题目:http://www.lydsy.com/JudgeOnline/problem.php?id=2152
树的点分治,搞个数组存mod 3=0,1,2的数的个数,然后直接搞就可以了。。
代码:
#include <cstdio>
#include <algorithm>
#include <cstring>
using namespace std ;
#define travel( v ) for ( edge *p = head[ v ] ; p ; p = p -> next )
#define AddEdge( s , t , d ) Add( s , t , d ) , Add( t , s , d )
#define check( ch ) ( ch >= '0' && ch <= '9' )
const int inf = 0x7fffffff ;
const int maxn = 20010 ;
void getint( int &t ) {
int ch ; for ( ch = getchar( ) ; ! check( ch ) ; ch = getchar( ) ) ;
t = ch - '0' ;
for ( ch = getchar( ) ; check( ch ) ; ch = getchar( ) ) {
t *= 10 ;
t += ch - '0' ;
}
}
int o[ 20 ] ;
void putint( int t ) {
if ( t ) {
o[ 0 ] = 0 ;
for ( ; t ; t /= 10 ) o[ ++ o[ 0 ] ] = t % 10 ;
while ( o[ 0 ] -- ) putchar( '0' + o[ o[ 0 ] + 1 ] ) ;
} else putchar( '0' ) ;
}
struct edge {
edge *next ;
int t , d ;
} *head[ maxn ] ;
void Add( int s , int t , int d ) {
edge *p = new( edge ) ;
p -> t = t , p -> d = d , p -> next = head[ s ] ;
head[ s ] = p ;
}
int gcd( int x , int y ) {
if ( x < y ) swap( x , y ) ;
for ( ; y ; ) {
int k = y ;
y = x % y ;
x = k ;
}
return x ;
}
int n , ans = 0 , cnt[ 3 ] ;
bool del[ maxn ] ;
int rt , roof , size[ maxn ] , depth[ maxn ] , rec ;
void dfs0( int v , int u ) {
size[ v ] = 1 ;
travel( v ) if ( p -> t != u && del[ p -> t ] ) {
dfs0( p -> t , v ) ;
size[ v ] += size[ p -> t ] ;
}
}
void chose( int v , int u ) {
int ret = size[ rt ] - size[ v ] ;
travel( v ) if ( p -> t != u && del[ p -> t ] ) {
ret = max( ret , size[ p -> t ] ) ;
chose( p -> t , v ) ;
}
if ( rec > ret ) {
rec = ret , roof = v ;
}
}
void dfs1( int v , int u ) {
travel( v ) if ( p -> t != u && del[ p -> t ] ) {
depth[ p -> t ] = depth[ v ] + p -> d ;
dfs1( p -> t , v ) ;
}
}
int b[ maxn ] , bn ;
void dfs2( int v , int u ) {
b[ ++ bn ] = v ;
travel( v ) if ( p -> t != u && del[ p -> t ] ) dfs2( p -> t , v ) ;
}
void divide( int v ) {
dfs0( v , 0 ) ;
rt = v , roof = 0 ;
rec = inf ;
chose( v , 0 ) ;
depth[ roof ] = 0 ;
dfs1( roof , 0 ) ;
memset( cnt , 0 , sizeof( cnt ) ) ;
cnt[ 0 ] ++ , ++ ans ;
travel( roof ) if ( del[ p -> t ] ) {
bn = 0 ;
dfs2( p -> t , roof ) ;
for ( int i = 0 ; i ++ < bn ; ) {
int t = depth[ b[ i ] ] % 3 ;
ans += ( cnt[ ( 3 - t ) % 3 ] * 2 ) ;
}
for ( int i = 0 ; i ++ < bn ; ) cnt[ depth[ b[ i ] ] % 3 ] ++ ;
}
del[ roof ] = false ;
travel( roof ) if ( del[ p -> t ] ) divide( p -> t ) ;
}
int main( ) {
getint( n ) ;
for ( int i = 1 ; i < n ; ++ i ) {
int s , t , d ; getint( s ) , getint( t ) , getint( d ) ;
AddEdge( s , t , d ) ;
}
memset( del , true , sizeof( del ) ) ;
divide( 1 ) ;
int ret = gcd( ans , n * n ) ;
putint( ans / ret ) ;
putchar( '/' ) ;
putint( ( n * n ) / ret ) ;
return 0 ;
}