3991: [SDOI2015]寻宝游戏

3991: [SDOI2015]寻宝游戏

https://www.lydsy.com/JudgeOnline/problem.php?id=3991

分析：

　　虚树+set。

　　要求树上许多点之间的路径的总长的2倍。就是虚树。

　　结论：如果将所有的点按dfs序拍好，答案就是相邻点之间的路径长度的和*2。所以这个可以按dfn维护一个set，每次操作查找前驱后继。

代码：

 #include<cstdio>
 #include<algorithm>
 #include<cstring>
 #include<cmath>
 #include<iostream>
 #include<cctype>
 #include<set>
 #include<vector>
 #include<queue>
 #include<map>
 using namespace std;
 typedef long long LL;

 inline int read() {
     int x=,f=;char ch=getchar();for(;!isdigit(ch);ch=getchar())if(ch=='-')f=-;
     for(;isdigit(ch);ch=getchar())x=x*+ch-'';return x*f;
 }

 const int INF = 1e9;
 const int N = ;

 int head[N], nxt[N << ], to[N << ], len[N << ], En;
 int deth[N], bel[N], siz[N], son[N], fa[N], id[N], dfn[N], TimeIndex;
 LL dis[N];
 bool vis[N];
 LL tmp, Ans;
 set<int> s;
 set<int> :: iterator it;

 void add_edge(int u,int v,int w) {
     ++En; to[En] = v; len[En] = w; nxt[En] = head[u]; head[u] = En;
     ++En; to[En] = u; len[En] = w; nxt[En] = head[v]; head[v] = En;
 }

 void dfs1(int u) {
     deth[u] = deth[fa[u]] + ;
     for (int i=head[u]; i; i=nxt[i]) {
         int v = to[i];
         if (v == fa[u]) continue;
         dis[v] = dis[u] + len[i];
         fa[v] = u;
         dfs1(v);
         siz[u] += siz[v];
         if (!son[u] || siz[son[u]] < siz[v]) son[u] = v;
     }
 }

 void dfs2(int u,int top) {
     bel[u] = top;
     dfn[u] = ++TimeIndex; id[TimeIndex] = u;
     if (!son[u]) return ;
     dfs2(son[u], top);
     for (int i=head[u]; i; i=nxt[i]) {
         int v = to[i];
         if (v != fa[u] && v != son[u]) dfs2(v, v);
     }
 }

 int LCA(int u,int v) {
     while (bel[u] != bel[v]) {
         if (deth[bel[u]] < deth[bel[v]]) swap(u, v);
         u = fa[bel[u]];
     }
     return deth[u] < deth[v] ? u : v;
 }

 LL getdis(int x,int y) {
     int lca = LCA(x, y);
     return dis[x] + dis[y] - (dis[lca] * );
 }

 void ins(int x) {
     int L = *(--s.lower_bound(dfn[x]));
     int R = *(s.upper_bound(dfn[x]));
     if (L != -INF) Ans += getdis(id[L], x);
     if (R != INF) Ans += getdis(id[R], x);
     if (L != -INF && R != INF) Ans -= getdis(id[L], id[R]);
     s.insert(dfn[x]); vis[x] = ;
 }

 void del(int x) {
     s.erase(dfn[x]); vis[x] = ;
     int L = *(--s.lower_bound(dfn[x]));
     int R = *(s.upper_bound(dfn[x]));
     if (L != -INF) Ans -= getdis(id[L], x);
     if (R != INF) Ans -= getdis(id[R], x);
     if (L != -INF && R != INF) Ans += getdis(id[L], id[R]);
 }

 int main() {
     int n = read(), Q = read();
     for (int i=; i<n; ++i) {
         int u = read(), v = read(), w = read();
         add_edge(u, v, w);
     }
     dfs1();
     dfs2(, );

     s.insert(-INF), s.insert(INF);

     while (Q--) {
         tmp = ;
         int x = read();
         if (!vis[x]) ins(x);
         else del(x);
         if (s.size() > ) {
             it = s.begin();
             int L = *(++it);
             it = s.end();
             int R = *(--(--it));
             tmp = getdis(id[L], id[R]);
         }
         printf("%lld\n",Ans + tmp);
     }
     return ;
 }