BZOJ-3648: 寝室管理(点分治+平衡树)

题目:http://www.lydsy.com/JudgeOnline/problem.php?id=3648

首先这题求树或一个环套树上面的长度>=k的路径数,那么如果是树直接点分治掉没问题,考虑环套树的情况,如果路径在同一棵树上面,对所有树点分治即可,如果在环上,那么我们沿着顺时针方向扫两圈,平衡树维护一下,然后加加路径上新出现的点,再减掉消掉的点,然后平衡树整体加减一个数这个东西可以弄个时间戳记录一下,然后弄个delta维护即可,这样就平均每个点进平衡树1次,删掉1次,所以复杂度是O(n log^2 n + n log n)前面那个是点分的复杂度。

代码(长的233啊,还好码了一个多小时后就一A了,要不实在调不动):

#include <cstdio>

#include <algorithm>

#include <cstring>

#include <cstdlib>

 

using namespace std ;

 

#define REP( i , l , r ) for ( int i = l ; i <= r ; ++ i )

#define rep( i , x ) for ( int i = 0 ; i ++ < x ; )

#define DOWN( i , r , l ) for ( int i = r ; i >= l ; -- i )

#define Rep( i , x ) for ( int i = 0 ; i < x ; ++ i )

 

const int maxn = 101000 ;

const int maxm = 201000 ;

const int maxv = 401000 ;

 

struct edge {

        edge *next ;

        int t , v ;

} E[ maxm ] ;

 

edge *ept = E , *head[ maxn ] ;

 

inline void Init_edge(  ) {

        memset( head , 0 , sizeof( head ) ) ;

}

 

inline void add( int s , int t , int v ) {

        ept -> t = t , ept -> v = v , ept -> next = head[ s ] ; head[ s ] = ept ++ ;

}

 

inline void addedge( int s , int t , int v ) {

        add( s , t , v ) , add( t , s , v ) ;

}

 

int delta[ maxv ] , idx = 0 ;

 

struct node {

        int ky , mn , pr , sz ;

        node *lc , *rc ;

        inline void update(  ) {

                sz = lc -> sz + rc -> sz + 1 ;

        }

} bst[ maxv ] ;

 

node *pt , *null , *root ;

 

inline void Init_bst(  ) {

        pt = bst ; null = pt ++ ;

        null -> lc = null -> rc = null , null -> pr = null -> sz = 0 ;

        root = null ;

}

 

inline void right( node* &t ) {

        node *k = t -> lc ;

        t -> lc = k -> rc ; t -> update(  ) ;

        k -> rc = t ; k -> update(  ) ;

        t = k ;

}

 

inline void left( node* &t ) {

        node *k = t -> rc ;

        t -> rc = k -> lc ; t -> update(  ) ;

        k -> lc = t ; k -> update(  ) ;

        t = k ;

}

 

void Insert( int key , node* &t ) {

        if ( t == null ) {

                t = pt ++ ;

                t -> lc = t -> rc = null , t -> sz = 1 , t -> ky = key , t -> mn = idx , t -> pr = rand(  ) ;

                return ;

        }

        t -> sz ++ ;

        if ( key <= t -> ky + delta[ idx ] - delta[ t -> mn ] ) {

                Insert( key , t -> lc ) ; if ( t -> lc -> pr > t -> pr ) right( t ) ;

        } else {

                Insert( key , t -> rc ) ; if ( t -> rc -> pr > t -> pr ) left( t ) ;

        }

}

 

inline int Rank( int key , node *t ) {

        int rec = 0 ;

        for ( ; t != null ; ) {

                if ( key <= t -> ky + delta[ idx ] - delta[ t -> mn ] ) {

                        rec += t -> rc -> sz + 1 ; t = t -> lc ;

                } else t = t -> rc ;

        }

        return rec ;

}

 

void Delete( int key , node* &t ) {

        int k = t -> ky + delta[ idx ] - delta[ t -> mn ] ;

        if ( key == k ) {

                if ( t -> lc == null ) {

                        t = t -> rc ; return ;

                } else if ( t -> rc == null ) {

                        t = t -> lc ; return ;

                } else if ( t -> lc -> pr > t -> rc -> pr ) {

                        right( t ) ; Delete( key , t -> rc ) ;

                } else {

                        left( t ) ; Delete( key , t -> lc ) ;

                }      

        } else if ( key < k ) Delete( key , t -> lc ) ; else Delete( key , t -> rc ) ;

        t -> update(  ) ;

}

 

bool used[ maxn ] , flag[ maxn ] ;

int n , m , k ;

 

typedef long long ll ;

ll ans = 0 ;

 

int sz[ maxn ] , dep[ maxn ] , rt , rv ;

 

#define travel( x ) for ( edge *p = head[ x ] ; p ; p = p -> next )

 

void gets( int now , int fa ) {

        sz[ now ] = 1 ;

        travel( now ) if ( p -> t != fa && ! flag[ p -> t ] && ! used[ p -> t ] ) {

                gets( p -> t , now ) ; sz[ now ] += sz[ p -> t ] ;

        }

}

 

void getr( int now , int fa ) {

        bool Flag = ( sz[ rv ] - sz[ now ] ) <= ( sz[ rv ] >> 1 ) ;

        if ( Flag ) travel( now ) if ( p -> t != fa && ! flag[ p -> t ] && ! used[ p -> t ] ) {

                if ( sz[ p -> t ] > ( sz[ rv ] >> 1 ) ) {

                        Flag = false ; break ;

                }

        }

        if ( Flag ) rt = now ; else travel( now ) if ( p -> t != fa && ! flag[ p -> t ] && ! used[ p -> t ] ) {

                getr( p -> t , now ) ;

                if ( rt ) break ;

        }

}

 

int ch[ maxn ] , cn ;

 

void getc( int now , int fa ) {

        ch[ ++ cn ] = now , dep[ now ] = dep[ fa ] + 1 ;

        travel( now ) if ( p -> t != fa && ! used[ p -> t ] && ! flag[ p -> t ] ) getc( p -> t , now ) ;

}

 

void solve( int now ) {

        gets( now , 0 ) ;

        rt = 0 , rv = now ; getr( now , 0 ) ;

        dep[ rt ] = 0 ; Init_bst(  ) ; idx = 0 ; Insert( 1 , root ) ;

        travel( rt ) if ( ! flag[ p -> t ] && ! used[ p -> t ] ) {

                cn = 0 ; getc( p -> t , rt ) ;

                rep( i , cn ) ans += ll( Rank( k - dep[ ch[ i ] ] , root ) ) ;

                rep( i , cn ) Insert( dep[ ch[ i ] ] + 1 , root ) ;

        }

        used[ rt ] = true ;

        travel( rt ) if ( ! flag[ p -> t ] && ! used[ p -> t ] ) solve( p -> t ) ;

}

 

int cv[ maxn ] , vn = 0 , sta[ maxn ] , tp = 0 , pos[ maxn ] ;

 

void dfs( int now , int v ) {

        sta[ pos[ now ] = ++ tp ] = now ;

        travel( now ) if ( p -> v != v ) {

                if ( ! pos[ p -> t ] ) dfs( p -> t , p -> v ) ; else {

                        REP( i , pos[ p -> t ] , tp ) {

                                flag[ cv[ vn ++ ] = sta[ i ] ] = true ;

                        }

                }

                if ( vn ) break ;

        }

        -- tp ;

}

 

int mes[ maxn ][ 2 ] ;

  

int main(  ) {

        srand( 12 ) ;

        Init_edge(  ) ;

        scanf( "%d%d%d" , &n , &m , &k ) ;

        rep( i , m ) {

                int s , t ; scanf( "%d%d" , &s , &t ) ; addedge( s , t , i ) ;

        }

        memset( flag , 0 , sizeof( flag ) ) , memset( used , false , sizeof( used ) ) ;

        if ( m == n - 1 ) {

                solve( 1 ) ;

        } else {

                memset( pos , 0 , sizeof( pos ) ) ; dfs( 1 , 0 ) ;

                Rep( i , vn ) {

                        flag[ cv[ i ] ] = false ; solve( cv[ i ] ) ; flag[ cv[ i ] ] = true ;

                }

                Init_bst(  ) ; delta[ idx = 0 ] = 0 ;

                memset( used , false , sizeof( used ) ) ;

                rep( i , ( vn - 1 ) ) {

                        delta[ idx + 1 ] = delta[ idx ] + 1 ; ++ idx ;

                        dep[ cv[ i ] ] = 1 , ch[ cn = 1 ] = cv[ i ] ;

                        travel( cv[ i ] ) if ( ! flag[ p -> t ] ) getc( p -> t , cv[ i ] ) ;

                        rep( j , cn ) {

                                Insert( dep[ ch[ j ] ] , root ) ;

                                mes[ ch[ j ] ][ 0 ] = dep[ ch[ j ] ] , mes[ ch[ j ] ][ 1 ] = idx ;

                        }

                }

                Rep( i , vn ) {

                        dep[ cv[ i ] ] = 1 , ch[ cn = 1 ] = cv[ i ] ;

                        travel( cv[ i ] ) if ( ! flag[ p -> t ] ) getc( p -> t , cv[ i ] ) ;

                        rep( j , cn ) ans += ll( Rank( k - dep[ ch[ j ] ] , root ) ) ;

                        if ( i == vn - 1 ) break ;

                        delta[ idx + 1 ] = delta[ idx ] + 1 ; ++ idx ;

                        rep( j , cn ) Insert( dep[ ch[ j ] ] , root ) ;

                        cn = 0 ; getc( cv[ i + 1 ] , 0 ) ;

                        rep( j , cn ) Delete( mes[ ch[ j ] ][ 0 ] + delta[ idx ] - delta[ mes[ ch[ j ] ][ 1 ] ] , root ) ;

                }

        }

        printf( "%lld\n" , ans ) ;

        return 0 ; 

}
    原文作者:AmadeusChan
    原文地址: https://www.jianshu.com/p/7d975f5ffb12
    本文转自网络文章,转载此文章仅为分享知识,如有侵权,请联系博主进行删除。
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