题目:http://www.lydsy.com/JudgeOnline/problem.php?id=1415
最短路预处理,然后DP求解即可。
代码:
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <deque>
#include <vector>
using namespace std ;
#define AddEdge( s , t ) e[ s ].pb( t ) , e[ t ].pb( s )
#define maxn 1010
#define pb push_back
#define pf push_front
#define inf 0x7fffffff
#define travel( s ) for ( vector < int > :: iterator p = e[ s ].begin( ) ; p != e[ s ].end( ) ; ++ p )
#define rep( i , x ) for ( int i = 0 ; i ++ < x ; )
vector < int > e[ maxn ] ;
int n , m , st , to , next[ maxn ][ maxn ] , d[ maxn ] ;
int dist[ maxn ] ;
deque < int > q ;
bool f[ maxn ] ;
void spfa( int S ) {
memset( f , false , sizeof( f ) ) , q.clear( ) ;
rep( i , n ) dist[ i ] = inf ;
dist[ S ] = 0 , f[ S ] = true , q.pf( S ) ;
while ( ! q.empty( ) ) {
int v = q.front( ) ; q.pop_front( ) , f[ v ] = false ;
travel( v ) if ( dist[ *p ] > dist[ v ] + 1 ) {
dist[ *p ] = dist[ v ] + 1 ;
if ( ! f[ *p ] ) {
f[ *p ] = true ;
if ( ! q.empty( ) && dist[ *p ] < dist[ q.front( ) ] ) q.pf( *p ) ; else q.pb( *p ) ;
}
}
}
}
double dp[ maxn ][ maxn ] ;
bool flag[ maxn ][ maxn ] ;
double Dp( int v , int u ) {
if ( flag[ v ][ u ] ) return dp[ v ][ u ] ;
if ( v == u ) {
dp[ v ][ u ] = 0 , flag[ v ][ u ] = true ;
return dp[ v ][ u ] ;
}
int k = next[ v ][ u ] ;
if ( k != u ) k = next[ k ][ u ] ;
dp[ v ][ u ] = 1 ;
if ( k != u ) {
travel( u ) dp[ v ][ u ] += Dp( k , *p ) / double( d[ u ] + 1 ) ;
dp[ v ][ u ] += Dp( k , u ) / double( d[ u ] + 1 ) ;
}
flag[ v ][ u ] = true ;
return dp[ v ][ u ] ;
}
int main( ) {
scanf( "%d%d" , &n , &m ) ;
scanf( "%d%d" , &st , &to ) ;
memset( d , 0 , sizeof( d ) ) ;
while ( m -- ) {
int s , t ; scanf( "%d%d" , &s , &t ) ; AddEdge( s , t ) ;
++ d[ s ] , ++ d[ t ] ;
}
memset( next , 0 , sizeof( next ) ) ;
rep( i , n ) {
spfa( i ) ;
rep( j , n ) travel( j ) if ( ! next[ j ][ i ] || dist[ *p ] < dist[ next[ j ][ i ] ] || ( dist[ *p ] == dist[ next[ j ][ i ] ] && *p < next[ j ][ i ] ) ) {
next[ j ][ i ] = *p ;
}
}
memset( flag , false , sizeof( flag ) ) ;
printf( "%.3f\n" , Dp( st , to ) ) ;
return 0 ;
}