【HDU】4670 Cube number on a tree 点分治

传送门：【HDU】4670 Cube number on a tree

题目分析：首先因为至多30个素数，3^30在long long以内，如果一条路径上的数的乘积是个立方数，则这条路径上每个素数因子的个数都应该是3的倍数，于是我们用三进制表示含有素数的状态，当且仅当状态为0（即所有素数的个数都是3的倍数）时这条路径上数的乘积为完全立方数。考虑树分治，每层分治，求出当前重心的一个儿子的一个子树内所有的点到重心的路径上的乘积的状态，然后查询map中是否有对应状态（两状态叠加为0），有的话更新答案。然后再将这个子树的状态转化一下再插入到map中去。不断分治求解便可得到最终的答案。

代码如下：

#include <map>#include <vector>#include <cstdio>#include <cstring>#include <iostream>#include <algorithm>using namespace std ;typedef long long LL ;#define rep( i , a , b ) for ( int i = ( a ) ; i <  ( b ) ; ++ i )#define For( i , a , b ) for ( int i = ( a ) ; i <= ( b ) ; ++ i )#define rev( i , a , b ) for ( int i = ( a ) ; i >= ( b ) ; -- i )#define clr( a , x ) memset ( a , x , sizeof a )const int MAXN = 50005 ;const int MAXE = 100005 ;struct Edge {int v , n ;Edge () {}Edge ( int var , int next ) : v ( var ) , n ( next ) {}} ;Edge E[MAXE] ;int H[MAXN] , cntE ;int siz[MAXN] ;int pre[MAXN] ;LL S[MAXN] , top ;LL val[MAXN] ;LL dis[MAXN] ;LL prime[35] ;LL pow[35] ;map < LL , int > mp ;int Q[MAXN] , head , tail ;int vis[MAXN] , Time ;int n , k ;LL ans ;void clear () {++ Time ;ans=0 ;cntE = 0 ;clr ( H , -1 ) ;}void addedge ( int u , int v ) {E[cntE] = Edge ( v , H[u] ) ;H[u] = cntE ++ ;}void init () {clr ( vis , 0 ) ;Time = 0 ;pow[0] = 1 ;rep ( i , 1 , 35 ) pow[i] = pow[i - 1] * 3 ;}LL match ( LL x , LL res = 0 ) {rep ( i , 0 , k ) res += ( 3 - x / pow[i] % 3 ) % 3 * pow[i] ;return res ;}LL add ( LL x , LL y , LL res = 0 ) {rep ( i , 0 , k ) res += ( x / pow[i] % 3 + y / pow[i] % 3 ) % 3 * pow[i] ;return res ;}int get_root ( int s ) {head = tail = 0 ;pre[s] = 0 ;Q[tail ++] = s ;for ( ; head < tail ; ++ head ) {int u = Q[head] ;for ( int i = H[u] ; ~i ; i = E[i].n ) {int v = E[i].v ;if ( v == pre[u] || vis[v] == Time ) continue ;pre[v] = u ;Q[tail ++] = v ;}}int root = s , max_size = tail , tot_size = tail ;for ( -- head ; head >= 0 ; -- head ) {int u = Q[head] ;siz[u] = 1 ;int cnt = 0 ;for ( int i = H[u] ; ~i ; i = E[i].n ) {int v = E[i].v ;if ( v == pre[u] || vis[v] == Time ) continue ;siz[u] += siz[v] ;if ( cnt < siz[v] ) cnt = siz[v] ;}cnt = max ( cnt , tot_size - siz[u] ) ;if ( cnt < max_size ) {max_size = cnt ;root = u ;}}return root ;}void get_dis ( int s , LL value ) {head = tail = 0 ;pre[s] = 0 ;Q[tail ++] = s ;dis[s] = value ;for ( ; head < tail ; ++ head ) {int u = Q[head] ;S[top ++] = dis[u] ;for ( int i = H[u] ; ~i ; i = E[i].n ) {int v = E[i].v ;if ( v == pre[u] || vis[v] == Time ) continue ;pre[v] = u ;dis[v] = add ( dis[u] , val[v] ) ;Q[tail ++] = v ;}}}void divide ( int u ) {int root = get_root ( u ) ;vis[root] = Time ;if ( !val[root] ) ++ ans ;mp.clear () ;for ( int i = H[root] ; ~i ; i = E[i].n ) if ( vis[E[i].v] != Time ) {int v = E[i].v ;top = 0 ;get_dis ( v , val[v] ) ;rep ( j , 0 , top ) if ( mp.count ( S[j] ) ) ans += mp[S[j]] ;rep ( j , 0 , top ) {LL x = add ( S[j] , val[root] ) ;LL y = match ( x ) ;if ( !x ) ++ ans ;if ( mp.count ( y ) ) mp[y] ++ ;else mp[y] = 1 ;}}for ( int i = H[root] ; ~i ; i = E[i].n ) if ( vis[E[i].v] != Time ) divide ( E[i].v ) ;}void solve () {LL x ;int u , v ;clear () ;rep ( i , 0 , k ) scanf ( "%I64d" , &prime[i] ) ;For ( i , 1 , n ) {scanf ( "%I64d" , &x ) ;val[i] = 0 ;if ( !x ) continue ;rep ( j , 0 , k ) {int cnt = 0 ;while ( x % prime[j] == 0 ) {++ cnt ;x /= prime[j] ;}val[i] += cnt % 3 * pow[j] ;}}rep ( i , 1 , n ) {scanf ( "%d%d" , &u , &v ) ;addedge ( u , v ) ;addedge ( v , u ) ;}divide ( 1 ) ;printf ( "%I64d\n" , ans ) ;}int main () {init () ;while ( ~scanf ( "%d%d" , &n , &k ) ) solve () ;return 0 ;}