「HEOI2014」大工程

问题分析

首先不难想到是虚树。建完虚树需要保持节点间原先的距离关系。

然后总距离和最小距离用树形DP求，最大距离用两遍dfs即可。注意统计的时候只对关键点进行统计。

真是麻烦

参考程序

ac的时候是loj上速度最后一页，代码第四长的……

#include <bits/stdc++.h>
using namespace std;

const int Maxn = 1000010;
const long long INF = 1000000000010;
const int MaxLog = 20;
struct edge {
	int To, Next;
	long long Length;
	edge() : To( 0 ), Next( 0 ), Length( 0LL ) {}
	edge( int _To, int _Next, long long _Length ) : 
		To( _To ), Next( _Next ), Length( _Length ) {}
};
int n, q, k, A[ Maxn ], Important[ Maxn ];
int DFa[ Maxn ][ MaxLog ], Deep[ Maxn ], Dfn[ Maxn ], Time;
int Stack[ Maxn ];
int Flag[ Maxn ];
struct graph {
	int Start[ Maxn ], Used, State;
	edge Edge[ Maxn << 1 ];
	graph() {}
	inline void Init( int _DYT ) {
		State = _DYT;
		Used = 0;
		return;
	}
	inline void AddDirectedEdge( int x, int y, long long Len ) {
		if( Flag[ x ] != State ) {
			Flag[ x ] = State;
			Start[ x ] = 0;
		}
		Edge[ ++Used ] = edge( y, Start[ x ], Len );
		Start[ x ] = Used;
		return;
	}
	inline void AddUndirectedEdge( int x, int y, long long Len ) {
		AddDirectedEdge( x, y, Len );
		AddDirectedEdge( y, x, Len );
		return;
	}
};
graph Prime, Now;
long long Ans, Max, Min;
int Size[ Maxn ], Id;

void Build( int u, int Fa ) {
	Deep[ u ] = Deep[ Fa ] + 1;
	Dfn[ u ] = ++Time;
	DFa[ u ][ 0 ] = Fa;
	for( int i = 1; i < MaxLog; ++i ) 
		DFa[ u ][ i ] = DFa[ DFa[ u ][ i - 1 ] ][ i - 1 ];
	for( int t = Prime.Start[ u ]; t; t = Prime.Edge[ t ].Next ) {
		int v = Prime.Edge[ t ].To;
		if( v == Fa ) continue;
		Build( v, u );
	}
	return;
}

inline bool Cmp( int x, int y ) {
	return Dfn[ x ] < Dfn[ y ];
}

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

struct info {
	long long Min, Sec;
	info() : Min( INF ), Sec( INF ) {}
	info( long long _Min, long long _Sec ) : Min( _Min ), Sec( _Sec ) {}
	inline info operator + ( const long long Other ) const {
		return info( Min + Other, Sec + Other );
	}
	inline info operator + ( const info Other ) const {
		return ( Min < Other.Min ) ? info( Min, min( Sec, Other.Min ) ) : info( Other.Min, min( Min, Other.Sec ) ) ;
	}
};

info GetMin( int u, int Fa ) {
	info Ans = info( INF, INF );
	if( Important[ u ] == Now.State ) Ans.Min = 0;
	for( int t = Now.Start[ u ]; t; t = Now.Edge[ t ].Next ) {
		int v = Now.Edge[ t ].To;
		if( v == Fa ) continue;
		Ans = Ans + ( GetMin( v, u ) + Now.Edge[ t ].Length );
	}
	Min = min( Min, Ans.Min + Ans.Sec );
	return Ans;
}

void GetMax( int u, int Fa, long long Len ) {
	if( Len > Max && Important[ u ] == Now.State ) {
		Max = Len; 
		Id = u;
	}
	for( int t = Now.Start[ u ]; t; t = Now.Edge[ t ].Next ) {
		int v = Now.Edge[ t ].To;
		if( v == Fa ) continue;
		GetMax( v, u, Len + Now.Edge[ t ].Length );
	}
	return;
}

long long GetAns( int u, int Fa ) {
	Size[ u ] = 0; long long Sum = 0;
	if( Important[ u ] == Now.State ) Size[ u ] = 1;
	for( int t = Now.Start[ u ]; t; t = Now.Edge[ t ].Next ) {
		int v = Now.Edge[ t ].To;
		if( v == Fa ) continue;
		long long SS = GetAns( v, u );
		Ans += Sum * Size[ v ] + Size[ u ] * ( Now.Edge[ t ].Length * Size[ v ] + SS );
		Sum += SS + Now.Edge[ t ].Length * Size[ v ];
		Size[ u ] += Size[ v ];
	}
	return Sum;
}

void Work( int Case ) {
	Now.Init( Case );
	scanf( "%d", &k );
	for( int i = 1; i <= k; ++i ) scanf( "%d", &A[ i ] );
	for( int i = 1; i <= k; ++i ) Important[ A[ i ] ] = Case;
	sort( A + 1, A + k + 1, Cmp );
	Stack[ 0 ] = 1; Stack[ 1 ] = 1;
	int Len, Lca;
	for( int i = 1; i <= k; ++i ) {
		if( i == 1 && A[ 1 ] == 1 ) continue;
		if( i > 1 && A[ i ] == A[ i - 1 ] ) continue;
		Lca = GetLca( Stack[ Stack[ 0 ] ], A[ i ] );
		if( Deep[ Lca ] == Deep[ Stack[ Stack[ 0 ] ] ] ) 
			Stack[ ++Stack[ 0 ] ] = A[ i ];
		else {
			while( Deep[ Stack[ Stack[ 0 ] - 1 ] ] > Deep[ Lca ] ) {
				Len = Deep[ Stack[ Stack[ 0 ] ] ] - Deep[ Stack[ Stack[ 0 ] - 1 ] ];
				Now.AddUndirectedEdge( Stack[ Stack[ 0 ] - 1 ], Stack[ Stack[ 0 ] ], Len );
				--Stack[ 0 ];
			}
			if( Deep[ Stack[ Stack[ 0 ] - 1 ] ] == Deep[ Lca ] ) {
				Len = Deep[ Stack[ Stack[ 0 ] ] ] - Deep[ Stack[ Stack[ 0 ]  - 1 ] ];
				Now.AddUndirectedEdge( Stack[ Stack[ 0 ] - 1 ], Stack[ Stack[ 0 ] ], Len );
				--Stack[ 0 ];
				Stack[ ++Stack[ 0 ] ] = A[ i ];
			} else {
				Len = Deep[ Stack[ Stack[ 0 ] ] ] - Deep[ Lca ];
				Now.AddUndirectedEdge( Stack[ Stack[ 0 ] ], Lca, Len );
				--Stack[ 0 ];
				Stack[ ++Stack[ 0 ] ] = Lca;
				Stack[ ++Stack[ 0 ] ] = A[ i ];
			}
		}
	}
	while( Stack[ 0 ] > 1 ) {
		Len = Deep[ Stack[ Stack[ 0 ] ] ] - Deep[ Stack[ Stack[ 0 ] - 1 ] ];
		Now.AddUndirectedEdge( Stack[ Stack[ 0 ] ], Stack[ Stack[ 0 ] - 1 ], Len );
		--Stack[ 0 ];
	}

	Min = INF;
	GetMin( 1, 0 );
	Max = -1;
	GetMax( A[ 1 ], 0, 0 );
	Max = -1;
	GetMax( Id, 0, 0 );
	Ans = 0;
	GetAns( 1, 0 );
	printf( "%lld %lld %lld
", Ans, Min, Max );
	return;
}

int main() {
	scanf( "%d", &n );
	for( int i = 1; i < n; ++i ) {
		int x, y;
		scanf( "%d%d", &x, &y );
		Prime.AddUndirectedEdge( x, y, 1 ); 
	}
	Build( 1, 0 );
	scanf( "%d", &q );
	for( int i = 1; i <= q; ++i ) Work( i );
	return 0;
}