BZOJ 2707: [SDOI2012]走迷宫 拓扑+高斯消元+期望概率dp+Tarjan

先Tarjan缩点 强连通分量里用高斯消元外面直接转移 注意删掉终点出边和拓扑

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<iostream>
#include<queue>
#include<vector>
#define N 10010
#define M 1000010
using namespace std;
typedef double D;
bool god=1;
int n,m,s,e;
struct Went
{
  int to,next;
}c[M],via[M],C[M];
int head[N],t,Head[N],T,adj[N],sz;
inline void Add(int x,int y)
{
    c[++t].to=y;
    c[t].next=head[x];
    head[x]=t;
    C[++T].to=x;
    C[T].next=Head[y];
    Head[y]=T;
}
inline void add(int x,int y)
{
   via[++sz].to=y;
   via[sz].next=adj[x];
   adj[x]=sz;
}
int dfn[N],low[N],num,sum[N],stack[N],top,belong[N],id[N];
D a[1200][1200],prob[N],exp[N],ans[1200];
int topo[N],out[N];
bool in[N],can_get[N];
vector<int> team[N];
int Time;
inline int Min(int x,int y)
{
   return x<y?x:y;
}
void tarjan(int x)
{
   dfn[x]=low[x]=++Time;
   in[x]=1;
   stack[++top]=x;
   for(int i=head[x];i;i=c[i].next)
   if(!dfn[c[i].to])
   {
    tarjan(c[i].to);
    low[x]=Min(low[x],low[c[i].to]);
   }
   else if(in[c[i].to])
    low[x]=Min(low[x],dfn[c[i].to]);
   if(low[x]==dfn[x])
   {
     int j;
     num++;
     do
     {
      j=stack[top--];
      in[j]=0;
      sum[num]++;
      team[num].push_back(j);
      id[j]=team[num].size();
      belong[j]=num;
     }while(j!=x);
   }
}
int bang[N];
void buildnew()
{
   for(int x=1;x<=n;x++)
   {
    for(int i=head[x];i;i=c[i].next)
    {
      bang[x]++;
      int y=c[i].to;
      if(belong[x]==belong[y])continue;
      add(belong[x],belong[y]);
    }
   }
}
int tool;
int indegree[N];
void light(int x)
{
  can_get[x]=1;
  for(int i=adj[x];i;i=via[i].next)
  {
    out[x]++;
    indegree[via[i].to]++;
    if(!can_get[via[i].to])
     light(via[i].to);
  }
  if(out[x]==0)tool++;
}
queue<int> q;
int size;
void bfs()
{
   q.push(belong[s]);
   while(!q.empty())
   {
     int x=q.front();
     q.pop();
     topo[++size]=x;
     for(int i=adj[x];i;i=via[i].next)
      {
       indegree[via[i].to]--;
       if(indegree[via[i].to]==0)
        q.push(via[i].to);
      }
   }
}
void dfs(int x)
{
   printf(" Now : %d
",x);
   for(int i=adj[x];i;i=via[i].next)
    dfs(via[i].to);
}
void arrange()
{
   buildnew();
   light(belong[s]);
   if(can_get[belong[e]]==0)god=0;
   if(!god)return;
   if(out[belong[e]]!=0)god=0;
   if(!god)return;
   if(tool!=1)god=0;
   if(!god)return;
   bfs();
}
void pre()
{
   scanf("%d%d%d%d",&n,&m,&s,&e);
   if(s==e)return;
   for(int i=1;i<=m;i++)
   {
     int x,y;
     scanf("%d%d",&x,&y);
     if(x==e)continue;
     Add(x,y);
   }
   for(int i=1;i<=n;i++)
    if(!dfn[i])
     tarjan(i);
   arrange();
   if(!god)return;
}
inline D abs(D x)
{
   return x<0.0?0.0-x:x;
}
inline void swap(D &x,D &y)
{
   D z=x;
   x=y;
   y=z;
}
void gauss(int len)
{
   for(int i=1,k=1;i<=len;i++,k++)
   {
     int temp=i;
     D host=abs(a[i][k]);
     for(int j=i+1;j<=len;j++)
      if(abs(a[j][k])>abs(a[temp][k]))
      {
        temp=j;
        host=abs(a[j][k]);
      }
     if(temp!=i)
     {
       for(int j=k;j<=len+1;j++)
        swap(a[i][j],a[temp][j]);
     }
     for(int j=i+1;j<=len;j++)
     {
       host=a[j][k]/a[i][k];
       for(int l=k;l<=len+1;l++)
        a[j][l]-=a[i][l]*host;
     }
   }
   for(int i=len;i>0;i--)
   {
     for(int j=i+1;j<=len;j++)
      a[i][len+1]-=a[i][j]*ans[j];
     ans[i]=a[i][len+1]/a[i][i];
   }

void work1()
{
   prob[s]=1.0;
   for(int i=1;i<=size;i++)
   {
      int len=sum[topo[i]];
      int x=topo[i];
      for(int j=0;j<=len+1;j++)
       for(int k=0;k<=len+1;k++)
        a[j][k]=0.0;
      for(int j=0;j<len;j++)
      {
        int y=team[x][j];
        a[j+1][len+1]-=prob[y];
        a[j+1][j+1]+=-1.0;
        for(int k=Head[y];k;k=C[k].next)
        {
          int z=C[k].to;
          if(belong[z]!=x)continue;
          a[j+1][id[z]]+=1.0/bang[z];
        }
      }
      gauss(len);
      for(int j=1;j<=len;j++)
       prob[team[x][j-1]]=ans[j];
      for(int j=0;j<len;j++)
      {
        int y=team[x][j];
        for(int k=head[y];k;k=c[k].next)
        {
          int z=c[k].to;
          if(belong[z]==x)continue;
          prob[z]+=1.0/bang[y]*prob[y];
        }
      }
   }
}
void work2()
{
   for(int i=1;i<=size;i++)
   {
      int len=sum[topo[i]];
      int x=topo[i];
      for(int j=0;j<=len+1;j++)
       for(int k=0;k<=len+1;k++)
        a[j][k]=0.0;
      for(int j=0;j<len;j++)
      {
        int y=team[x][j];
        a[j+1][len+1]-=exp[y];
        a[j+1][j+1]-=prob[y];
        for(int k=Head[y];k;k=C[k].next)
        {
          int z=C[k].to;
          if(belong[z]!=x)continue;
          a[j+1][id[z]]+=prob[z]*1.0/bang[z];
          a[j+1][len+1]-=prob[z]*1.0/bang[z];
        }
      }
      gauss(len);
      for(int j=1;j<=len;j++)
       exp[team[x][j-1]]=ans[j];
      for(int j=0;j<len;j++)
      {
        int y=team[x][j];
        for(int k=head[y];k;k=c[k].next)
        {
          int z=c[k].to;
          if(belong[z]==x)continue;
          exp[z]+=(1.0/bang[y]*prob[y])*(exp[y]+1.0);
        }
      }
   }
}
void work()
{
   work1();
   work2();
}
int main()
{
    pre();
    if(s==e)
    {
     printf("0.000");
     return 0;
    }
    if(!god)
    {
     printf("INF");
     return 0;
    }
    work();
    printf("%.3lf",exp[e]);
    return 0;
}