BZOJ3351: [ioi2009]Regions(根号分治)

题意

题目链接

Sol

很神仙的题

我们考虑询问(a, b)(a是b的祖先)，直接对b根号分治

如果b的出现次数\(< \sqrt{n}\)，我们可以直接对每个b记录下与它有关的询问，这样每个询问至多扫\(\sqrt{n}\)个点即可知道答案，那么dfs的时候暴力统计答案即可，复杂度\(q\sqrt{n}\)

如果b的出现次数\(> \sqrt{n}\)，显然这样的b最多只有\(\sqrt{n}\)个，也就是说在询问中最多会有\(\sqrt{n}\)个这样的b，那么我们可以对每个a，暴力统计，复杂度\(n\sqrt{n}\)

然后用天天爱跑步那题的差分技巧搞一下就行了

代码十分好写~

#include<bits/stdc++.h>
#define Pair pair<int, int>
#define MP(x, y) make_pair(x, y)
#define fi first
#define se second
//#define int long long
#define LL long long
#define Fin(x) {freopen(#x".in","r",stdin);}
#define Fout(x) {freopen(#x".out","w",stdout);}
using namespace std;
const int MAXN = 1e6 + 10;
inline int read() {
    char c = getchar(); int x = 0, f = 1;
    while(c < '0' || c > '9') {if(c == '-') f = -1; c = getchar();}
    while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = getchar();
    return x * f;
}
int N, R, Q, base;
vector<int> v[MAXN];
vector<Pair> a1[MAXN], a2[MAXN];
int r[MAXN], fa[MAXN], ti[MAXN], ha[MAXN], ans[MAXN];
void dfs1(int x) {
	for(auto &a : a1[r[x]]) ans[a.se] += ha[a.fi]; ha[r[x]]++;
	for(auto &to : v[x]) dfs1(to); ha[r[x]]--;
}
void dfs2(int x) {
	for(auto &b: a2[r[x]]) ans[b.se] -= ha[b.fi];
	for(auto &to: v[x]) dfs2(to);
	for(auto &b: a2[r[x]]) ans[b.se] += ha[b.fi];
	ha[r[x]]++;
}
signed main() {
//	Fin(9); Fout(b);
	N = read(); R = read(); Q = read(); base = sqrt(N);
	r[1] = read(); ti[r[1]]++;
	for(int i = 2; i <= N; i++) {
		int f = read(); r[i] = read();
		v[f].push_back(i);
		ti[r[i]]++;
	}
	for(int i = 1; i <= Q; i++) {
		int a = read(), b = read();
		if(ti[b] < base) {
			a1[b].push_back({a, i});
		} else {
			a2[a].push_back({b, i});
		}
	}
	dfs1(1);
	memset(ha, 0, sizeof(ha));
	dfs2(1);
	for(int i = 1; i <= Q; i++) printf("%d\n", ans[i]);
    return 0;
}