GDOI2016 Day2 T3 机密网络

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题目大意

给一棵环套树，每个点有点权ei，求所有距离≤K的点对数，以及这些点对权值积的和。

Data Constraint
n≤105,K≤n,ei≤104

题解

这题与 bzoj3648寝室管理类似
。先考虑没有环的情况，这时就是裸的点剖了，所以我们可以先点剖求出环上每个外向树的答案，再统计经过环边的答案。
具体来说就是，先找环上任意一点作为起点，任一方向为起始方向编号。然后对于环上一点i，只统计1∼i−1对i的贡献。找到一点j满足1∼j的点到i最短距离为Len−i+k,j+1∼i−1为i−k，即分为两个不同的方向。
现在分析第二种情况，第一种类似。
如果(u,v)合法，那么满足du+dv+i−k≤K
即dv−k≤K−du−i
所以只需要按dv−k建一棵线段树就可以统计答案了。

SRC

#include<cstdio>#include<cstdlib>#include<cstring>#include<iostream>#include<algorithm>using namespace std ;#define N 100000 + 10typedef long long ll ;const int LB = -1e5 ;struct Tree {    int Son[2] ;    ll tot , sum ;} T[36*N] ;bool vis[N] , ori[N] ;int Node[2*N] , Next[2*N] , Head[N] , tot = 1 ;int DFN[N] , LOW[N] , s[N] , Tim = 0 , top = 0 ;int Cir[N] , Size[N] , D[N] , Dis[N] , Maxs[N] ;int Rt[N] ;ll e[N] ;int n , K ;int Root , All , Mins , last , tail , Cnt ;ll ans , sum , rettot , retsum ;bool cmp( int i , int j ) { return Dis[i] < Dis[j] ; }void link( int u , int v ) {    Node[++tot] = v ;    Next[tot] = Head[u] ;    Head[u] = tot ;}void FindCir( int x , int fe ) {    if ( Cir[0] ) return ;    DFN[x] = LOW[x] = ++ Tim ;    s[++top] = x ;    for (int p = Head[x] ; p ; p = Next[p] ) {        if ( p == (fe ^ 1) ) continue ;        if ( !DFN[Node[p]] ) {            FindCir( Node[p] , p ) ;            LOW[x] = min( LOW[x] , LOW[Node[p]] ) ;        }        else LOW[x] = min( LOW[x] , DFN[Node[p]] ) ;     }    if ( LOW[x] == DFN[x] ) {        bool exist = 0 ;        while ( s[top] != x ) {            exist = 1 ;            Cir[++Cir[0]] = s[top] ;            vis[s[top]] = 1 ;            top -- ;        }        if ( exist ) Cir[++Cir[0]] = s[top] , vis[s[top]] = 1 ;        top -- ;    }}void GetSize( int x , int Fa ) {    Size[x] = Maxs[x] = 1 ;    for (int p = Head[x] ; p ; p = Next[p] ) {        if ( Node[p] == Fa || 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 Fa ) {    Maxs[x] = max( Maxs[x] , Size[All] - Maxs[x] ) ;    if ( Maxs[x] < Mins ) Mins = Maxs[x] , Root = x ;    for (int p = Head[x] ; p ; p = Next[p] ) {        if ( Node[p] == Fa || vis[Node[p]] ) continue ;        GetRoot( Node[p] , x ) ;    }}void DFS( int x , int Fa ) {    for (int p = Head[x] ; p ; p = Next[p] ) {        if ( Node[p] == Fa || vis[Node[p]] ) continue ;        Dis[Node[p]] = Dis[x] + 1 ;        D[++tail] = Node[p] ;        DFS( Node[p] , x ) ;    }}void Qsort( int l , int r ) {    if ( l > r ) return  ;    sort( D + l , D + r + 1 , cmp ) ;}void Calc( int Root ) {    Qsort( 1 , last ) ;    Qsort( last + 1 , tail ) ;    ll lsum = 0 ;    int head = 1 ;    for (int j = tail ; j > last ; j -- ) {        while ( head <= last && Dis[D[head]] + Dis[D[j]] <= K ) {            lsum += e[D[head]] ;            head ++ ;        }        ans += head - 1 + (Dis[D[j]] <= K) ;        sum += e[D[j]] * lsum + e[D[j]] * e[Root] * (Dis[D[j]] <= K) ;    }    last = tail ;}void DIV( int x ) {    last = tail = 0 ;    Mins = 0x7FFFFFFF ;    Root = All = x ;    GetSize( x , 0 ) ;    GetRoot( x , 0 ) ;    Dis[Root] = 0 ;    vis[Root] = 1 ;    for (int p = Head[Root] ; p ; p = Next[p] ) {        if ( vis[Node[p]] ) continue ;        D[++tail] = Node[p] ;        Dis[Node[p]] = 1 ;        DFS( Node[p] , Root ) ;        Calc( Root ) ;    }    for (int p = Head[Root] ; p ; p = Next[p] ) if ( !vis[Node[p]] ) DIV( Node[p] ) ;}void SolveTree() {    for (int i = 1 ; i <= Cir[0] ; i ++ ) {        vis[Cir[i]] = 0 ;        DIV( Cir[i] ) ;        vis[Cir[i]] = 1 ;    }}bool Sign = 0 ;int Search( int i ) {    int l = 0 , r = i , ret = 0 ;    while ( l <= r ) {        int mid = (l + r) / 2 ;        if ( i - mid > Cir[0] - i + mid ) ret = mid , l = mid + 1 ;        else r = mid - 1 ;    }    return ret ;}int NewNode() {    Cnt ++ ;    T[Cnt].Son[0] = T[Cnt].Son[1] = 0 ;    T[Cnt].tot = T[Cnt].sum = 0 ;    return Cnt ;}void Update( int v ) {    int ls = T[v].Son[0] ;    int rs = T[v].Son[1] ;    T[v].tot = T[ls].tot + T[rs].tot ;    T[v].sum = T[ls].sum + T[rs].sum ;}void ADDTree( int v , int l , int r , int x , ll e ) {    if ( l == x && r == x ) {        T[v].tot ++ ;        T[v].sum += e ;        return ;    }    int mid = (l + r) / 2 ;    if ( l + r < 0 && (l + r) / 2 * 2 != l + r ) mid -- ;    if ( x <= mid ) {        int ls = NewNode() ;        T[ls] = T[T[v].Son[0]] ;        T[v].Son[0] = ls ;        ADDTree( ls , l , mid , x , e ) ;    } else {        int rs = NewNode() ;        T[rs] = T[T[v].Son[1]] ;        T[v].Son[1] = rs ;        ADDTree( rs , mid + 1 , r , x , e ) ;    }    Update( v ) ;}void SearchTree( int lv , int rv , int l , int r , int x , int y ) {    if ( l == x && r == y ) {        rettot += T[rv].tot - T[lv].tot ;        retsum += T[rv].sum - T[lv].sum ;        return ;    }    int mid = (l + r) / 2 ;    if ( l + r < 0 && (l + r) / 2 * 2 != l + r ) mid -- ;    if ( y <= mid ) SearchTree( T[lv].Son[0] , T[rv].Son[0] , l , mid , x , y ) ;    else if ( x > mid ) SearchTree( T[lv].Son[1] , T[rv].Son[1] , mid + 1 , r , x , y ) ;    else {        SearchTree( T[lv].Son[0] , T[rv].Son[0] , l , mid , x , mid ) ;        SearchTree( T[lv].Son[1] , T[rv].Son[1] , mid + 1 , r , mid + 1 , y ) ;    }}void GetDist( int x , int i , int j , int Fa , int deep ) {    if ( !Sign ) {        if ( deep + i + LB <= K ) {            rettot = retsum = 0 ;            SearchTree( Rt[j] , Rt[i-1] , LB , -LB , LB , K - deep - i ) ;            ans += rettot ;            sum += e[x] * retsum ;        }        if ( !Rt[i] ) {            Rt[i] = NewNode() ;            T[Rt[i]] = T[Rt[i-1]] ;        }        ADDTree( Rt[i] , LB , -LB , deep - i , e[x] ) ;    } else {        if ( deep + Cir[0] - i <= K ) {            rettot = retsum = 0 ;            SearchTree( 0 , Rt[j] , 0 , -LB , 0 , K - deep - Cir[0] + i ) ;            ans += rettot ;            sum += e[x] * retsum ;        }        if ( !Rt[i] ) {            Rt[i] = NewNode() ;            T[Rt[i]] = T[Rt[i-1]] ;        }        ADDTree( Rt[i] , 0 , -LB , deep + i , e[x] ) ;    }    for (int p = Head[x] ; p ; p = Next[p] ) {        if ( vis[Node[p]] || Node[p] == Fa ) continue ;        GetDist( Node[p] , i , j , x , deep + 1 ) ;    }}void SolveCircle() {    for (int i = 1 ; i <= Cir[0] ; i ++ ) {        int j = Search( i ) ;        GetDist( Cir[i] , i , j , 0 , 0 ) ;    }    Cnt = 0 ;    Sign = 1 ;    memset( T , 0 , sizeof(T) ) ;    memset( Rt , 0 , sizeof(Rt) ) ;    for (int i = 1 ; i <= Cir[0] ; i ++ ) {        int j = Search( i ) ;        GetDist( Cir[i] , i , j , 0 , 0 ) ;    }}void Solve() {    SolveTree() ;    memcpy( vis , ori , sizeof(ori) ) ;    SolveCircle() ;}int main() {    freopen( "pronet.in" , "r" , stdin ) ;    freopen( "pronet.out" , "w" , stdout ) ;    scanf( "%d%d" , &n , &K ) ;    for (int i = 1 ; i <= n ; i ++ ) {        int x ;        scanf( "%d" , &x ) ;        if ( !x ) continue ;        link( x , i ) ;        link( i , x ) ;    }    for (int i = 1 ; i <= n ; i ++ ) scanf( "%lld" , &e[i] ) ;    for (int i = 1 ; i <= n ; i ++ ) if ( !DFN[i] ) FindCir( i , 0 ) ;    memcpy( ori , vis , sizeof(vis) ) ;    if ( Cir[0] ) Solve() ;    else DIV( 1 ) ;    printf( "%lld %lld\n" , ans , sum ) ;    return 0 ;}

以上.

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