BZOJ3351: [ioi2009]Regions(根号分治)

2019-03-05 10:36:15 浏览数 (1)

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(qsqrt{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(nsqrt{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~

代码语言:javascript复制
#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("%dn", ans[i]);
    return 0;
}

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