【LG3248】[HNOI2016]树

【LG3248】[HNOI2016]树

题面

洛谷

题解

因为每次你加入的点是原树上某一棵子树

那么我们一次加入一个点，代表一棵子树加到大树下面

那么我们要找到一个点在一个大点中用主席树在\(dfs\)序中\(kth\)即可

询问的话，先将所有的点权(深度)转化为边权

查询时先将两点跳到它所在大点的根

再倍增跳到大点1(原树)的下面，再在原树上倍增跳一跳即可。

虽然说起来容易，但是其实还是很码的qaq。

代码

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <algorithm>
using namespace std; 

template<typename T>
inline void read(T &data) {
    data = 0; T w = 1;
    char ch = getchar();
    while (ch != '-' && (!isdigit(ch))) ch = getchar();
    if (ch == '-') w = -1, ch = getchar();
    while (isdigit(ch)) data = data * 10 + (ch ^ 48), ch = getchar();
    data *= w;
}
typedef long long ll;
const int MAX_N = 1e5 + 5;
int N, M, Q, lg[MAX_N];
namespace Ptree {
	struct Node { int ls, rs, v; } t[MAX_N * 20];
	int root[MAX_N], tot;
	void build(int &o, int l = 1, int r = N) {
		o = ++tot;
		if (l == r) return ;
		int mid = (l + r) >> 1;
		build(t[o].ls, l, mid);
		build(t[o].rs, mid + 1, r);
	}
	void insert(int &o, int p, int v, int l = 1, int r = N) {
		o = ++tot, t[o] = t[p];
		t[o].v++;
		if (l == r) return ;
		int mid = (l + r) >> 1;
		if (v <= mid) insert(t[o].ls, t[p].ls, v, l, mid);
		else insert(t[o].rs, t[p].rs, v, mid + 1, r);
	}
	int query(int x, int y, int k, int l = 1, int r = N) {
		if (l == r) return l;
		int mid = (l + r) >> 1, s = t[t[y].ls].v - t[t[x].ls].v;
		if (k <= s) return query(t[x].ls, t[y].ls, k, l, mid);
		else return query(t[x].rs, t[y].rs, k - s, mid + 1, r);
	}
}
namespace Template {
	int fa[20][MAX_N], dep[MAX_N], pos[MAX_N], R[MAX_N], cnt, L[MAX_N];
	struct Graph { int next, to; } e[MAX_N << 1]; int fir[MAX_N], e_cnt;
	void clearGraph() { memset(fir, -1, sizeof(fir)); e_cnt = 0; }
	void Add_Edge(int u, int v) { e[e_cnt] = (Graph){fir[u], v}; fir[u] = e_cnt++; }
	void dfs(int x, int f) {
		L[pos[x] = ++cnt] = x;
		fa[0][x] = f;
		dep[x] = dep[f] + 1;
		for (int i = 1; i < 20; i++) fa[i][x] = fa[i - 1][fa[i - 1][x]];
		for (int i = fir[x]; ~i; i = e[i].next) if (e[i].to != f) dfs(e[i].to, x);
		R[x] = cnt;
	} 

	int Dis(int x, int y) {
		if (dep[x] < dep[y]) swap(x, y);
		int res = dep[x] - dep[y];
		for (int i = 20 - 1; ~i; i--)
			if (dep[fa[i][x]] >= dep[y]) x = fa[i][x];
		if (x == y) return res;
		for (int i = 20 - 1; ~i; i--)
			if (fa[i][x] != fa[i][y])
				res += 1 << (i + 1), x = fa[i][x], y = fa[i][y];
		return res + 2;
	}
}

namespace BigTree {
	int N, fa[20][MAX_N], dep[MAX_N], pre[MAX_N];
	ll dis[20][MAX_N], pos[MAX_N], R[MAX_N], cur, link[MAX_N];
	int getRoot(ll x) {
		int l = 1, r = N;
		while (l <= r) {
			int mid = (l + r) >> 1;
			if (pos[mid] <= x) l = mid + 1;
			else r = mid - 1;
		}
		return r;
	} 

	int getPre(ll x) {
		int rt = getRoot(x);
		return Ptree::query(Ptree::root[Template::pos[pre[rt]] - 1], Ptree::root[Template::R[pre[rt]]],
							x - pos[rt] + 1);
	}

	void Init() {
		pos[1] = N = dep[1] = pre[1] = 1;
		cur = R[1] = ::N;
		int x; ll to;
		for (int i = 1; i <= M; i++) {
			read(x), read(to);
			int rt = getRoot(to);
			++N, dep[N] = dep[rt] + 1, link[N] = to, pre[N] = x;
			pos[N] = cur + 1, R[N] = cur + Template::R[x] - Template::pos[x] + 1;
			cur = R[N], fa[0][N] = rt;
			dis[0][N] = Template::dep[getPre(to)] - Template::dep[pre[rt]] + 1;
			for (int j = 1; j < 20; j++)
				fa[j][N] = fa[j - 1][fa[j - 1][N]], dis[j][N] = dis[j - 1][N] + dis[j - 1][fa[j - 1][N]];
		}
	}

	ll Dis(ll x, ll y) {
		ll ans = 0;
		int fx = getRoot(x), fy = getRoot(y);
		if (fx == fy) return Template::Dis(getPre(x), getPre(y));
		if (dep[fx] < dep[fy]) swap(x, y), swap(fx, fy);
		ans += Template::dep[getPre(x)] - Template::dep[pre[fx]], x = fx;
		for (int i = 20 - 1; ~i; i--)
			if (dep[fa[i][x]] > dep[fy]) ans += dis[i][x], x = fa[i][x];
		if (getRoot(link[x]) == fy)
			return ans + 1 + Template::Dis(getPre(link[x]), getPre(y));
		ans += Template::dep[getPre(y)] - Template::dep[pre[fy]], y = fy;
		if (dep[x] > dep[y]) ans += dis[0][x], x = fa[0][x];
		for (int i = 20 - 1; ~i; i--)
			if (fa[i][x] != fa[i][y]) ans += dis[i][x] + dis[i][y], x = fa[i][x], y = fa[i][y];
		x = link[x], y = link[y];
		ans += 2;
		return ans + Template::Dis(getPre(x), getPre(y));
	}
}

int main() {
#ifndef ONLINE_JUDGE
	freopen("cpp.in", "r", stdin);
#endif
    read(N), read(M), read(Q);
    for (int i = 2; i <= N; i++) lg[i] = lg[i >> 1] + 1;
	Template::clearGraph();
    for (int i = 1, a, b; i < N; i++)
        read(a), read(b), Template::Add_Edge(a, b), Template::Add_Edge(b, a);
    Template::dfs(1, 0);
    Ptree::build(Ptree::root[0]);
    for (int i = 1; i <= N; i++) Ptree::insert(Ptree::root[i], Ptree::root[i - 1], Template::L[i]);
    BigTree::Init();
    ll x, y;
    while (Q--) read(x), read(y), printf("%lld\n", BigTree::Dis(x, y));
    return 0;
}