bzoj2791 Rendevous

花了差不多兩個鍾才AC這道題，所以寫了下題解

這道題很明顯，是求在基環樹上求lca。

對於基環樹的題，我們都是先將環去掉，然後在去掉環以後每一棵樹上面搜索一次，查詢的時候再將環插進去就好了。

特別地，要注意題目的限定條件。

參考代碼

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
template<typename T>inline void read(T &x) {
	x = 0; int f = 0; char s = getchar();
	while (!isdigit(s)) f |= s=='-', s = getchar();
	while ( isdigit(s)) x = (x<<3) + (x<<1) + (s-48), s = getchar();
	x = f ? -x : x;
}
int ss, buf[31];
template<typename T>inline void print(T x) {
	if (x < 0) x = -x, putchar('-');
	do { buf[++ss] = int(x%10); x /= 10; }while(x);
	while (ss) putchar(buf[ss--]+'0');
}
template<typename T>inline void write(T x) { print(x); putchar(' '); }
template<typename T>inline void writeln(T x) { print(x); puts(""); }
const int N = 5e5 + 10;
int n, q;
bool vis[N], bk[N];
int d[N], fa[N][23];
int tp, sta[N];
int cnt, id[N], ys[N], size[N];
//cnt環的個數，id所在環的編號，ys環上節點的編號，size[環編號]=該環節點數 
void Dfs(int u) {
	vis[u] = bk[u] = 1; sta[++tp] = u;
	int v = fa[u][0];
	if (bk[v]) {
		int j = tp, z = 0; cnt++;
		while(sta[j] != v) {
			id[sta[j]] = cnt;
			ys[sta[j]] = ++z;
			j--;
		}
		id[sta[j]] = cnt;
		ys[sta[j]] = ++z;
		size[cnt] = z;
	}
	if (!vis[v] && !bk[v]) Dfs(v);
	bk[u] = 0; sta[tp--] = 0;
}
int anc[N];
void Dfs2(int u) {
	bk[u] = 1;
	if (id[u]) {
		anc[u] = u;
		d[u] = 0;
		fa[u][0] = 0;
		return;
	}
	if (!bk[fa[u][0]]) Dfs2(fa[u][0]);
	anc[u] = anc[fa[u][0]];
	d[u] = d[fa[u][0]] + 1;
	for (int i = 1; i <= 20; i++)
		fa[u][i] = fa[fa[u][i-1]][i-1];
}
int Lca(int x, int y) {
	if (d[x] < d[y]) swap(x, y);
	for (int i = 20; i >= 0; i--)
		if (d[x] - d[y] >= (1<<i))
			x = fa[x][i];
	if (x == y) return x;
	for (int i = 20; i >= 0; i--)
		if (fa[x][i] != fa[y][i])
			x = fa[x][i], y = fa[y][i];
	return fa[x][0];
}
int main() {
	cin >> n >> q;
	for (int u = 1, v; u <= n; u++) 
		read(v), fa[u][0] = v;
	for (int i = 1; i <= n; i++)
		if (!vis[i]) Dfs(i);
	for (int i = 1; i <= n; i++) Dfs2(i);
	int x, y, s1, s2, p1, p2, ans1, ans2;
	while (q--) {
		read(x), read(y);
		if (id[anc[x]] != id[anc[y]]) puts("-1 -1");
		else if (anc[x] == anc[y]) {
			int lca = Lca(x,y);
			s1 = d[x] - d[lca], s2 = d[y] - d[lca];
			write(s1); writeln(s2);
		}
		else {
			s1 = d[x], s2 = d[y];
			x = anc[x], y = anc[y];
			bool bk = 0;
			if (ys[x] < ys[y]) swap(x, y), swap(s1, s2), bk = 1;
			p1 = ys[x] - ys[y] , p2 = size[id[y]] - p1;
			if (bk) swap(p1, p2), swap(s1, s2);
			if (max(s1+p1,s2) > max(s1,s2+p2)) 
				ans1 = s1, ans2 = s2+p2;
			else if(max(s1+p1,s2) == max(s1,s2+p2)) {
				if (min(s1+p1,s2) < min(s1,s2+p2))
					ans1 = s1+p1, ans2 = s2;
				else if (min(s1+p1,s2) == min(s1,s2+p2)){
					if (s1 + p1 >= s2) ans1 = s1+p1, ans2 = s2;
					else ans1 = s1, ans2 = s2+p2;
				}
				else 
					ans1 = s1, ans2 = s2+p2;
			}
			else
				ans1 = s1+p1, ans2 = s2;
			write(ans1), writeln(ans2);
		}
	}
	return 0;
}