bzoj 4034

我写的是 DFS序+线段树

DFS序（出去的位置要单独建点）上，进入的位置是权值，出去的位置是权值的相反数，可以证明节点i到根节点的路径上的点的权值和是DFS序上1～in[i]的和。

只要搞出每个区间的进入位置和出去位置的和，就可以打标记了。

 /**************************************************************
     Problem: 4034
     User: idy002
     Language: C++
     Result: Accepted
     Time:2748 ms
     Memory:26616 kb
 ****************************************************************/

 #include <cstdio>
 #include <cstdlib>
 #define fprintf(...)
 #define N 100010 

 typedef long long dnt;
 struct Node {
     dnt s, tag;
     int tc[];
     Node *ls, *rs;
 }pool[N*], *tail=pool, *root; 

 int n, m;
 int head[N], dest[N+N], next[N+N], etot;
 int in[N], out[N], type[N+N], ww[N], sww[N+N], idc;
 bool vis[N]; 

 Node *build( int lf, int rg ) {
     Node *nd = ++tail;
     if( lf==rg ) {
         nd->s = sww[lf];
         nd->tc[type[lf]]=;
         nd->tc[type[lf]^]=;
         return nd;
     }
     int mid=(lf+rg)>>;
     nd->ls = build( lf, mid );
     nd->rs = build( mid+, rg );
     nd->tc[] = nd->ls->tc[] + nd->rs->tc[];
     nd->tc[] = nd->ls->tc[] + nd->rs->tc[];
     nd->s = nd->ls->s + nd->rs->s;
     fprintf( stderr, "[%d,%d] tc[0]=%d tc[1]=%d\n", lf, rg, nd->tc[], nd->tc[] );
     return nd;
 }
 inline void pushdown( Node *nd ) {
     if( nd->tag ) {
         nd->ls->s += nd->ls->tc[]*nd->tag - nd->ls->tc[]*nd->tag;
         nd->rs->s += nd->rs->tc[]*nd->tag - nd->rs->tc[]*nd->tag;
         nd->ls->tag += nd->tag;
         nd->rs->tag += nd->tag;
         nd->tag = ;
     }
 }
 inline void update( Node *nd ) {
     nd->s = nd->ls->s + nd->rs->s;
 }
 void modify( Node *nd, int lf, int rg, int L, int R, dnt delta ) {
     if( L<=lf && rg<=R ) {
         nd->s += nd->tc[]*delta - nd->tc[]*delta;
         nd->tag += delta;
         return;
     }
     int mid=(lf+rg)>>;
     pushdown(nd);
     if( L<=mid ) modify( nd->ls, lf, mid, L, R, delta );
     if( R>mid ) modify( nd->rs, mid+, rg, L, R, delta );
     update( nd );
 }
 dnt query( Node *nd, int lf, int rg, int L, int R ) {
     if( L<=lf && rg<=R ) {
         fprintf( stderr, "( %d %d ) = %lld\n", lf, rg, nd->s );
         return nd->s;
     }
     int mid=(lf+rg)>>;
     pushdown(nd);
     dnt rt = ;
     if( L<=mid ) rt += query( nd->ls, lf, mid, L, R );
     if( R>mid ) rt += query( nd->rs, mid+, rg, L, R );
     update(nd);
     return rt;
 }
 void adde( int u, int v ) {
     etot++;
     next[etot] = head[u];
     dest[etot] = v;
     head[u] = etot;
 }
 void dfs( int u, int fa ) {
     if( vis[u] ) {
         exit();
         return;
     }
     vis[u] = true;
     idc++;
     in[u] = idc;
     type[idc] = ;
     sww[idc] = ww[u];
     for( int t=head[u]; t; t=next[t] ) {
         int v=dest[t];
         if( v==fa ) continue;
         dfs(v,u);
     }
     idc++;
     out[u] = idc;
     type[idc] = ;
     sww[idc] = -ww[u];
 }
 void mdf_sig( int u, int a ) {
     modify( root, , idc, in[u], in[u], +a );
     modify( root, , idc, out[u], out[u], +a );
     fprintf( stderr, "modify( %d %d %d )\n", in[u], in[u], +a );
     fprintf( stderr, "modify( %d %d %d )\n", out[u], out[u], +a );
 }
 void mdf_sub( int u, int a ) {
     modify( root, , idc, in[u], out[u], +a );
     fprintf( stderr, "modify( %d %d %d )\n", in[u], out[u], +a );
 }
 dnt query( int u ) {
     dnt rt = query( root, , idc, , in[u] );
     fprintf( stderr, "query( %d %d ) = %lld\n", , in[u], rt );
     return rt;
 }
 int main() {
     scanf( "%d%d", &n, &m );
     for( int i=; i<=n; i++ )
         scanf( "%d", ww+i );
     for( int i=,u,v; i<n; i++ ) {
         scanf( "%d%d", &u, &v );
         adde( u, v );
         adde( v, u );
     }
     fprintf( stderr, "dfs(...)\n" );
     dfs(,);
     fprintf( stderr, "\n" );
     fprintf( stderr, "build(...)\n" );
     root = build( , idc );
     for( int t=; t<m; t++ ) {
         int opt, u, a;
         scanf( "%d", &opt );
         fprintf( stderr, "%d\n", opt );
         if( opt== ) {
             scanf( "%d%d", &u, &a );
             mdf_sig( u, a );
         } else if( opt== ) {
             scanf( "%d%d", &u, &a );
             mdf_sub( u, a );
         } else {
             scanf( "%d", &u );
             printf( "%lld\n", query(u) );
         }
     }
 }
 

---

还有一种做法：链剖

以前一直以为链剖只能用于链修改和链查询。。。。

其实，链剖是一种特殊的DFS序，它合理地安排了DFS的顺序（先重儿子，再轻儿子），让我们可以把任意一条路径映射为O(logn)条连续的线段，然后就可以做很多问题了。

其次是和子树相关的问题，我们一般是把DFS序弄出来，然后一个子树就是连续的一段，这样实现子树相关的操作。

我们把两个结合起来就可以做到：链修改与查询+子树修改与查询。

（好像还有一种链剖解决子树问题的方法，就是每个节点再记录所有轻边代表的子树的信息）。

 #include <cstdio>
 #include <cstdlib>
 #define fprintf(...)
 #define N 100010 

 typedef long long dnt;
 struct Node {
     dnt s, tag;
     int tc[];
     Node *ls, *rs;
 }pool[N*], *tail=pool, *root; 

 int n, m;
 int head[N], dest[N+N], next[N+N], etot;
 int in[N], out[N], type[N+N], ww[N], sww[N+N], idc;
 bool vis[N]; 

 Node *build( int lf, int rg ) {
     Node *nd = ++tail;
     if( lf==rg ) {
         nd->s = sww[lf];
         nd->tc[type[lf]]=;
         nd->tc[type[lf]^]=;
         return nd;
     }
     int mid=(lf+rg)>>;
     nd->ls = build( lf, mid );
     nd->rs = build( mid+, rg );
     nd->tc[] = nd->ls->tc[] + nd->rs->tc[];
     nd->tc[] = nd->ls->tc[] + nd->rs->tc[];
     nd->s = nd->ls->s + nd->rs->s;
     fprintf( stderr, "[%d,%d] tc[0]=%d tc[1]=%d\n", lf, rg, nd->tc[], nd->tc[] );
     return nd;
 }
 inline void pushdown( Node *nd ) {
     if( nd->tag ) {
         nd->ls->s += nd->ls->tc[]*nd->tag - nd->ls->tc[]*nd->tag;
         nd->rs->s += nd->rs->tc[]*nd->tag - nd->rs->tc[]*nd->tag;
         nd->ls->tag += nd->tag;
         nd->rs->tag += nd->tag;
         nd->tag = ;
     }
 }
 inline void update( Node *nd ) {
     nd->s = nd->ls->s + nd->rs->s;
 }
 void modify( Node *nd, int lf, int rg, int L, int R, dnt delta ) {
     if( L<=lf && rg<=R ) {
         nd->s += nd->tc[]*delta - nd->tc[]*delta;
         nd->tag += delta;
         return;
     }
     int mid=(lf+rg)>>;
     pushdown(nd);
     if( L<=mid ) modify( nd->ls, lf, mid, L, R, delta );
     if( R>mid ) modify( nd->rs, mid+, rg, L, R, delta );
     update( nd );
 }
 dnt query( Node *nd, int lf, int rg, int L, int R ) {
     if( L<=lf && rg<=R ) {
         fprintf( stderr, "( %d %d ) = %lld\n", lf, rg, nd->s );
         return nd->s;
     }
     int mid=(lf+rg)>>;
     pushdown(nd);
     dnt rt = ;
     if( L<=mid ) rt += query( nd->ls, lf, mid, L, R );
     if( R>mid ) rt += query( nd->rs, mid+, rg, L, R );
     update(nd);
     return rt;
 }
 void adde( int u, int v ) {
     etot++;
     next[etot] = head[u];
     dest[etot] = v;
     head[u] = etot;
 }
 void dfs( int u, int fa ) {
     if( vis[u] ) {
         exit();
         return;
     }
     vis[u] = true;
     idc++;
     in[u] = idc;
     type[idc] = ;
     sww[idc] = ww[u];
     for( int t=head[u]; t; t=next[t] ) {
         int v=dest[t];
         if( v==fa ) continue;
         dfs(v,u);
     }
     idc++;
     out[u] = idc;
     type[idc] = ;
     sww[idc] = -ww[u];
 }
 void mdf_sig( int u, int a ) {
     modify( root, , idc, in[u], in[u], +a );
     modify( root, , idc, out[u], out[u], +a );
     fprintf( stderr, "modify( %d %d %d )\n", in[u], in[u], +a );
     fprintf( stderr, "modify( %d %d %d )\n", out[u], out[u], +a );
 }
 void mdf_sub( int u, int a ) {
     modify( root, , idc, in[u], out[u], +a );
     fprintf( stderr, "modify( %d %d %d )\n", in[u], out[u], +a );
 }
 dnt query( int u ) {
     dnt rt = query( root, , idc, , in[u] );
     fprintf( stderr, "query( %d %d ) = %lld\n", , in[u], rt );
     return rt;
 }
 int main() {
     scanf( "%d%d", &n, &m );
     for( int i=; i<=n; i++ )
         scanf( "%d", ww+i );
     for( int i=,u,v; i<n; i++ ) {
         scanf( "%d%d", &u, &v );
         adde( u, v );
         adde( v, u );
     }
     fprintf( stderr, "dfs(...)\n" );
     dfs(,);
     fprintf( stderr, "\n" );
     fprintf( stderr, "build(...)\n" );
     root = build( , idc );
     for( int t=; t<m; t++ ) {
         int opt, u, a;
         scanf( "%d", &opt );
         fprintf( stderr, "%d\n", opt );
         if( opt== ) {
             scanf( "%d%d", &u, &a );
             mdf_sig( u, a );
         } else if( opt== ) {
             scanf( "%d%d", &u, &a );
             mdf_sub( u, a );
         } else {
             scanf( "%d", &u );
             printf( "%lld\n", query(u) );
         }
     }
 }