CF1178G The Awesomest Vertex

题目上的式子很难维护，可以转换成 a_i = \sum\limits_{w\in R(i)}a_w，b_i = \left | \sum\limits_{w\in R(i)}b_w \right |，修改就变成了子树加。此时就能直接拍到序列上做。
定义 end_i=dfn_i+siz_i-1，我们要求的就是 \max\limits_{dfn_u \le dfn_v \le end_u} \left \{ \left | a_v \right | \times b_v \right \}。
把tag加上，再把绝对值拆开，中间的式子就变成了 \max \left \{ (a_v + tag) \times b_v,-(a_v + tag) \times b_v \right \}。
中间的这两个本质上是直线，可以用李超线段树维护，区间加可以用分块。
code：

#include <bits/stdc++.h>
using namespace std;
#define ll long long
const int N = 2e5+5;
namespace tianyu{
    const int W = 1e9;
    int n;
    vector<int> G[N];
    int fa[N], dfn[N], rnk[N], tot1;
    ll a[N];
    int b[N];
    int end[N];
    void dfs(int u, int f){
        rnk[dfn[u] = ++tot1] = u;
        for (int v : G[u]){
            if (v == f) continue;
            a[v] += a[u];
            b[v] += b[u];
            dfs(v, u);
        }
        b[u] = abs(b[u]);
        end[u] = tot1;
    }
    struct node{
        int ls, rs;
        ll a, b;
        node() : ls(0), rs(0) {}
    }tr[3200005];
    int tot;
    int root[505];
    #define calc(a, b, x) (abs(a + x) * b)
    #define calc1(a, b, x) ((a + x) * b)
    #define cmp(x) (calc1(a, b, x) > calc1(tr[p].a, tr[p].b, x))
    void insert(int &p, int l, int r, ll a, ll b){
        if (!p){
            p = ++tot;
            tr[p].a = a, tr[p].b = b;
            return;
        }int mid = (l + r) >> 1;
        if (cmp(mid)) swap(tr[p].a, a), swap(tr[p].b, b);
        if (cmp(l)) insert(tr[p].ls, l, mid, a, b);
        if (cmp(r)) insert(tr[p].rs, mid + 1, r, a, b);
    }
    ll query(int p, int l, int r, int x){
        if (!p) return -1145141919810;
        ll res = calc1(tr[p].a, tr[p].b, x);
        if (l == r) return res;
        int mid = (l + r) >> 1;
        if (x <= mid) return max(res, query(tr[p].ls, l, mid, x));
        else return max(res, query(tr[p].rs, mid + 1, r, x));
    }
    int bel[N];
    int bl[505], br[505], tag[505];
    inline void ins(int i){
        insert(root[bel[i]], 0, W, a[rnk[i]], b[rnk[i]]);
        insert(root[bel[i]], 0, W, a[rnk[i]], -b[rnk[i]]);
    }
    inline void rebuild(int bid){
        root[bid] = 0;
        for (int i = bl[bid];i <= br[bid];i++){
            a[rnk[i]] += tag[bid];
            ins(i);
        }
        tag[bid] = 0;
    }
    void add(int l, int r, int k){
        int L = bel[l], R = bel[r];
        if (L == R){
            for (int i = l;i <= r;i++){
                a[rnk[i]] += k;
            }
            rebuild(L);
            return;
        }
        if (l != bl[L]){
            for (int i = l;i <= br[L];i++){
                a[rnk[i]] += k;
            }rebuild(L);
            ++L;
        }
        if (r != br[R]){
            for (int i = r;i >= bl[R];i--){
                a[rnk[i]] += k;
            }rebuild(R);
            --R;
        }
        for (int i = L;i <= R;i++){
            tag[i] += k;
        }
    }
    ll query(int l, int r){
        int L = bel[l], R = bel[r];
        ll res = -1145141919810;
        if (L == R){
            for (int i = l;i <= r;i++){
                res = max(res, calc(a[rnk[i]], b[rnk[i]], tag[L]));
            }return res;
        }
        for (int i = l;i <= br[L];i++){
            res = max(res, calc(a[rnk[i]], b[rnk[i]], tag[L]));
        }
        for (int i = r;i >= bl[R];i--){
            res = max(res, calc(a[rnk[i]], b[rnk[i]], tag[R]));
        }
        for (int i = L + 1;i < R;i++){
            res = max(res, query(root[i], 0, W, tag[i]));
        }
        return res;
    }
    int q;
    void awa(){
        cin >> n >> q;
        for (int i = 2;i <= n;i++){cin >> fa[i];G[fa[i]].emplace_back(i);}
        for (int i = 1;i <= n;i++) cin >> a[i];
        for (int i = 1;i <= n;i++) cin >> b[i];
        dfs(1, 0);
        int len = 600;
        for (int i = 1;i <= n;i++){
            bel[i] = (i - 1) / len + 1;
            if (!bl[bel[i]]) bl[bel[i]] = i;
            br[bel[i]] = i;
            ins(i);
        }
        while (q--){
            int op, x, k;
            cin >> op >> x;
            if (op == 1){
                cin >> k;
                if (!k) continue;
                add(dfn[x], end[x], k);
            }
            else{
                cout << query(dfn[x], end[x]) << '\n';
            }
        }
    }
}
signed main(){
    int T = 1;
    while (T--) tianyu::awa();
    return 0;
}