Split The Tree

Problem E. Split The Tree

Time Limit: 7000/4000 MS (Java/Others)    Memory Limit: 262144/262144 K (Java/Others)
Total Submission(s): 409    Accepted Submission(s): 109

Problem Description

You are given a tree with n vertices, numbered from 1 to n. ith vertex has a value wi
We define the weight of a tree as the number of different vertex value in the tree.
If we delete one edge in the tree, the tree will split into two trees. The score is the sum of these two trees’ weights.
We want the know the maximal score we can get if we delete the edge optimally

 

Input

Input is given from Standard Input in the following format:
n
p2 p3 . . . pn
w1 w2 . . . wn
Constraints
2 ≤ n ≤ 100000
1 ≤ pi < i
1 ≤ wi ≤ 100000(1 ≤ i ≤ n), and they are integers
pi means there is a edge between pi and i

 

Output

Print one number denotes the maximal score

 

Sample Input

3 1 1 1 2 2 3 1 1 1 1 1

 

Sample Output

3 2

 

Source

2018 东北地区大学生程序设计竞赛

 

#include <bits/stdc++.h>

using namespace std;
const int maxn = 6e5 + 10;
int n;
int val[maxn], dfn[maxn], l[maxn], r[maxn], tot, cnt, nx[maxn], to[maxn], c[maxn], vis[maxn];
vector<int> G[maxn];

struct node {
    int L, R, pos;

    bool operator<(const node &cur) const {
        if (L == cur.L)return R < cur.R;
        return L < cur.L;
    }

} o[maxn];

inline void dfs(int cur, int f) {
    l[cur] = ++tot;
    dfn[tot] = val[cur];
    for (register int i = 0; i < G[cur].size(); ++i) {
        int to = G[cur][i];
        if (to == f)continue;
        dfs(to, cur);
    }
    r[cur] = tot;
}

inline int lowbit(int x) {
    return x & (-x);
}

inline void update(int pos, int val) {
    while (pos <= n) {
        c[pos] += val;
        pos += lowbit(pos);
    }
}

inline int query(int pos) {
    int res = 0;
    while (pos) {
        res += c[pos];
        pos -= lowbit(pos);
    }
    return res;
}

int q[maxn];

int main() {
#ifndef ONLINE_JUDGE
    freopen("1.txt", "r", stdin);
#endif
    while (scanf("%d", &n) != EOF) {
        tot = 0;
        memset(q, 0, sizeof(q));
        for (register int i = 1; i <= n; ++i) {
            G[i].clear();
        }
        for (register int i = 2, pi; i <= n; ++i) {
            scanf("%d", &pi);
            G[pi].emplace_back(i);
            G[i].emplace_back(pi);
        }
        int mx = -1;
        for (register int i = 1; i <= n; ++i) {
            scanf("%d", &val[i]);
            mx = max(mx, val[i]);
        }
        dfs(1, -1);
        cnt = 0;
        for (register int i = 0; i <= mx; ++i) {
            to[i] = 2 * n + 1;
            vis[i] = 0;
        }
        for (register int i = 1; i <= n; ++i) {
            dfn[i + n] = dfn[i];
            o[++cnt] = node{l[i], r[i], i};
            o[++cnt] = node{r[i] + 1, l[i] - 1 + n, i};
        }
        sort(o + 1, o + 1 + cnt);
        n *= 2;

        for (register int i = n; i >= 1; --i) {
            nx[i] = to[dfn[i]];
            to[dfn[i]] = i;
            c[i] = 0;
        }
        for (register int i = 1; i <= n; ++i) {
            if (!vis[dfn[i]]) {
                vis[dfn[i]] = 1;
                update(i, 1);
            }
        }
        int Left = 1, res = 0;
        for (register int i = 1; i <= cnt; ++i) {
            while (Left < o[i].L) {
                if (nx[Left] <= n)update(nx[Left], 1);
                ++Left;
            }
            q[o[i].pos] += query(o[i].R) - query(o[i].L - 1);
            res = max(res, q[o[i].pos]);
        }
        printf("%d
", res);
    }
    return 0;
}