JZOJ3997. 树

题目大意

给定一棵$n$个结点的树，和$m$个询问。
每个询问，查询编号在$[L,R]$的结点中到给定点$pos$的最近距离是多少？
强制在线。

Data Constraint
$n\leq100000,m\leq100000$

题解

考虑点剖。先构出点剖树，每个结点维护一棵线段树。
然后对于每一个询问在点剖树上跑，每次查询线段树上对应的区间。

时间复杂度：$O(nlog^2n)$

SRC

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std ;

#define N 100000 + 10
typedef long long ll ;
const int MAXN = 18 ;
struct Tree {
    int Son[2] ;
    int val ;
} T[100*N] ;

bool vis[N] ;
int f[N][MAXN] , Deep[N] ;
int Node[2*N] , Next[2*N] , Len[2*N] , Head[N] , tot ;
int Size[N] , Maxs[N] , Dis[N] , Dist[N] , fa[N] , Rt[N] ;
int Root , All , Minv , ret ;
int n , m , Cnt ;
ll ans ;

void link( int u , int v , int w ) {
    Node[++tot] = v ;
    Len[tot] = w ;
    Next[tot] = Head[u] ;
    Head[u] = tot ;
}

int NewNode() {
    ++ Cnt ;
    T[Cnt].Son[0] = T[Cnt].Son[1] = 0 ;
    T[Cnt].val = 0 ;
    return Cnt ;
}

void Insert( int v , int l , int r , int x , int val ) {
    if ( l == x && r == x ) {
        T[v].val = val ;
        return ;
    }
    int mid = (l + r) / 2 ;
    if ( x <= mid ) {
        if ( !T[v].Son[0] ) T[v].Son[0] = NewNode() ;
        Insert( T[v].Son[0] , l , mid , x , val ) ;
    } else {
        if ( !T[v].Son[1] ) T[v].Son[1] = NewNode() ;
        Insert( T[v].Son[1] , mid + 1 , r , x , val ) ;
    }
    T[v].val = min( T[T[v].Son[0]].val , T[T[v].Son[1]].val ) ;
}

void Search( int v , int l , int r , int x , int y ) {
    if ( !v ) return ;
    if ( l == x && r == y ) {
        ret = min( ret , T[v].val ) ;
        return ;
    }
    int mid = (l + r) / 2 ;
    if ( y <= mid ) Search( T[v].Son[0] , l , mid , x , y ) ;
    else if ( x > mid ) Search( T[v].Son[1] , mid + 1 , r , x , y ) ;
    else {
        Search( T[v].Son[0] , l , mid , x , mid ) ;
        Search( T[v].Son[1] , mid + 1 , r , mid + 1 , y ) ;
    }
}

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 ) Minv = Maxs[x] , Root = 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 )  {
    for (int p = Head[x] ; p ; p = Next[p] ) {
        if ( vis[Node[p]] || Node[p] == F ) continue ;
        Dis[Node[p]] = Dis[x] + Len[p] ;
        Insert( Rt[Root] , 1 , n , Node[p] , Dis[Node[p]] ) ;
        DFS( Node[p] , x ) ;
    }
}

void DIV( int x , int F ) {
    GetSize( x , 0 ) ;
    Minv = 0x7FFFFFFF ;
    Root = All = x ;
    GetRoot( x , 0 ) ;
    vis[Root] = 1 ;
    fa[Root] = F ;
    Rt[Root] = ++ Cnt  ;
    Insert( Rt[Root] , 1 , n , Root , 0 ) ;
    Dis[Root] = 0 ;
    for (int p = Head[Root] ; p ; p = Next[p] ) {
        if ( vis[Node[p]] ) continue ;
        Dis[Node[p]] = Len[p] ;
        Insert( Rt[Root] , 1 , n , Node[p] , Dis[Node[p]] ) ;
        DFS( Node[p] , Root ) ;
    }
    int now = Root ;
    for (int p = Head[Root] ; p ; p = Next[p] ) {
        if ( vis[Node[p]] ) continue ;
        DIV( Node[p] , now ) ;
    }
}

void Pre( int x ) {
    for (int p = Head[x] ; p ; p = Next[p] ) {
        if ( Node[p] == f[x][0] ) continue ;
        f[Node[p]][0] = x ;
        Deep[Node[p]] = Deep[x] + 1 ;
        Dist[Node[p]] = Dist[x] + Len[p] ;
        Pre( Node[p] ) ;
    }
}

int LCA( int x , int y ) {
    if ( Deep[x] < Deep[y] ) swap( x , y ) ;
    for (int i = MAXN - 1 ; i >= 0 ; i -- ) {
        if ( Deep[f[x][i]] >= Deep[y] ) x = f[x][i] ;
    }
    if ( x == y ) return x ;
    for (int i = MAXN - 1 ; i >= 0 ; i -- ) {
        if ( f[x][i] != f[y][i] ) x = f[x][i] , y = f[y][i] ;
    }
    return f[x][0] ;
}

int Calc( int u , int v ) {
    return Dist[u] + Dist[v] - 2 * Dist[LCA(u,v)] ;
}

int main() {
    scanf( "%d" , &n ) ;
    for (int i = 1 ; i < n ; i ++ ) {
        int x , y , d ;
        scanf( "%d%d%d" , &x , &y , &d ) ;
        link( x , y , d ) ;
        link( y , x , d ) ;
    }
    Deep[1] = 1 ;
    Pre( 1 ) ;
    for (int j = 1 ; j < MAXN ; j ++ ) {
        for (int i = 1 ; i <= n ; i ++ ) f[i][j] = f[f[i][j-1]][j-1] ;
    }
    T[0].val = 0x7FFFFFFF ;
    DIV( 1 , 0 ) ;
    scanf( "%d" , &m ) ;
    ans = 0 ;
    for (int i = 1 ; i <= m ; i ++ ) {
        int L , R , pos ;
        scanf( "%d%d%d" , &L , &R , &pos ) ;
        pos ^= ans ;
        ans = 1e15 ;
        if ( pos >= L && pos <= R ) {
            ans = 0 ;
            printf( "0\n" ) ;
            continue ;
        }
        int now = pos ;
        while ( now ) {
            ret = 0x7FFFFFFF ;
            Search( Rt[now] , 1 , n , L , R ) ;
            ans = min( ans , (ll)Calc( pos , now ) + ret ) ;
            now = fa[now] ;
        }
        printf( "%lld\n" , ans ) ;
    }
    return 0 ;
}

以上.