CF165D Beard Graph（dfs序+树状数组）

题面

题解

乍一看，单点修改，单链查询，用树链剖分维护每条链上白边的数量就完了，

还是……得写树链剖分吗？……3e5，乘两个log会T吗……

（双手颤抖）

（纠结）

不！绝不写树链剖分！

这题如果能维护每个点到根节点路径上的白边数量，就可以用lca直接算，怎么维护呢

把点按dfs序排序，每个点存它到根节点路径上白边数量，当边的颜色变化时，就把以该边下端点为根的子树内的值整体加一或减一，也就是在按dfs序排序后的序列上做区间修改，然后单点查询

把单点修改、区间查询变成区间修改、单点查询了耶！

然后也可以不用线段树，用差分树状数组，三行解决

把区间修改、单点查询又变成单点修改、区间查询了耶！（滑稽

CODE

#include<cstdio>
#include<cstring>
#include<iostream>
#include<cmath>
#include<queue>
#include<stack>
#include<map>
#include<vector>
#include<algorithm>
#define MAXN 300005
#define MAXM 300005
#define ENDL putchar('\n')
#define LL long long
#define DB double
#define lowbit(x) ((-x)&(x))
//#define int LL
//#pragma GCC optimize(2)
using namespace std;
inline LL read() {
	LL f = 1,x = 0;char s = getchar();
	while(s < '0' || s > '9') {if(s == '-')f = -1;s = getchar();}
	while(s >= '0' && s <= '9') {x = x * 10 + (s - '0');s = getchar();}
	return x * f;
}
const int jzm = 1000000007;
int n,m,i,j,s,o,k;
int u[MAXN],v[MAXN],cl[MAXN];
struct it{
	int v,w;
	it(){v = w = 0;}
	it(int V,int W){v = V;w = W;}
};
vector<int> g[MAXN];
int d[MAXN],dfn[MAXN],rr[MAXN],cnt;
int f[MAXN][20];
int c[MAXN];
void addt(int x,int y) {while(x<=n) c[x] += y,x += lowbit(x);}
int sum(int x) {int as=0;while(x>0) as += c[x],x -= lowbit(x);return as;}
void dfs(int x,int fa) {
	d[x] = d[fa] + 1;
	dfn[x] = ++ cnt;
	f[x][0] = fa;
	for(int i = 1;i <= 18;i ++) f[x][i] = f[f[x][i-1]][i-1];
	for(int i = 0;i < g[x].size();i ++) {
		if(g[x][i] != fa) {
			dfs(g[x][i],x);
		}
	}
	rr[x] = cnt;
	return ;
}
int lca(int a,int b) {
	if(d[b] > d[a]) swap(a,b);
	if(d[a] > d[b]) {
		for(int i = 18;i >= 0;i --) {
			if(d[f[a][i]] >= d[b]) {
				a = f[a][i];
			}
		}
	}
	if(a == b) return a;
	for(int i = 18;i >= 0;i --) {
		if(f[a][i] != f[b][i]) {
			a = f[a][i],b = f[b][i];
		}
	}
	return f[a][0];
}
int main() {
	n = read();
	for(int i = 1;i < n;i ++) {
		s = u[i] = read();
		o = v[i] = read();
		g[s].push_back(o);
		g[o].push_back(s);
	}
	dfs(1,1);
	m = read();
	for(int i = 1;i <= m;i ++) {
		k = read();
		if(k == 1) {
			s = read();
			int p = (d[u[s]] > d[v[s]] ? u[s] : v[s]);
			if(cl[s]) addt(dfn[p],-1),addt(rr[p]+1,1),cl[s] = 0;
		}
		else if(k == 2) {
			s = read();
			int p = (d[u[s]] > d[v[s]] ? u[s] : v[s]);
			if(!cl[s]) addt(dfn[p],1),addt(rr[p]+1,-1),cl[s] = 1;
		}
		else {
			s = read();o = read();
			int lc = lca(s,o);
			if(sum(dfn[s]) + sum(dfn[o]) - 2*sum(dfn[lc])) {
				printf("-1\n");
			}
			else printf("%d\n",d[s] + d[o] - d[lc] * 2);
		}
	}
	return 0;
}