5077. 树的难题

来源：互联网发布：淘宝为什么刷关键词编辑：程序博客网时间：2024/05/16 14:54

题目大意

给定一棵n个点的树，每条边有一种颜色，对于一条路径，可以写出一个颜色序列，将颜色序列划分成很多相同颜色的颜色段，定义一条路径的权值是颜色序列的颜色段数。
求树中经过边数在l,r之间的路径的最大权值。

Data Constraint
n≤2×105

题解

考虑点剖，对于当前的分治重心，将每个儿子按照颜色排序。
然后维护两棵线段树即可。

时间复杂度：O(nlog2n)

SRC

#include<cstdio>#include<cstdlib>#include<cstring>#include<iostream>#include<algorithm>using namespace std ;#define N 200000 + 10const int inf = 2e9 ;int T[2][4*N] ;bool vis[N] , Clear[2][4*N] ;int Node[2*N] , Next[2*N] , Col[2*N] , Head[N] , tot ;int C[N] , Size[N] , Maxs[N] , Son[N] , MaxDeep[N] , flag[N] , D[N][2] ;int n , m , L , R ;int Root , All , Minv , Cnt , MaxDep , tag ;int ans = -inf , ret , nowv ;int Read() {    int ret = 0 , sign = 1 ;    char ch = getchar() ;    while ( ch < '0' || ch > '9' ) {        if ( ch == '-' ) sign = -1 ;        ch = getchar() ;    }    while ( ch >= '0' && ch <= '9' ) {        ret = ret * 10 + ch - '0' ;        ch = getchar() ;    }    return sign * ret ;}void link( int u , int v , int w ) {    Node[++tot] = v ;    Next[tot] = Head[u] ;    Col[tot] = w ;    Head[u] = tot ;}bool cmp( int a , int b ) { return Col[a] < Col[b] ; }void GetSize( int x , int F ) {    Size[x] = Maxs[x] = 1 ;    for (int p = Head[x] ; p ; p = Next[p] ) {        if ( Node[p] == F || vis[Node[p]] ) continue ;        GetSize( Node[p] , x ) ;        Size[x] += Size[Node[p]] ;        if ( Size[Node[p]] > Maxs[x] ) Maxs[x] = Size[Node[p]] ;    }}void GetRoot( int x , int F ) {    Maxs[x] = max( Maxs[x] , Size[All] - Maxs[x] ) ;    if ( Maxs[x] < Minv ) Root = x , Minv = Maxs[x] ;    for (int p = Head[x] ; p ; p = Next[p] ) {        if ( Node[p] == F || vis[Node[p]] ) continue ;        GetRoot( Node[p] , x ) ;    }}void DFS( int x , int F , int last , int sum , int deep ) {    if ( flag[deep] != tag ) {        flag[deep] = tag ;        MaxDeep[deep] = -inf ;        MaxDep = max( MaxDep , deep ) ;    }    MaxDeep[deep] = max( MaxDeep[deep] , sum ) ;    if ( deep >= L && deep <= R ) ans = max( ans , sum ) ;    D[++Cnt][0] = deep , D[Cnt][1] = sum ;    for (int p = Head[x] ; p ; p = Next[p] ) {        if ( Node[p] == F || vis[Node[p]] ) continue ;        DFS( Node[p] , x , Col[p] , sum + (Col[p] != last) * C[Col[p]] , deep + 1 ) ;    }}void Insert( int type , int v , int l , int r , int x , int val ) {    if ( l == r ) {        T[type][v] = max( T[type][v] , val ) ;        return ;    }    if ( Clear[type][v] ) {        T[type][v+v] = -inf ;        T[type][v+v+1] = -inf ;        Clear[type][v+v] = Clear[type][v+v+1] = 1 ;        Clear[type][v] = 0 ;    }    int mid = (l + r) >> 1 ;    if ( x <= mid ) Insert( type , v + v , l , mid , x , val ) ;    else Insert( type , v + v + 1 , mid + 1 , r , x , val ) ;    T[type][v] = max( T[type][v+v] , T[type][v+v+1] ) ;}void Search( int type , int v , int l , int r , int x , int y ) {    if ( nowv + T[type][v] <= ans || T[type][v] <= ret ) return ;    if ( l == x && r == y ) {        ret = max( ret , T[type][v] ) ;        return ;    }    if ( Clear[type][v] ) {        T[type][v+v] = -inf ;        T[type][v+v+1] = -inf ;        Clear[type][v+v] = Clear[type][v+v+1] = 1 ;        Clear[type][v] = 0 ;    }    int mid = (l + r) >> 1 ;    if ( y <= mid ) Search( type , v + v , l , mid , x , y ) ;    else if ( x > mid ) Search( type , v + v + 1 , mid + 1 , r , x , y ) ;    else {        Search( type , v + v , l , mid , x , mid ) ;        Search( type , v + v + 1 , mid + 1 , r , mid + 1 , y ) ;    }    T[type][v] = max( T[type][v+v] , T[type][v+v+1] ) ;}void Solve( int x ) {    Root = All = x , Minv = inf ;    GetSize( x , 0 ) ;    GetRoot( x , 0 ) ;    vis[Root] = 1 ;    Son[0] = 0 ;    for (int p = Head[Root] ; p ; p = Next[p] ) {        if ( vis[Node[p]] ) continue ;        Son[++Son[0]] = p ;    }    sort( Son + 1 , Son + Son[0] + 1 , cmp ) ;    Clear[0][1] = 1 ;    T[0][1] = -inf ;    MaxDep = 0 ;    for (int i = 1 ; i <= Son[0] ; i ++ ) {        int p = Son[i] ;        if ( i == 1 || Col[p] != Col[Son[i-1]] ) {            Clear[1][1] = 1 , tag ++ ;            T[1][1] = -inf ;            for (int k = 1 ; k <= MaxDep ; k ++ ) {                Insert( 0 , 1 , 1 , n , k , MaxDeep[k] ) ;            }            MaxDep = 0 ;        }        Cnt = 0 ;        DFS( Node[p] , Root , Col[p] , C[Col[p]] , 1 ) ;        for (int k = 1 ; k <= Cnt ; k ++ ) {            int deep = D[k][0] , val = D[k][1] ;            nowv = val ;            if ( R > deep && i > 1 && val + T[0][1] > ans ) {                ret = -inf ;                Search( 0 , 1 , 1 , n , max( L - deep , 1 ) , R - deep ) ;                ans = max( ans , val + ret ) ;            }            if ( i > 1 && R > deep && Col[p] == Col[Son[i-1]] && val + T[1][1] - C[Col[p]] > ans ) {                ret = -inf ;                nowv -= C[Col[p]] ;                Search( 1 , 1 , 1 , n , max( L - deep , 1 ) , R - deep ) ;                ans = max( ans , val + ret - C[Col[p]] ) ;            }        }        for (int k = 1 ; k <= Cnt ; k ++ ) Insert( 1 , 1 , 1 , n , D[k][0] , D[k][1] ) ;    }    for (int p = Head[Root] ; p ; p = Next[p] ) {        if ( vis[Node[p]] ) continue ;        Solve( Node[p] ) ;    }}int main() {    freopen( "journey.in" , "r" , stdin ) ;    freopen( "journey.out" , "w" , stdout ) ;    scanf( "%d%d%d%d" , &n , &m , &L , &R ) ;    for (int i = 1 ; i <= m ; i ++ ) C[i] = Read() ;    for (int i = 1 ; i < n ; i ++ ) {        int u = Read() , v = Read() , w = Read() ;        link( u , v , w ) ;        link( v , u , w ) ;    }    Solve( (n + 1) / 2 ) ;    printf( "%d\n" , ans ) ;    return 0 ;}

以上.

1 0