POJ 1966 Cable TV Network【SAP】

http://poj.org/problem?id=1966
POJ 1966 Cable TV Network
算法核心：网络流-SAP

#include<stdio.h>

#include<string.h>

const int N = 50*2+5;

const int INF = N;

const int MAXN=N;

const int maxn = N;

int map[N][N];

int cmap[N][N];

int getNum()

{

 char c;

 int num = 0;

 while(c=getchar())

 {

  if(c<='9'&&c>='0')break;

 }



 while(c<='9'&&c>='0')

 {

  num=num*10+c-'0';

  c = getchar();

 }

 return num;

}



int cur_arc[MAXN],label[MAXN],neck[MAXN];         //当前弧，标号，瓶颈边的入点（姑且这么叫吧）   

int label_count[MAXN],back_up[MAXN],pre[MAXN];    //标号为i节点的数量，cur_flow的纪录,当前流路径中前驱  

//back_up[i]表示当前流流到点i能达到的最大流量

int SAP(int map[][maxn],int v_count,int s,int t)      //邻接矩阵，节点总数，始点，汇点   

{   

 int i;   

 int cur_flow,max_flow,cur;         //当前流，最大流，当前节点，最小标号，临时变量   

 char flag;                                        //标志当前是否有可行流   

 

 memset(label,0,sizeof(label));

 memset(label_count,0,sizeof(label_count));

 memset(cur_arc,0,sizeof(cur_arc));//cur_arc[i]为与i相连最近的点

 label_count[0]=v_count;

 neck[s]=s;//neck[i]表示当前流的瓶颈点

 max_flow = 0;

 cur = s;

 cur_flow = INF;

 //循环代替递归

 while(label[s]<v_count)

 {

    back_up[cur]=cur_flow;

    flag = false;//记录当前点是否存在下一层

    //寻找当前可行流的下一点

    for(i=cur_arc[cur];i<v_count;i++)

    {

     if(map[cur][i]!=0&&label[i]==label[cur]-1)//寻找到下一层

     {

      flag=true;

      cur_arc[cur]=i;//更新

      //更新当前流

      if(map[cur][i]<cur_flow)

      {

       cur_flow = map[cur][i];

       neck[i]=cur;

      }else

       neck[i]=neck[cur];//瓶颈相对前驱节点不变

      pre[i]=cur;

      cur = i;

      if(i==t)//找到可行流

      {

       max_flow+=cur_flow;

       while(cur!=s)

       {

        //当前弧的流量并非无限。。。。若无限，则无需减

        if(map[pre[cur]][cur]!=INF)

        {

         map[pre[cur]][cur]-=cur_flow;

        }

        back_up[cur]-=cur_flow;

        if(map[cur][pre[cur]]!=INF)

         map[cur][pre[cur]]+=cur_flow;

        cur=pre[cur];

       }

       cur = neck[t];//返回至瓶颈节点，继续做

       cur_flow = back_up[cur];

      }

      break;

     }

    }



    if(flag)continue;//下层已经找到

        //未找到下层点

    int nextid;

    int min_label = v_count-1;

    for(i=0;i<v_count;i++)

    {

     if(map[cur][i]!=0&&label[i]<min_label)

     {

      min_label = label[i];

      nextid = i;

     }

    }



    label_count[label[cur]]--;

    if(label_count[label[cur]]==0)break;//GAP优化

    label[cur]=min_label+1;

    cur_arc[cur]=nextid;

    label_count[label[cur]]++;

    if(cur!=s)//从栈中弹出一个节点

    {

     cur = pre[cur];

     cur_flow = back_up[cur];

    }

 }

 return max_flow;

}

int main()

{

   int n,m;

   while(scanf("%d%d",&n,&m)!=EOF)

   {

    memset(map,0,sizeof(map));

    int mid = n;

       while(m--)

    {

     int u =getNum();

     int v = getNum();

     int uu=u+n;

     int vv=v+n;

     map[vv][u]=n+1;

     map[uu][v]=n+1;

    }



    int i,j,t;

    for(i=0;i<n;i++)

     map[i][i+n]=1;



    int ans = n;

    int s = n;

    for(i=0;i<n+n;i++)

     for(j=0;j<n+n;j++)

      cmap[i][j]=map[i][j];

    for(i=1;i<n;i++)

    {

     //if(map[s][i]==0)

     {

      int temp = SAP(cmap,n+n,s,i);

         if(ans>temp)ans = temp;

   for(t=0;t<n+n;t++)

    for(j=0;j<n+n;j++)

     cmap[t][j]=map[t][j];

     }

    }



    printf("%d\n",ans);

   }

   return 0;

}