JZOJ3997. 树

来源：互联网发布：小区网络装iptv服务器编辑：程序博客网时间：2024/06/06 12:53

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≤100000,m≤100000

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(nlog2n)

SRC

#include<cstdio>#include<cstdlib>#include<cstring>#include<iostream>#include<algorithm>using namespace std ;#define N 100000 + 10typedef 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.

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