1 #include<cstdio>
2 #include<iostream>
3 #include<algorithm>
4 #include<cstring>
5 #include<cmath>
6 #include<queue>
7 #include<map>
8 using namespace std;
9 #define MOD 1000000007
10 const int INF=0x3f3f3f3f;
11 const double eps=1e-5;
12 typedef long long ll;
13 #define cl(a) memset(a,0,sizeof(a))
14 #define ts printf("*****\n");
15 int n,m,tt;
16 const int MAXN = 1010;
17 const int MAXM = 1010*4;
18 int mp[MAXN][MAXN];
19 struct Edge
20 {
21 int to,next;
22 }edge[MAXM];
23 int head[MAXN],tot;
24 void addedge(int u,int v)
25 {
26 edge[tot].to = v;
27 edge[tot].next = head[u];
28 head[u] = tot++;
29
30 }
31
32 void init()
33 {
34 tot = 0;
35 memset(head,-1,sizeof(head));
36 }
37
38 void bfs(int st)
39 {
40 queue<int> q;
41 q.push(st);
42 mp[st][st]=0;
43 while(!q.empty())
44 {
45 int u=q.front();
46 q.pop();
47 for(int i=head[u];i!=-1;i=edge[i].next)
48 {
49 int v=edge[i].to;
50 if(v==u) continue;
51 if(mp[st][v]==-1)
52 {
53 mp[st][v]=mp[st][u]+1;
54 q.push(v);
55 }
56 }
57 }
58 }
59 int to[MAXN][MAXN];
60 double f[MAXN][MAXN];
61 bool vis[MAXN][MAXN];
62 double F(int x,int y)
63 {
64 if(vis[x][y]) return f[x][y];
65 vis[x][y]=1;
66 if(mp[x][y]==0) return f[x][y]=0.0;
67 if(mp[x][y]<=2) return f[x][y]=1.0;
68 double val=0;
69 int cnt=0;
70 int v;
71 for(int i=head[y];i!=-1;i=edge[i].next)
72 {
73 cnt++;
74 v=edge[i].to;
75 val+=F(to[to[x][y]][y],v);
76 }
77 return f[x][y]=val/cnt+1.0;
78 }
79 void fun()
80 {
81 for(int i=1;i<=n;i++)
82 {
83 for(int j=1;j<=n;j++)
84 {
85 printf("%.2lf ",f[i][j]);
86 }
87 printf("\n");
88 }
89 }
90 int main()
91 {
92 int s,t;
93 int i,j,k;
94 #ifndef ONLINE_JUDGE
95 freopen("1.in","r",stdin);
96 #endif
97 init();
98 scanf("%d%d%d%d",&n,&m,&s,&t);
99 int u,v;
100 for(i=0;i<m;i++)
101 {
102 scanf("%d%d",&u,&v);
103 addedge(u,v);
104 addedge(v,u);
105 }
106 memset(mp,-1,sizeof(mp));
107 int mx;
108 for(k=1;k<=n;k++)
109 {
110 bfs(k);
111 for(j=1;j<=n;j++)
112 {
113 if(j==k) continue;
114 mx=INF;
115 for(i=head[j];i!=-1;i=edge[i].next)
116 {
117 int v=edge[i].to;
118 if(mx>mp[k][v])
119 {
120 mx=mp[k][v];
121 to[j][k]=v;
122 }
123 else if(mx==mp[k][v])
124 {
125 to[j][k]=min(v,to[j][k]);
126 }
127 }
128 }
129 }
130 for(i=1;i<=n;i++)
131 {
132 addedge(i,i);
133 }
134 printf("%.3lf\n",F(s,t));
135 return 0;
136 }
