luogu 3248
直接向原树加子树是不可能的
考虑重新建立这样一颗树，我们称之为 S 树
将每次需要添加的子树看做一个点，称之为 S 点
新建的树就是由这些点构成的，
那么树的大小是合理的
初始节点为整棵原树
由于添加的子树的节点的编号一定是连续的一段区间
树上的每个节点维护 l, r, rt
分别表示 左端点， 右端点， 这棵子树的根在原树上的编号
定义
宏观树：只有 S 点构成的树 -> S 树
微观树：按照题目描述所形成的树，当然这棵树是不会建立出来的
所有的询问操作都需要微观树的信息
首先考虑对于任意合法的点 B， 如何找出它在原树上的对应点 b， 显然 b 的值域为 [1, n]
S 点满足 l, r 单调
因此首先二分出 B 点在那个 S 点中，
S 点代表的子树的编号是 [S.l, S.r]
所以 B 在该子树中的编号的大小次序为第 B - S.l + 1;
查询区间 k 大 => 主席树
这样的话只需对原树建立主席树
查询以 S.rt 为根的子树中编号第 B - S.l + 1 小的编号就是 b
Link_super 函数是核心
然后考虑查询时所要维护的东西
由于查询树上点对之间的距离，所以只需知道深度就可以解决
维护这么 3 种深度
deep[] 原树的深度
Super_dep[] S 树的深度（宏观树）
Big_deep[] 微观树的深度，当然并不去维护所有存在的点的深度
Big_deep[] 相当于是维护的宏观树，只不过所有 S 点的 Big_deep[] 都是微观树上 S 的真实深度值
这里可以这样理解:
若 Link_super(u, v), u 的值域 [1, n]，
查询的 v 所在 S 树的 S 点的编号为 X；
S 的当前总数 + 1 为 Y;
这样的话 Big_deep[y] = Big_deep[x] + Dis(v, X.rt);
Dis 函数为查询原树上两点之间的距离
查询时分类讨论
#include <iostream> #include <cstdio> #include <algorithm> #include <cmath> #include <cstring> #include <string> using namespace std; #define LL long long #define gc getchar() inline int read() {int x = 0; char c = gc; while(c < '0' || c > '9') c = gc; while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = gc; return x;} inline LL read_LL() {LL x = 0; char c = gc; while(c < '0' || c > '9') c = gc; while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = gc; return x;} #undef gc const int N = 5e5 + 10; int n, m, q; int head[N], cnt; LL deep[N]; int Super_node; LL total; struct Node {int u, v, nxt;} G[N << 1]; inline void Link(int u, int v) { G[++ cnt].v = v, G[cnt].nxt = head[u], head[u] = cnt; } int Hjtjs; struct NOde { int fa[N], size[N], topp[N], tree[N], lst[N], rst[N], tree_js, son[N], bef[N]; int Lson[N << 2], Rson[N << 2], Size[N << 2], Root[N]; void Dfs_1(int u, int F_, int depth) { deep[u] = depth, fa[u] = F_, size[u] = 1; for(int i = head[u]; ~ i; i = G[i].nxt) { if(G[i].v == F_) continue; Dfs_1(G[i].v, u, depth + 1); size[u] += size[G[i].v]; if(size[G[i].v] > size[son[u]]) son[u] = G[i].v; } } void Dfs_2(int u, int tp) { topp[u] = tp, tree[u] = ++ tree_js, lst[u] = tree[u], bef[tree_js] = u; if(!son[u]) {rst[u] = tree[u]; return ;} Dfs_2(son[u], tp); for(int i = head[u]; ~ i; i = G[i].nxt) {if(G[i].v != fa[u] && G[i].v != son[u]) Dfs_2(G[i].v, G[i].v);} rst[u] = tree_js; } void Fill(int x, int y) {Lson[x] = Lson[y], Rson[x] = Rson[y], Size[x] = Size[y];} void Insert(int &rt, int l, int r, int x) { Fill(++ Hjtjs, rt); rt = Hjtjs; Size[rt] ++; if(l == r) return ; int mid = (l + r) >> 1; if(x <= mid) Insert(Lson[rt], l, mid, x); else Insert(Rson[rt], mid + 1, r, x); } void Build_tree() { Dfs_1(1, 0, 1); Dfs_2(1, 1); for(int i = 1; i <= n; i ++) {Root[i] = Root[i - 1]; Insert(Root[i], 1, n, bef[i]);} } inline int Lca(int x, int y) { int tpx = topp[x], tpy = topp[y]; while(tpx != tpy) { if(deep[tpx] < deep[tpy]) swap(x, y), swap(tpx, tpy); x = fa[tpx], tpx = topp[x]; } return deep[x] < deep[y] ? x : y; } inline int Dis(int x, int y) {int lca = Lca(x, y); return deep[x] + deep[y] - 2 * deep[lca];} int Sec_A(int ljd, int rjd, int l, int r, int k) { if(l == r) return l; int mid = (l + r) >> 1; int imp = Size[Lson[rjd]] - Size[Lson[ljd]]; if(k <= (Size[Lson[rjd]] - Size[Lson[ljd]])) return Sec_A(Lson[ljd], Lson[rjd], l, mid, k); else return Sec_A(Rson[ljd], Rson[rjd], mid + 1, r, k - (Size[Lson[rjd]] - Size[Lson[ljd]])); } } Tree; struct Node_ { #define E exit(0) struct Node_3 {LL l, r; int rt;} Super_graph[N]; struct Pair { // yvan shu zhong de bian hao, fei shu shang int Bef_number; // chao ji shu de dian de gen , shi yvan shu shang de dian de bian hao int Super_rt; // chao ji shu de dian de bian hao int Super_number; }; int Super_dep[N]; LL Big_deep[N]; int f[N][25]; int fa[N]; Pair Get_information(LL x) { int l = 1, r = Super_node, ans; while(l <= r) { int mid = (l + r) >> 1; if(x <= Super_graph[mid].r) ans = mid, r = mid - 1; else l = mid + 1; } int nottree = Super_graph[ans].rt; int imp = Tree.Sec_A(Tree.Root[Tree.lst[nottree] - 1], Tree.Root[Tree.rst[nottree]], 1, n, x - Super_graph[ans].l + 1); return (Pair) {imp, nottree, ans}; } void Link_Super(LL u, LL v) { Super_node ++; Pair Nodev = Get_information(v); Super_graph[Super_node].l = total + 1, Super_graph[Super_node].r = total + Tree.size[u], Super_graph[Super_node].rt = u; total += Tree.size[u]; Super_dep[Super_node] = Super_dep[Nodev.Super_number] + 1; int a = Nodev.Super_rt, b = Nodev.Bef_number; Big_deep[Super_node] = Big_deep[Nodev.Super_number] + Tree.Dis(b, a) + 1; f[Super_node][0] = Nodev.Super_number; fa[Super_node] = Nodev.Bef_number; for(int i = 1; i <= 16; i ++) f[Super_node][i] = f[f[Super_node][i - 1]][i - 1]; } int Lca(int x, int y) { if(Super_dep[x] < Super_dep[y]) swap(x, y); int del = Super_dep[x] - Super_dep[y]; for(int i = 0; i <= 18; i ++) if((1 << i) & del) x = f[x][i]; if(x == y) return x; for(int i = 18; i >= 0; i --) if(f[x][i] != f[y][i]) x = f[x][i], y = f[y][i]; return f[x][0]; } LL Ask(LL x, LL y) { Pair Nodex = Get_information(x), Nodey = Get_information(y); if(Super_dep[Nodex.Super_number] <= Super_dep[Nodey.Super_number]) swap(Nodex, Nodey); if(Nodex.Super_number == Nodey.Super_number) return Tree.Dis(Nodex.Bef_number, Nodey.Bef_number); else { int lca = Lca(Nodex.Super_number, Nodey.Super_number); LL ret; if(lca == Nodey.Super_number) { int g = Nodex.Super_number; for(int i = 18; i >= 0; i --) if(f[g][i] && Super_dep[f[g][i]] > Super_dep[lca]) g = f[g][i]; ret = Big_deep[Nodex.Super_number] - Big_deep[g] + 1 + Tree.Dis(Nodex.Super_rt, Nodex.Bef_number); ret += Tree.Dis(fa[g], Nodey.Bef_number); } else { int a = Nodex.Super_number, b = Nodey.Super_number; for(int i = 18; i >= 0; i --) {if(f[a][i] && Super_dep[f[a][i]] > Super_dep[lca]) a = f[a][i];} for(int i = 18; i >= 0; i --) {if(f[b][i] && Super_dep[f[b][i]] > Super_dep[lca]) b = f[b][i];} ret = Big_deep[Nodex.Super_number] - Big_deep[a] + 1 + Big_deep[Nodey.Super_number] - Big_deep[b] + 1 + Tree.Dis(fa[a], fa[b]); ret += Tree.Dis(Nodex.Super_rt, Nodex.Bef_number) + Tree.Dis(Nodey.Super_rt, Nodey.Bef_number); } return ret; } } #undef E } S_graph; int main() { n = read(), m = read(), q = read(); for(int i = 1; i <= n; i ++) head[i] = -1; for(int i = 1; i < n; i ++) {int u = read(), v = read(); Link(u, v), Link(v, u);} Tree.Build_tree(); total = n, Super_node = 1; S_graph.Super_dep[1] = 1; S_graph.f[1][0] = 1; S_graph.Super_graph[1].l = 1, S_graph.Super_graph[1].r = n, S_graph.Super_graph[1].rt = 1; for(int i = 1; i <= m; i ++) { LL x = read_LL(), y = read_LL(); S_graph.Link_Super(x, y); } for(int i = 1; i <= q; i ++) { LL x = read_LL(), y = read_LL(); cout << S_graph.Ask(x, y) << "\n"; } return 0; }
