[SDOI2011]消耗战

题目链接

问题分析

显然是虚树题。由于\(\sum k\leqslant 500000\)，所以直接套个虚树就好了。时间经过实践是可以的。

参考代码

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

const int Maxn = 250010;
const long long INF = 125000000010;
const int MaxLog = 20;
struct edge {
	int To, Next;
	long long c;
	edge() : To( 0 ), Next( 0 ), c( 0 ) {} 
	edge( int _To, int _Next, long long _c ) : To( _To ), Next( _Next ), c( _c ) {}
};
edge Edge[ Maxn << 1 ];
int Start[ Maxn ], UsedEdge;
inline void AddEdge( int x, int y, long long z ) {
	Edge[ ++UsedEdge ] = edge( y, Start[ x ], z );
	Start[ x ] = UsedEdge;
	return;
}
int n, Dfn[ Maxn ], Deep[ Maxn ], Time;
struct step {
	int To;
	long long Min;
	step() : To( 0 ), Min( INF ) {}
	step( int _To, long long _Min ) : To( _To ), Min( _Min ) {} 
};
step Step[ Maxn ][ MaxLog ];
int m, k, H[ Maxn ];

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

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

edge Edge2[ Maxn << 1 ];
int Start2[ Maxn ], UsedEdge2, Flag[ Maxn ], IsFlag[ Maxn ], Emmm;
int Stack[ Maxn ];
long long GetCost( int x, int y );
inline void AddEdge_2( int x, int y, long long z, int flag ) {
	if( Flag[ x ] != flag ) {
		Start2[ x ] = 0;
		Flag[ x ] = flag;
	}
	Edge2[ ++UsedEdge2 ] = edge( y, Start2[ x ], z );
	Start2[ x ] = UsedEdge2;
	return;
}
inline void AddEdge2( int x, int y, int flag ) {
	long long z = GetCost( x, y );
	AddEdge_2( x, y, z, flag );
	AddEdge_2( y, x, z, flag );
	return;
}

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

long long GetCost( int x, int y ) {
	if( Deep[ x ] < Deep[ y ] ) swap( x, y );
	long long Ans = INF;
	for( int i = MaxLog - 1; i >= 0; --i ) 
		if( Deep[ Step[ x ][ i ].To ] >= Deep[ y ] ) {
			Ans = min( Ans, Step[ x ][ i ].Min );
			x = Step[ x ][ i ].To;
		}
	return Ans;
}

long long Dp( int u, int Fa ) {
	long long Ans = 0;
	int Cnt = 0;
	for( int t = Start2[ u ]; t; t = Edge2[ t ].Next ) {
		int v = Edge2[ t ].To;
		if( v == Fa ) continue;
		++Cnt;
		if( IsFlag[ v ] == Emmm )
			Ans += Edge2[ t ].c;
		else
			Ans += min( Edge2[ t ].c, Dp( v, u ) );
	}
	if( Cnt ) return Ans; else return INF;
}

int main() {
	scanf( "%d", &n );
	for( int i = 1; i < n; ++i ) {
		int x, y; long long z;
		scanf( "%d%d%lld", &x, &y, &z );
		AddEdge( x, y, z );
		AddEdge( y, x, z );
	}
	Build( 1, 1, INF );
	scanf( "%d", &m );
	for( int i = 1; i <= m; ++i ) {
		scanf( "%d", &k );
		for( int j = 1; j <= k; ++j ) scanf( "%d", &H[ j ] );
		sort( H + 1, H + k + 1, Cmp );
		for( int j = 1; j <= k; ++j ) IsFlag[ H[ j ] ] = i;
		Emmm = i;
		UsedEdge2 = 0;
		Stack[ 0 ] = 1; Stack[ 1 ] = 1;
		for( int j = 1; j <= k; ++j ) {
			int Lca = GetLca( Stack[ Stack[ 0 ] ], H[ j ] );
			if( Deep[ Lca ] == Deep[ Stack[ Stack[ 0 ] ] ] ) {
				Stack[ ++Stack[ 0 ] ] = H[ j ];
			}
			else {
				while( Deep[ Lca ] < Deep[ Stack[ Stack[ 0 ] - 1 ] ] ) {
					AddEdge2( Stack[ Stack[ 0 ] ], Stack[ Stack[ 0 ] - 1 ], i );
					--Stack[ 0 ];
				}
				if( Deep[ Lca ] == Deep[ Stack[ Stack[ 0 ] - 1 ] ] ) {
					AddEdge2( Stack[ Stack[ 0 ] ], Stack[ Stack[ 0 ] - 1 ], i );
					--Stack[ 0 ];
					Stack[ ++Stack[ 0 ] ] = H[ j ];
				} else {
					AddEdge2( Stack[ Stack[ 0 ] ], Lca, i );
					--Stack[ 0 ];
					Stack[ ++Stack[ 0 ] ] = Lca;
					Stack[ ++Stack[ 0 ] ] = H[ j ];
				}
			}
		}
		while( Stack[ 0 ] >= 2 ) {
			AddEdge2( Stack[ Stack[ 0 ] ], Stack[ Stack[ 0 ] - 1 ], i );
			--Stack[ 0 ];
		}
		printf( "%lld\n", Dp( 1, 0 ) );
	}
	return 0;
}