luoguP5024 保卫王国

题目链接

问题分析

其实是比较明显的动态DP。

懒于再推一遍式子,直接用 最小权点覆盖=全集-最大权独立集,然后就和这道题一样了。题解可以看这里

然后必须选或者不选的话,就直接把相应的点权变成\(-\infty\)\(\infty\)就好了。如果是必须选,最后答案里不要忘了加回原来的值。

参考程序

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

const long long Maxn = 100010;
const long long INF = 10000000010;
struct matrix {
    long long A[ 2 ][ 2 ];
    matrix() {
        A[ 0 ][ 0 ] = A[ 0 ][ 1 ] = A[ 1 ][ 0 ] = A[ 1 ][ 1 ] = -INF;
        return;
    }
    matrix( long long *T ) {
        A[ 0 ][ 0 ] = A[ 0 ][ 1 ] = T[ 0 ];
        A[ 1 ][ 0 ] = T[ 1 ];
        A[ 1 ][ 1 ] = -INF;
        return;
    }
    matrix( long long a, long long b, long long c, long long d ) {
        A[ 0 ][ 0 ] = a; A[ 0 ][ 1 ] = b; A[ 1 ][ 0 ] = c; A[ 1 ][ 1 ] = d;
        return;
    }
    inline matrix operator * ( const matrix Other ) const {
        return matrix( max( A[ 0 ][ 0 ] + Other.A[ 0 ][ 0 ], A[ 0 ][ 1 ] + Other.A[ 1 ][ 0 ] ),
                max( A[ 0 ][ 0 ] + Other.A[ 0 ][ 1 ], A[ 0 ][ 1 ] + Other.A[ 1 ][ 1 ] ),
                max( A[ 1 ][ 0 ] + Other.A[ 0 ][ 0 ], A[ 1 ][ 1 ] + Other.A[ 1 ][ 0 ] ),
                max( A[ 1 ][ 0 ] + Other.A[ 0 ][ 1 ], A[ 1 ][ 1 ] + Other.A[ 1 ][ 1 ] ) );
    }
};
struct edge {
    long long To, Next;
    edge() : To( 0 ), Next( 0 ) {}
    edge( long long _To, long long _Next ) : To( _To ), Next( _Next ) {}
};
edge Edge[ Maxn << 1 ];
long long Start[ Maxn ], UsedEdge;
inline void AddEdge( long long x, long long y ) {
    Edge[ ++UsedEdge ] = ( edge ) { y, Start[ x ] };
    Start[ x ] = UsedEdge;
    return;
}
long long n, m, Cost[ Maxn ], NowCost[ Maxn ], Sum;
char Ch[ 10 ];
long long Deep[ Maxn ], Father[ Maxn ], Size[ Maxn ], Son[ Maxn ], Top[ Maxn ], Index[ Maxn ], Ref[ Maxn ], Dfn[ Maxn ], Used;
long long Dp[ Maxn ][ 2 ], LDp[ Maxn ][ 2 ];
matrix Tree[ Maxn << 2 ];

void Build_Cut();
void Build();
void Change( long long u, long long Key );
matrix Query( long long Ind, long long Left, long long Right, long long L, long long R );

int main() {
    scanf( "%lld%lld", &n, &m ); scanf( "%s", Ch );
    for( long long i = 1; i <= n; ++i ) scanf( "%lld", &Cost[ i ] );
    for( long long i = 1; i < n; ++i ) {
        long long x, y; scanf( "%lld%lld", &x, &y );
        AddEdge( x, y ); AddEdge( y, x );
    }
    Build_Cut();
    Build();
    for( long long i = 1; i <= m; ++i ) {
        long long a, x, b, y;
        scanf( "%lld%lld%lld%lld", &a, &x, &b, &y);
        if( x == 0 ) { Sum -= Cost[ a ]; Sum += INF; Change( a, INF ); }
        else { Sum -= Cost[ a ]; Sum += -INF; Change( a, -INF ); }
        if( y == 0 ) { Sum -= Cost[ b ]; Sum += INF; Change( b, INF ); }
        else { Sum -= Cost[ b ]; Sum += -INF; Change( b, -INF ); }

        matrix Temp = Query( 1, 1, n, Index[ 1 ], Dfn[ 1 ] );
        long long Ans = max( Temp.A[ 0 ][ 0 ], Temp.A[ 1 ][ 0 ] );
        Ans = Sum - Ans;
        if( x == 1 ) Ans = Ans + INF + Cost[ a ];
        if( y == 1 ) Ans = Ans + INF + Cost[ b ];
        if( Ans >= INF ) printf( "-1\n" ); else printf( "%lld\n", Ans );

        if( x == 0 ) { Sum -= INF; Sum += Cost[ a ]; Change( a, Cost[ a ] ); } 
        else { Sum -= -INF; Sum += Cost[ a ]; Change( a, Cost[ a ] ); }
        if( y == 0 ) { Sum -= INF; Sum += Cost[ b ]; Change( b, Cost[ b ] ); }
        else { Sum -= -INF; Sum += Cost[ b ]; Change( b, Cost[ b ] ); }
    }
    return 0;
}

void Dfs1( long long u, long long Fa ) {
    Deep[ u ] = Deep[ Fa ] + 1;
    Father[ u ] = Fa;
    Size[ u ] = 1;
    for( long long t = Start[ u ]; t; t = Edge[ t ].Next ) {
        long long v = Edge[ t ].To;
        if( v == Fa ) continue;
        Dfs1( v, u );
        if( Size[ v ] > Size[ Son[ u ] ] ) Son[ u ] = v;
        Size[ u ] += Size[ v ];
    }
    return;
}

void Dfs2( long long u, long long Fa ) {
    if( Son[ u ] ) {
        Top[ Son[ u ] ] = Top[ u ];
        Index[ Son[ u ] ] = ++Used;
        Ref[ Used ] = Son[ u ];
        Dfs2( Son[ u ], u );
    }
    for( long long t = Start[ u ]; t; t = Edge[ t ].Next ) {
        long long v = Edge[ t ].To;
        if( v == Fa || v == Son[ u ] ) continue;
        Top[ v ] = v; Index[ v ] = ++Used; Ref[ Used ] = v;
        Dfs2( v, u );
    }
    return;
}

void Build_Cut() {
    Dfs1( 1, 0 );
    Top[ 1 ] = 1; Index[ 1 ] = ++Used; Ref[ Used ] = 1;
    Dfs2( 1, 0 );
    for( int i = 1; i <= n; ++i ) Dfn[ Top[ i ] ] = max( Dfn[ Top[ i ] ], Index[ i ] );
    return;
}

void Dfs3( long long u, long long Fa ) {
    LDp[ u ][ 1 ] = NowCost[ u ];
    for( long long t = Start[ u ]; t; t = Edge[ t ].Next ) {
        long long v = Edge[ t ].To;
        if( v == Fa || v == Son[ u ] ) continue;
        Dfs3( v, u );
        LDp[ u ][ 0 ] += max( Dp[ v ][ 0 ], Dp[ v ][ 1 ] );
        LDp[ u ][ 1 ] += Dp[ v ][ 0 ];
    }
    if( Son[ u ] ) Dfs3( Son[ u ], u );
    Dp[ u ][ 0 ] = LDp[ u ][ 0 ] + max( Dp[ Son[ u ] ][ 0 ], Dp[ Son[ u ] ][ 1 ] );
    Dp[ u ][ 1 ] = LDp[ u ][ 1 ] + Dp[ Son[ u ] ][ 0 ];
    return;
}

void RealBuild( long long Ind, long long Left, long long Right ) {
    if( Left == Right ) {
        Tree[ Ind ] = matrix( LDp[ Ref[ Left ] ] );
        return;
    }
    long long Mid = ( Left + Right ) >> 1;
    RealBuild( Ind << 1, Left, Mid );
    RealBuild( Ind << 1 | 1, Mid + 1, Right );
    Tree[ Ind ] = Tree[ Ind << 1 ] * Tree[ Ind << 1 | 1 ];
    return;
}

matrix Query( long long Ind, long long Left, long long Right, long long L, long long R ) {
    if( L <= Left && Right <= R ) return Tree[ Ind ];
    long long Mid = ( Left + Right ) >> 1;
    if( R <= Mid ) return Query( Ind << 1, Left, Mid, L, R );
    if( L > Mid ) return Query( Ind << 1 | 1, Mid + 1, Right, L, R );
    return Query( Ind << 1, Left, Mid, L, R ) * Query( Ind << 1 | 1, Mid + 1, Right, L, R );
}

void Build() {
    for( long long i = 1; i <= n; ++i ) NowCost[ i ] = Cost[ i ];
    for( long long i = 1; i <= n; ++i ) Sum += NowCost[ i ];
    Dfs3( 1, 0 );
    RealBuild( 1, 1, n );
    return;
}

void Update( long long Ind, long long Left, long long Right, long long x ) {
    if( Left == Right ) {
        Tree[ Ind ] = matrix( LDp[ Ref[ Left ] ] );
        return;
    }
    long long Mid = ( Left + Right ) >> 1;
    if( x <= Mid ) Update( Ind << 1, Left, Mid, x );
    if( x > Mid ) Update( Ind << 1 | 1, Mid + 1, Right, x );
    Tree[ Ind ] = Tree[ Ind << 1 ] * Tree[ Ind << 1 | 1 ];
    return;
}

void Change( long long u, long long Key ) {
    matrix Last = Query( 1, 1, n, Index[ Top[ u ] ], Dfn[ Top[ u ] ] );
    LDp[ u ][ 1 ] += -NowCost[ u ] + Key; NowCost[ u ] = Key;
    Update( 1, 1, n, Index[ u ] );
    matrix Temp = Query( 1, 1, n, Index[ Top[ u ] ], Dfn[ Top[ u ] ] );
    u = Father[ Top[ u ] ];
    while( u ) {
        matrix TTT = Query( 1, 1, n, Index[ Top[ u ] ], Dfn[ Top[ u ] ] );
        LDp[ u ][ 0 ] += -max( Last.A[ 0 ][ 0 ], Last.A[ 1 ][ 0 ] ) + max( Temp.A[ 0 ][ 0 ], Temp.A[ 1 ][ 0 ] );
        LDp[ u ][ 1 ] += -Last.A[ 0 ][ 0 ] + Temp.A[ 0 ][ 0 ];
        Last = TTT;
        Update( 1, 1, n, Index[ u ] );
        Temp = Query( 1, 1, n, Index[ Top[ u ] ], Dfn[ Top[ u ] ] );
        u = Father[ Top[ u ] ];
    }
    return;
}
posted @ 2019-09-21 10:45 chy_2003 阅读(...) 评论(...) 编辑 收藏