ACM_Notebook_new

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:heavy_check_mark: DataStructure/test/aizu_grl_5_e_hld_edge.test.cpp

Depends on

Code

#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_5_E"

#include "../../template.h"
#include "../LazySegTree.h"
#include "../HeavyLight_adamant.h"

using ll = long long;
struct S {
    ll sum, sz;
};

S op(S l, S r) {
    return S { l.sum + r.sum, l.sz + r.sz };
}
S e() { return S {0, 0}; }

S mapping(ll f, S s) {
    return S { s.sum + s.sz * f, s.sz };
}
ll composition(ll f, ll g) { return f + g; }
ll id() { return 0; }


void solve() {
    int n; cin >> n;
    vector<vector<int>> adj(n);
    REP(i,n) {
        int k; cin >> k;
        while (k--) {
            int j; cin >> j;
            adj[i].push_back(j);
            adj[j].push_back(i);
        }
    }

    HLD hld(adj, 0);
    vector<S> nodes;
    for (int i = 0; i < n; i++) nodes.push_back(S{0, 1});
    LazySegTree<S, op, e, ll, mapping, composition, id> st(nodes);

    int q; cin >> q;
    while (q--) {
        int typ; cin >> typ;
        if (typ == 0) {
            int u, val; cin >> u >> val;
            hld.apply_path(u, 0, true, [&] (int l, int r) {
                st.apply(l, r + 1, val);
            });
        } else {
            int u; cin >> u;
            cout << hld.prod_path_commutative<S, op, e>(
                    0, u, true, [&] (int l, int r) {
                        return st.prod(l, r+1);
                    }).sum << '\n';
        }
    }
}
#line 1 "DataStructure/test/aizu_grl_5_e_hld_edge.test.cpp"
#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_5_E"

#line 1 "template.h"
#include <bits/stdc++.h>
using namespace std;

#define FOR(i,a,b) for(int i=(a),_b=(b); i<=_b; i++)
#define FORD(i,a,b) for(int i=(a),_b=(b); i>=_b; i--)
#define REP(i,a) for(int i=0,_a=(a); i<_a; i++)
#define EACH(it,a) for(__typeof(a.begin()) it = a.begin(); it != a.end(); ++it)

#define DEBUG(x) { cout << #x << " = "; cout << (x) << endl; }
#define PR(a,n) { cout << #a << " = "; FOR(_,1,n) cout << a[_] << ' '; cout << endl; }
#define PR0(a,n) { cout << #a << " = "; REP(_,n) cout << a[_] << ' '; cout << endl; }

#define sqr(x) ((x) * (x))

// For printing pair, container, etc.
// Copied from https://quangloc99.github.io/2021/07/30/my-CP-debugging-template.html
template<class U, class V> ostream& operator << (ostream& out, const pair<U, V>& p) {
    return out << '(' << p.first << ", " << p.second << ')';
}

template<class Con, class = decltype(begin(declval<Con>()))>
typename enable_if<!is_same<Con, string>::value, ostream&>::type
operator << (ostream& out, const Con& con) {
    out << '{';
    for (auto beg = con.begin(), it = beg; it != con.end(); it++) {
        out << (it == beg ? "" : ", ") << *it;
    }
    return out << '}';
}
template<size_t i, class T> ostream& print_tuple_utils(ostream& out, const T& tup) {
    if constexpr(i == tuple_size<T>::value) return out << ")"; 
    else return print_tuple_utils<i + 1, T>(out << (i ? ", " : "(") << get<i>(tup), tup); 
}
template<class ...U> ostream& operator << (ostream& out, const tuple<U...>& t) {
    return print_tuple_utils<0, tuple<U...>>(out, t);
}

mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
long long get_rand(long long r) {
    return uniform_int_distribution<long long> (0, r-1)(rng);
}

template<typename T>
vector<T> read_vector(int n) {
    vector<T> res(n);
    for (int& x : res) cin >> x;
    return res;
}

void solve();

int main() {
    ios::sync_with_stdio(0); cin.tie(0);
    solve();
    return 0;
}
#line 1 "DataStructure/LazySegTree.h"
// Lazy Segment Tree, copied from AtCoder {{{
// Source: https://github.com/atcoder/ac-library/blob/master/atcoder/lazysegtree.hpp
// Doc: https://atcoder.github.io/ac-library/master/document_en/lazysegtree.html
//
// Notes:
// - Index of elements from 0
// - Range queries are [l, r-1]
// - composition(f, g) should return f(g())
//
// Tested:
// - https://oj.vnoi.info/problem/qmax2
// - https://oj.vnoi.info/problem/lites
// - (range set, add, mult, sum) https://oj.vnoi.info/problem/segtree_itmix
// - (range add (i-L)*A + B, sum) https://oj.vnoi.info/problem/segtree_itladder
// - https://atcoder.jp/contests/practice2/tasks/practice2_l
// - https://judge.yosupo.jp/problem/range_affine_range_sum

int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (unsigned int)(n)) x++;
    return x;
}
template<
    class S,                 // node data type
    S (*op) (S, S),          // combine 2 nodes
    S (*e) (),               // identity element
    class F,                 // lazy propagation tag
    S (*mapping) (F, S),     // apply tag F on a node
    F (*composition) (F, F), // combine 2 tags
    F (*id)()                // identity tag
>
struct LazySegTree {
    LazySegTree() : LazySegTree(0) {}
    explicit LazySegTree(int n) : LazySegTree(vector<S>(n, e())) {}
    explicit LazySegTree(const vector<S>& v) : _n((int) v.size()) {
        log = ceil_pow2(_n);
        size = 1 << log;
        d = std::vector<S>(2 * size, e());
        lz = std::vector<F>(size, id());
        for (int i = 0; i < _n; i++) d[size + i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }

    // 0 <= p < n
    void set(int p, S x) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    // 0 <= p < n
    S get(int p) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        return d[p];
    }

    // Get product in range [l, r-1]
    // 0 <= l <= r <= n
    // For empty segment (l == r) -> return e()
    S prod(int l, int r) {
        assert(0 <= l && l <= r && r <= _n);
        if (l == r) return e();

        l += size;
        r += size;

        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        S sml = e(), smr = e();
        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }

        return op(sml, smr);
    }

    S all_prod() {
        return d[1];
    }

    // 0 <= p < n
    void apply(int p, F f) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = mapping(f, d[p]);
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    // Apply f on all elements in range [l, r-1]
    // 0 <= l <= r <= n
    void apply(int l, int r, F f) {
        assert(0 <= l && l <= r && r <= _n);
        if (l == r) return;

        l += size;
        r += size;

        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        {
            int l2 = l, r2 = r;
            while (l < r) {
                if (l & 1) all_apply(l++, f);
                if (r & 1) all_apply(--r, f);
                l >>= 1;
                r >>= 1;
            }
            l = l2;
            r = r2;
        }

        for (int i = 1; i <= log; i++) {
            if (((l >> i) << i) != l) update(l >> i);
            if (((r >> i) << i) != r) update((r - 1) >> i);
        }
    }

    // Binary search on SegTree to find largest r:
    //    f(op(a[l] .. a[r-1])) = true   (assuming empty array is always true)
    //    f(op(a[l] .. a[r])) = false    (assuming op(..., a[n]), which is out of bound, is always false)
    template <bool (*g)(S)> int max_right(int l) {
        return max_right(l, [](S x) { return g(x); });
    }
    template <class G> int max_right(int l, G g) {
        assert(0 <= l && l <= _n);
        assert(g(e()));
        if (l == _n) return _n;
        l += size;
        for (int i = log; i >= 1; i--) push(l >> i);
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!g(op(sm, d[l]))) {
                while (l < size) {
                    push(l);
                    l = (2 * l);
                    if (g(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    // Binary search on SegTree to find smallest l:
    //    f(op(a[l] .. a[r-1])) = true      (assuming empty array is always true)
    //    f(op(a[l-1] .. a[r-1])) = false   (assuming op(a[-1], ..), which is out of bound, is always false)
    template <bool (*g)(S)> int min_left(int r) {
        return min_left(r, [](S x) { return g(x); });
    }
    template <class G> int min_left(int r, G g) {
        assert(0 <= r && r <= _n);
        assert(g(e()));
        if (r == 0) return 0;
        r += size;
        for (int i = log; i >= 1; i--) push((r - 1) >> i);
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!g(op(d[r], sm))) {
                while (r < size) {
                    push(r);
                    r = (2 * r + 1);
                    if (g(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }


private:
    int _n, size, log;
    vector<S> d;
    vector<F> lz;

    void update(int k) {
        d[k] = op(d[2*k], d[2*k+1]);
    }
    void all_apply(int k, F f) {
        d[k] = mapping(f, d[k]);
        if (k < size) lz[k] = composition(f, lz[k]);
    }
    void push(int k) {
        all_apply(2*k, lz[k]);
        all_apply(2*k+1, lz[k]);
        lz[k] = id();
    }
};
// }}}

// Examples {{{
// https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/2/DSL_2_D
// https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/2/DSL_2_E
// https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/2/DSL_2_F
// https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/2/DSL_2_G
// https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/2/DSL_2_H
// https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/2/DSL_2_I
// supports:
// - set a(l -> r) to val; val > NOT_SET
// - add a(l -> r) += val
// - find sum a(l -> r)
// - find min a(l -> r)
struct RangeSetAddMinSumOps {
    struct S { long long sum, min, sz; };
    static S op(S l, S r) { return S { l.sum + r.sum, min(l.min, r.min), l.sz + r.sz }; }
    static S e() { return S {0LL, INT_MAX, 0}; }

    static const long long NOT_SET = -1000111000;
    struct F { long long set, add; };

    static S mapping(F f, S s) {
        if (f.set == NOT_SET) {
            return S {
                s.sum + f.add * s.sz,
                s.min + f.add,
                s.sz,
            };
        }
        return S {
            (f.set + f.add) * s.sz,
            f.set + f.add,
            s.sz,
        };
    }
    static F composition(F f, F g) {
        if (f.set == NOT_SET) {
            return F { g.set, g.add + f.add };
        }
        return f;
    }
    static F id() {
        return F { NOT_SET, 0 };
    }
};
// }}}
#line 1 "DataStructure/HeavyLight_adamant.h"
// Index from 0
// Best used with SegTree.h
//
// Usage:
// HLD hld(g, root);
// // build segment tree. Note that we must use hld.order[i]
// vector<T> nodes;
// for (int i = 0; i < n; i++)
//   nodes.push_back(initial_value[hld.order[i]])
// SegTree<S, op, e> st(nodes);
//
// // Update single vertex
// st.set(hld.in[u], new_value)
//
// // Update path
// hld.apply_path(from, to, is_edge, [&] (int l, int r) {
//   st.apply(l, r+1, F);
// });
//
// // Query path
// hld.prod_path_commutative<S, op, e> (from, to, is_edge, [&] (int l, int r) {
//   return st.prod(l, r+1);
// });
//
// Tested:
// - (vertex, path) https://judge.yosupo.jp/problem/vertex_add_path_sum
// - (vertex, path, non-commutative) https://judge.yosupo.jp/problem/vertex_set_path_composite
// - (vertex, subtree) https://judge.yosupo.jp/problem/vertex_add_subtree_sum
// - (vertex, path, non-commutative, 1-index) https://oj.vnoi.info/problem/icpc21_mt_l
// - (vertex, path) https://oj.vnoi.info/problem/qtree3
//
// - (edge, path) https://oj.vnoi.info/problem/qtreex
// - (edge, path) https://oj.vnoi.info/problem/lubenica
// - (edge, path) https://oj.vnoi.info/problem/pwalk
// - (edge, path, lazy) https://oj.vnoi.info/problem/kbuild
// - (edge, path, lazy) https://oj.vnoi.info/problem/onbridge
//
// - (lca) https://oj.vnoi.info/problem/fselect
// - (kth_parent) https://cses.fi/problemset/task/1687
// HeavyLight {{{
struct HLD {
    HLD(const vector<vector<int>>& _g, int root)
            : n(_g.size()), g(_g),
            parent(n), depth(n), sz(n),
            dfs_number(0), nxt(n), in(n), out(n), order(n)
    {
        assert(0 <= root && root < n);

        // init parent, depth, sz
        // also move most heavy child of u to g[u][0]
        depth[root] = 0;
        dfs_sz(root, -1);

        // init nxt, in, out
        nxt[root] = root;
        dfs_hld(root);
    }

    int lca(int u, int v) const {
        assert(0 <= u && u < n);
        assert(0 <= v && v < n);
        while (true) {
            if (in[u] > in[v]) swap(u, v); // in[u] <= in[v]
            if (nxt[u] == nxt[v]) return u;
            v = parent[nxt[v]];
        }
    }

    // return k-th parent
    // if no such parent -> return -1
    int kth_parent(int u, int k) const {
        assert(0 <= u && u < n);
        if (depth[u] < k) return -1;

        while (true) {
            int v = nxt[u];
            if (in[u] - k >= in[v]) return order[in[u] - k];
            k -= in[u] - in[v] + 1;
            u = parent[v];
        }
    }

    // return k-th vertex on path from u -> v (0 <= k)
    // if k > distance -> return -1
    int kth_vertex_on_path(int u, int v, int k) const {
        assert(0 <= u && u < n);
        assert(0 <= v && v < n);

        int l = lca(u, v);
        int ul = depth[u] - depth[l];
        if (k <= ul) return kth_parent(u, k);
        k -= ul;
        int vl = depth[v] - depth[l];
        if (k <= vl) return kth_parent(v, vl - k);
        return -1;
    }

    int dist(int u, int v) const {
        assert(0 <= u && u < n);
        assert(0 <= v && v < n);
        int l = lca(u, v);
        return depth[u] + depth[v] - 2*depth[l];
    }

    // apply f on vertices on path [u, v]
    // edge = true -> apply on edge
    //
    // f(l, r) should update segment tree [l, r] INCLUSIVE
    void apply_path(int u, int v, bool edge, const function<void(int, int)> &f) {
        assert(0 <= u && u < n);
        assert(0 <= v && v < n);
        if (u == v && edge) return;

        while (true) {
            if (in[u] > in[v]) swap(u, v); // in[u] <= in[v]
            if (nxt[u] == nxt[v]) break;
            f(in[nxt[v]], in[v]);
            v = parent[nxt[v]];
        }
        if (u == v && edge) return;
        f(in[u] + edge, in[v]);
    }

    // get prod of path u -> v
    // edge = true -> get on edges
    //
    // f(l, r) should query segment tree [l, r] INCLUSIVE
    // f must be commutative. For non-commutative, use getSegments below
    template<class S, S (*op) (S, S), S (*e)()>
    S prod_path_commutative(
            int u, int v, bool edge,
            const function<S(int, int)>& f) const {
        assert(0 <= u && u < n);
        assert(0 <= v && v < n);
        if (u == v && edge) {
            return e();
        }
        S su = e(), sv = e();
        while (true) {
            if (in[u] > in[v]) { swap(u, v); swap(su, sv); }
            if (nxt[u] == nxt[v]) break;
            sv = op(sv, f(in[nxt[v]], in[v]));
            v = parent[nxt[v]];
        }
        if (u == v && edge) {
            return op(su, sv);
        } else {
            return op(su, op(sv, f(in[u] + edge, in[v])));
        }
    }

    // f(l, r) modify seg_tree [l, r] INCLUSIVE
    void apply_subtree(int u, bool edge, const function<void(int, int)>& f) {
        assert(0 <= u && u < n);
        f(in[u] + edge, out[u] - 1);
    }

    // f(l, r) queries seg_tree [l, r] INCLUSIVE
    template<class S>
    S prod_subtree_commutative(int u, bool edge, const function<S(S, S)>& f) {
        assert(0 <= u && u < n);
        return f(in[u] + edge, out[u] - 1);
    }

    // Useful when functions are non-commutative
    // Return all segments on path from u -> v
    // For this problem, the order (u -> v is different from v -> u)
    vector< pair<int,int> > getSegments(int u, int v) const {
        assert(0 <= u && u < n);
        assert(0 <= v && v < n);
        vector< pair<int,int> > upFromU, upFromV;

        int fu = nxt[u], fv = nxt[v];
        while (fu != fv) {  // u and v are on different chains
            if (depth[fu] >= depth[fv]) { // move u up
                upFromU.push_back({u, fu});
                u = parent[fu];
                fu = nxt[u];
            } else { // move v up
                upFromV.push_back({fv, v});
                v = parent[fv];
                fv = nxt[v];
            }
        }
        upFromU.push_back({u, v});
        reverse(upFromV.begin(), upFromV.end());
        upFromU.insert(upFromU.end(), upFromV.begin(), upFromV.end());
        return upFromU;
    }

    // return true if u is ancestor
    bool isAncestor(int u, int v) const {
        return in[u] <= in[v] && out[v] <= out[u];
    }

// private:
    int n;
    vector<vector<int>> g;
    vector<int> parent;   // par[u] = parent of u. par[root] = -1
    vector<int> depth;    // depth[u] = distance from root -> u
    vector<int> sz;       // sz[u] = size of subtree rooted at u
    int dfs_number;
    vector<int> nxt;      // nxt[u] = vertex on heavy path of u, nearest to root
    vector<int> in, out;  // subtree(u) is in range [in[u], out[u]-1]
    vector<int> order;    // euler tour

    void dfs_sz(int u, int fu) {
        parent[u] = fu;
        sz[u] = 1;
        // remove parent from adjacency list
        auto it = std::find(g[u].begin(), g[u].end(), fu);
        if (it != g[u].end()) g[u].erase(it);

        for (int& v : g[u]) {
            depth[v] = depth[u] + 1;
            dfs_sz(v, u);

            sz[u] += sz[v];
            if (sz[v] > sz[g[u][0]]) swap(v, g[u][0]);
        }
    }

    void dfs_hld(int u) {
        order[dfs_number] = u;
        in[u] = dfs_number++;

        for (int v : g[u]) {
            nxt[v] = (v == g[u][0] ? nxt[u] : v);
            dfs_hld(v);
        }
        out[u] = dfs_number;
    }
};
// }}}
#line 6 "DataStructure/test/aizu_grl_5_e_hld_edge.test.cpp"

using ll = long long;
struct S {
    ll sum, sz;
};

S op(S l, S r) {
    return S { l.sum + r.sum, l.sz + r.sz };
}
S e() { return S {0, 0}; }

S mapping(ll f, S s) {
    return S { s.sum + s.sz * f, s.sz };
}
ll composition(ll f, ll g) { return f + g; }
ll id() { return 0; }


void solve() {
    int n; cin >> n;
    vector<vector<int>> adj(n);
    REP(i,n) {
        int k; cin >> k;
        while (k--) {
            int j; cin >> j;
            adj[i].push_back(j);
            adj[j].push_back(i);
        }
    }

    HLD hld(adj, 0);
    vector<S> nodes;
    for (int i = 0; i < n; i++) nodes.push_back(S{0, 1});
    LazySegTree<S, op, e, ll, mapping, composition, id> st(nodes);

    int q; cin >> q;
    while (q--) {
        int typ; cin >> typ;
        if (typ == 0) {
            int u, val; cin >> u >> val;
            hld.apply_path(u, 0, true, [&] (int l, int r) {
                st.apply(l, r + 1, val);
            });
        } else {
            int u; cin >> u;
            cout << hld.prod_path_commutative<S, op, e>(
                    0, u, true, [&] (int l, int r) {
                        return st.prod(l, r+1);
                    }).sum << '\n';
        }
    }
}
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