二分+最短路判定 BZOJ 2709: [Violet 1]迷宫花园

BZOJ 2709: [Violet 1]迷宫花园

Sample Input

5

10.28  

#########

#       #

# # # # #

#S#     #

##### # #

##  #   #

# ### ###

##E     #

#########

4.67  

#########

#  ##  ##

### #S# #

#  # E ##

# # #####

# ##  ###

# ##### #

#    #  #

#########

39.06  

#########

#       #

# # # # #

# E# #  #

# # # # #

## ###  #

# # #S# #

#####   #

#########

24.00  

#########

#      ##

# # ## ##

#   #  ##

###S## E#

### #  ##

# #   # #

##### # #

#########

25.28  

#########

# S##E# #

# ### # #

# ##    #

# ##  ###

# #  ####

# # # ###

#       #

#########
Sample Output

0.41000

4.67000

3.34000

5.00000

1.69000

HINT

 /*
 分析：符合二分的原理：当v变大，dis一定变大，而且v的具体范围很小，才是0--10，符合二分原理。
 二分出一个V，就用spfa求一次最短路，看看最短的长度与L大小关系，以此来二分。
 */
 #include<cmath>
 #include<iostream>
 using namespace std;
 #include<cstdio>
 #include<queue>
 #include<cstring>
 #define R 110
 int T,r,c;
 bool inque[R*R];
 char ditu[R][R];
 double L,z,y;
 double dist[R*R];
 int head[],bh=,sta,endd,bhh[R][R];
 struct Edge{
     int v,last;
     double w;
 }edge[];
 int t=;
 void input()
 {
     scanf("%lf%d%d\n",&L,&r,&c);
     for(int i=;i<=r;++i)
     {
         for(int j=;j<=c;++j)
         {
             scanf("%c",&ditu[i][j]);
             if(ditu[i][j]==)
             {
                 bh++;
                 bhh[i][j]=bh;
             }
             if(ditu[i][j]=='S')bhh[i][j]=sta=++bh;
             if(ditu[i][j]=='E')bhh[i][j]=endd=++bh;
          }
         scanf("\n");
      } 

 }
 void add_edge(int i,int j)
 {
     if(i->&&ditu[i-][j]!='#') {++t;edge[t].v=bhh[i-][j];edge[t].w=-;edge[t].last=head[bhh[i][j]];head[bhh[i][j]]=t;}
     if(i<r&&ditu[i+][j]!='#')   {++t;edge[t].v=bhh[i+][j];edge[t].w=-;edge[t].last=head[bhh[i][j]];head[bhh[i][j]]=t;}
     if(j->&&ditu[i][j-]!='#') {++t;edge[t].v=bhh[i][j-];edge[t].w=;edge[t].last=head[bhh[i][j]];head[bhh[i][j]]=t;}
     if(j<c&&ditu[i][j+]!='#')   {++t;edge[t].v=bhh[i][j+];edge[t].w=;edge[t].last=head[bhh[i][j]];head[bhh[i][j]]=t;}
 }
 void build_tu()
 {
    for(int i=;i<=r;++i)
      for(int j=;j<=c;++j)
      if(ditu[i][j]!='#')
      {
          add_edge(i,j);
      }
 }
 double SPFA(double ww)
 {
     for(int i=;i<=bh;++i)
       dist[i]=(<<)-;
     dist[sta]=;
     memset(inque,false,sizeof(inque));
     queue<int>Q;
     Q.push(sta);
     inque[sta]=true;
     while(!Q.empty())
     {
         int nowt=Q.front();
         Q.pop();
         inque[nowt]=false;
         for(int l=head[nowt];l;l=edge[l].last)
         {
             if(edge[l].w<)
             {
                 if(dist[edge[l].v]>dist[nowt]+ww)
                 {
                     dist[edge[l].v]=dist[nowt]+ww;
                     if(!inque[edge[l].v])
                     {
                         inque[edge[l].v]=true;
                         Q.push(edge[l].v);
                     }
                 }
             }
             else {
                 if(dist[edge[l].v]>dist[nowt]+edge[l].w)
                 {
                     dist[edge[l].v]=dist[nowt]+edge[l].w;
                     if(!inque[edge[l].v])
                     {
                         inque[edge[l].v]=true;
                         Q.push(edge[l].v);
                     }
                 }
             }
         }
     }
     return dist[endd];
 }
 int main()
 {
     cin>>T;
     while(T--)
     {
       input();
       build_tu();
       z=;y=;
       while(z<=y)
       {
           double mid=(z+y)/;
           double ans=SPFA(mid);
           if(ans>=L) y=mid-0.000001;/*注意这里要加0.000001，之前的二分加1，是为了去一个区间（int），但是现在是double，所以要+0
 .000001。*/
           else z=mid+0.000001;
       }
       printf("%0.5lf\n",y);
     }

     return ;
 }