[pp][3];
                         suminf[i]+=e[pp][3]; sumouf[row]+=e[pp][3];
                     }
                     else
                    {
                     e[nume][0]=i;e[nume][1]=head[row];head[row]=nume;
                     e[nume][2]=lim-1;e[nume][3]=0;e[nume++][4]=lim-1;hash[row][i]=1;
                     //inf[i]+=lim; sumouf[row]+=lim;
                     e[nume][0]=row;e[nume][1]=head[i];head[i]=nume;
                     e[nume++][2]=0;
                    }
                   }
             }
             else if(row==0&&col==0)
             {
                 if(cc=='=')
                  {
                    for(int i=1;i<=n;i++)
                     for(int j=n+1;j<=n+m;j++)
                     {
                        if(hash[i][j])
                     {   int pp;
                         for( pp=head[i];e[pp][0]!=j;pp=e[pp][1])
                         ;
                         suminf[j]-=e[pp][3]; sumouf[i]-=e[pp][3];
                         if(lim>e[pp][3])e[pp][3]=lim;
                         if(lim<e[pp][4])e[pp][4]=lim;
                         if(e[pp][3]>e[pp][4])mark=1;
                         e[pp][2]=e[pp][4]-e[pp][3];
                         suminf[j]+=e[pp][3]; sumouf[i]+=e[pp][3];
                     }
                     else
                       {
                        e[nume][0]=j;e[nume][1]=head[i];head[i]=nume;
                        e[nume][2]=0;e[nume][3]=lim;e[nume++][4]=lim;
                        suminf[j]+=lim; sumouf[i]+=lim;hash[i][j]=1;
                        e[nume][0]=i;e[nume][1]=head[j];head[j]=nume;
                        e[nume++][2]=0;
                      }
                     }
                  }
                if(cc=='>')
                {
                   for(int i=1;i<=n;i++)
                     for(int j=n+1;j<=n+m;j++)
                     {
                        if(hash[i][j])
                       {  int pp;
                         for( pp=head[i];e[pp][0]!=j;pp=e[pp][1])
                         ;
                         suminf[j]-=e[pp][3]; sumouf[i]-=e[pp][3];
                         if(lim+1>e[pp][3])e[pp][3]=lim+1;
                         if(inf<e[pp][4])e[pp][4]=inf;
                         if(e[pp][3]>e[pp][4])mark=1;
                         e[pp][2]=e[pp][4]-e[pp][3];
                         suminf[j]+=e[pp][3]; sumouf[i]+=e[pp][3];
                      }
                     else
                        {
                        e[nume][0]=j;e[nume][1]=head[i];head[i]=nume;
                        e[nume][2]=inf-lim-1;e[nume][3]=lim+1;e[nume++][4]=inf;
                        suminf[j]+=lim+1; sumouf[i]+=lim+1;hash[i][j]=1;
                        e[nume][0]=i;e[nume][1]=head[j];head[j]=nume;
                        e[nume++][2]=0;
                        }
                     }
                }
                 if(cc=='<')
                   for(int i=1;i<=n;i++)
                     for(int j=n+1;j<=n+m;j++)
                     {
                   if(hash[i][j])
                     {    int pp;
                         for( pp=head[i];e[pp][0]!=j;pp=e[pp][1])
                         ;
                         suminf[j]-=e[pp][3]; sumouf[i]-=e[pp][3];
                         if(0>e[pp][3])e[pp][3]=0;
                         if(lim-1<e[pp][4])e[pp][4]=lim-1;
                         if(e[pp][3]>e[pp][4])mark=1;
                         e[pp][2]=e[pp][4]-e[pp][3];
                         suminf[j]+=e[pp][3]; sumouf[i]+=e[pp][3];
                     }
                     else
                        {
                        e[nume][0]=j;e[nume][1]=head[i];head[i]=nume;
                        e[nume][2]=lim-1;e[nume][3]=0;e[nume++][4]=lim-1;hash[i][j]=1;
                        //inf[j]+=lim; sumouf[i]+=lim;
                        e[nume][0]=i;e[nume][1]=head[j];head[j]=nume;
                        e[nume++][2]=0;
                        }
                     }
             }
             else
             {
                 if(cc=='=')
               {
                    if(hash[row][n+col])
                     {    int pp;
                         for(pp=head[row];e[pp][0]!=n+col;pp=e[pp][1])
                         ;
                         suminf[n+col]-=e[pp][3]; sumouf[row]-=e[pp][3];
                         if(lim>e[pp][3])e[pp][3]=lim;
                         if(lim<e[pp][4])e[pp][4]=lim;
                         if(e[pp][3]>e[pp][4])mark=1;
                         e[pp][2]=e[pp][4]-e[pp][3];
                         suminf[n+col]+=e[pp][3]; sumouf[row]+=e[pp][3];
                     }
                   else
                     {
                e[nume][0]=col+n;e[nume][1]=head[row];head[row]=nume;
                e[nume][2]=0;e[nume][3]=lim;e[nume++][4]=lim;
                suminf[col+n]+=lim; sumouf[row]+=lim;hash[row][col+n]=1;
                e[nume][0]=row;e[nume][1]=head[col+n];head[col+n]=nume;
                e[nume++][2]=0;
                    }
               }
               else if(cc=='>')
               {
                    if(hash[row][n+col])
                     {   int pp;
                         for(pp=head[row];e[pp][0]!=n+col;pp=e[pp][1])
                         ;
                         suminf[n+col]-=e[pp][3]; sumouf[row]-=e[pp][3];
                         if(lim+1>e[pp][3])e[pp][3]=lim+1;
                         if(inf<e[pp][4])e[pp][4]=inf;
                         if(e[pp][3]>e[pp][4])mark=1;
                         e[pp][2]=e[pp][4]-e[pp][3];
                         suminf[n+col]+=e[pp][3]; sumouf[row]+=e[pp][3];
                     }
                     else
                        {
                e[nume][0]=col+n;e[nume][1]=head[row];head[row]=nume;
                e[nume][2]=inf-lim-1;e[nume][3]=lim+1;e[nume++][4]=inf;
                suminf[col+n]+=lim+1; sumouf[row]+=lim+1;hash[row][col+n]=1;
                e[nume][0]=row;e[nume][1]=head[col+n];head[col+n]=nume;
                e[nume++][2]=0;
                        }
               }
               else if(cc=='<')
               {
                    if(hash[row][n+col])
                     {   int pp;
                         for( pp=head[row];e[pp][0]!=n+col;pp=e[pp][1])
                         ;
                         suminf[n+col]-=e[pp][3]; sumouf[row]-=e[pp][3];
                         if(0>e[pp][3])e[pp][3]=0;
                         if(lim-1<e[pp][4])e[pp][4]=lim-1;
                         if(e[pp][3]>e[pp][4])mark=1;
                         e[pp][2]=e[pp][4]-e[pp][3];
                         suminf[n+col]+=e[pp][3]; sumouf[row]+=e[pp][3];
                     }
                     else
                    {

                   e[nume][0]=col+n;e[nume][1]=head[row];head[row]=nume;
                    e[nume][2]=lim-1;e[nume][3]=0;e[nume++][4]=lim-1;hash[row][col+n]=1;
               // inf[col]+=lim; sumouf[row]+=lim;
                  e[nume][0]=row;e[nume][1]=head[col+n];head[col+n]=nume;
                    e[nume++][2]=0;
                    }
               }
             }
         }
           for(int i=1;i<=n;i++)    //有些边没有限制，不要忘记加边！！
             for(int j=n+1;j<=n+m;j++)
               if(!hash[i][j])
               {
                   e[nume][0]=j;e[nume][1]=head[i];head[i]=nume;
                   e[nume][4]=inf;e[nume++][2]=inf;
                   e[nume][0]=i;e[nume][1]=head[j];head[j]=nume;
                   e[nume++][2]=0;
               }
                                //无源无汇添加ss,tt
           for(int i=0;i<=n+m+1;i++)
           {
                e[nume][0]=i;e[nume][1]=head[n+m+2];head[n+m+2]=nume;
                e[nume++][2]=suminf[i];
                e[nume][0]=n+m+2;e[nume][1]=head[i];head[i]=nume;
                e[nume++][2]=0;

                e[nume][0]=n+m+3;e[nume][1]=head[i];head[i]=nume;
                e[nume++][2]=sumouf[i];
                e[nume][0]=i;e[nume][1]=head[n+m+3];head[n+m+3]=nume;
                e[nume++][2]=0;
           }
           dinic();     //从ss->tt，判断有无解
          if(mark||!check())printf("IMPOSSIBLE
");
          else             //输出答案
          {
              for(int i=1;i<=n;i++)
                for(int j=head[i];j!=-1;j=e[j][1])
                  ans[i][e[j][0]]=e[j][4]-e[j][2];   //原来上限-残留量，即为所用（上限-下限-残留+下限）
               for(int i=1;i<=n;i++)
                 for(int j=n+1;j<=n+m;j++)
                  {
                      if(j!=n+m)printf("%d ",ans[i][j]);
                      else printf("%d
",ans[i][j]);
                  }
          }
          if(N!=0)printf("
");
    }
      return 0;
}