5077. 树的难题

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
#include
#include
#include
#include
using namespace std ;

#define N 200000 + 10
const 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.