test/data_structure/Vertex_Add_Path_Sum.test.cpp

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• Last update: 2023-11-24 15:39:05+09:00
• Problem: https://judge.yosupo.jp/problem/vertex_add_path_sum

Depends on

• segtree (data_structure/segtree.hpp)
• テンプレート (template/template.hpp)
• Heavy Light Decomposition (tree/HeavyLightDecomposition.hpp)

Code

#define PROBLEM "https://judge.yosupo.jp/problem/vertex_add_path_sum"

#include "../../data_structure/segtree.hpp"
#include "../../template/template.hpp"
#include "../../tree/HeavyLightDecomposition.hpp"

using i64 = std::int64_t;
i64 op(i64 a, i64 b) {
    return a + b;
}
i64 e() {
    return 0;
}

int main() {
    int n, q;
    std::cin >> n >> q;
    std::vector<i64> a(n);
    for (int i = 0; i < n; ++i) {
        std::cin >> a[i];
    }
    std::vector g(n, std::vector<int>());
    for (int i = 0; i < n - 1; ++i) {
        int u, v;
        std::cin >> u >> v;
        g[u].emplace_back(v);
        g[v].emplace_back(u);
    }
    lib::HeavyLightDecomposition hld(g);
    lib::segtree<i64, op, e> seg(n);
    i64 ans = e();
    auto set = [&](int u, i64 x) {
        int idx = hld.idx(u);
        seg.set(idx, seg.get(idx) + x);
    };
    auto f = [&](int l, int r) {
        if (l <= r)
            ans = op(ans, seg.prod(l, r));
        else
            ans = op(ans, seg.prod(r, l));
    };
    for (int i = 0; i < n; i++) {
        set(i, a[i]);
    }
    while (q--) {
        int flag;
        std::cin >> flag;
        if (flag == 0) {
            int p;
            i64 x;
            std::cin >> p >> x;
            set(p, x);
        } else {
            int u, v;
            std::cin >> u >> v;
            ans = e();
            hld.path_noncommutative_query(u, v, true, f);
            std::cout << ans << '\n';
        }
    }
}

#line 1 "test/data_structure/Vertex_Add_Path_Sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_add_path_sum"

#line 2 "data_structure/segtree.hpp"

#line 2 "template/template.hpp"

#include <bits/stdc++.h>

#define rep(i, s, n) for (int i = (int)(s); i < (int)(n); i++)
#define rrep(i, s, n) for (int i = (int)(n)-1; i >= (int)(s); i--)
#define all(v) v.begin(), v.end()

using ll = long long;
using ld = long double;
using ull = unsigned long long;

template <typename T> bool chmin(T &a, const T &b) {
    if (a <= b) return false;
    a = b;
    return true;
}
template <typename T> bool chmax(T &a, const T &b) {
    if (a >= b) return false;
    a = b;
    return true;
}

namespace lib {

using namespace std;

}  // namespace lib

// using namespace lib;
#line 4 "data_structure/segtree.hpp"

namespace lib {

using namespace std;

template <class S, S (*op)(S, S), S (*e)()> struct segtree {
  private:
    int n;
    int sz;
    vector<S> data;

    void update(int i) {
        data[i] = op(data[2 * i], data[2 * i + 1]);
    }

  public:
    segtree(int n) : segtree(vector<S>(n, e())) {}
    segtree(const vector<S> &v) : n((int)v.size()), sz(1) {
        while (sz < n) sz *= 2;
        data = vector<S>(2 * sz, e());
        rep(i, 0, n) {
            data[sz + i] = v[i];
        }
        rrep(i, 1, sz) update(i);
    }

    void set(int p, S x) {
        assert(0 <= p && p < n);
        p += sz;
        data[p] = x;
        while (p > 1) {
            p >>= 1;
            update(p);
        }
    }

    S get(int p) {
        assert(0 <= p && p < n);
        return data[p + sz];
    }

    S prod(int l, int r) {
        assert(0 <= l && l <= r && r <= n);
        S sml = e(), smr = e();
        l += sz;
        r += sz;
        while (l < r) {
            if (l & 1) sml = op(sml, data[l++]);
            if (r & 1) smr = op(data[--r], smr);
            l >>= 1;
            r >>= 1;
        }
        return op(sml, smr);
    }

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

    template <class F> int max_right(int l, F f) {
        assert(0 <= l && l <= n);
        assert(f(e()));
        if (l == n) return n;
        l += sz;
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!f(op(sm, data[l]))) {
                while (l < sz) {
                    l = 2 * l;
                    if (f(op(sm, data[l]))) {
                        sm = op(sm, data[l]);
                        l++;
                    }
                }
                return l - sz;
            }
            sm = op(sm, data[l]);
            l++;
        } while ((l & -l) != l);
        return n;
    }

    template <class F> int min_left(int r, F f) {
        assert(0 <= r && r <= n);
        assert(f(e()));
        if (r == 0) return 0;
        r += sz;
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!f(op(data[r], sm))) {
                while (r < sz) {
                    r = 2 * r + 1;
                    if (f(op(data[r], sm))) {
                        sm = op(data[r], sm);
                        r--;
                    }
                }
                return r + 1 - sz;
            }
            sm = op(data[r], sm);
        } while ((r & -r) != r);
        return 0;
    }
};

}  // namespace lib
#line 2 "tree/HeavyLightDecomposition.hpp"

#line 4 "tree/HeavyLightDecomposition.hpp"

namespace lib {

using namespace std;

struct HeavyLightDecomposition {
  private:
    void dfs_sz(int v) {
        for (auto &nv : g[v]) {
            if (nv == par[v]) continue;
            par[nv] = v;
            depth[nv] = depth[v] + 1;
            dfs_sz(nv);
            sz[v] += sz[nv];
            if (sz[nv] > sz[g[v][0]] || g[v][0] == par[v]) swap(nv, g[v][0]);
        }
    }

    void dfs_hld(int v) {
        in[v] = t++;
        for (auto nv : g[v]) {
            if (nv == par[v]) continue;
            nxt[nv] = (nv == g[v][0] ? nxt[v] : nv);
            dfs_hld(nv);
        }
        out[v] = t;
    }

    // [u, v) パスの取得 (v は u の祖先)
    vector<pair<int, int>> ascend(int u, int v) const {
        vector<pair<int, int>> res;
        while (nxt[u] != nxt[v]) {
            res.emplace_back(in[u], in[nxt[u]]);
            u = par[nxt[u]];
        }
        if (u != v) res.emplace_back(in[u], in[v] + 1);
        return res;
    }

    // (u, v] パスの取得 (u は v の祖先)
    vector<pair<int, int>> descend(int u, int v) const {
        if (u == v) return {};
        if (nxt[u] == nxt[v]) return {{in[u] + 1, in[v]}};
        auto res = descend(u, par[nxt[v]]);
        res.emplace_back(in[nxt[v]], in[v]);
        return res;
    }

  public:
    HeavyLightDecomposition(const vector<vector<int>> &gh, int root = 0)
        : n(gh.size()),
          g(gh),
          sz(n, 1),
          in(n),
          out(n),
          nxt(n),
          par(n, -1),
          depth(n, 0) {
        nxt[root] = root;
        dfs_sz(root);
        dfs_hld(root);
    }

    int idx(int u) const {
        return in[u];
    }

    int lca(int u, int v) const {
        while (nxt[u] != nxt[v]) {
            if (in[u] < in[v]) swap(u, v);
            u = par[nxt[u]];
        }
        return depth[u] < depth[v] ? u : v;
    }

    int distance(int u, int v) const {
        return depth[u] + depth[v] - 2 * depth[lca(u, v)];
    }

    template <class F>
    void path_noncommutative_query(int u, int v, bool vertex,
                                   const F &f) const {
        int l = lca(u, v);
        for (auto [a, b] : ascend(u, l)) f(a + 1, b);
        if (vertex) f(in[l], in[l] + 1);
        for (auto [a, b] : descend(l, v)) f(a, b + 1);
    }

    template <class F> void subtree_query(int u, bool vertex, const F &f) {
        f(in[u] + int(!vertex), out[u]);
    }

    int parent(int v) {
        return par[v];
    }

    std::vector<std::pair<int,int>> lca_based_auxiliary_tree(std::vector<int>);

  private:
    int n, t = 0;
    vector<vector<int>> g;
    vector<int> sz, in, out, nxt, par, depth;
};

}  // namespace lib
#line 6 "test/data_structure/Vertex_Add_Path_Sum.test.cpp"

using i64 = std::int64_t;
i64 op(i64 a, i64 b) {
    return a + b;
}
i64 e() {
    return 0;
}

int main() {
    int n, q;
    std::cin >> n >> q;
    std::vector<i64> a(n);
    for (int i = 0; i < n; ++i) {
        std::cin >> a[i];
    }
    std::vector g(n, std::vector<int>());
    for (int i = 0; i < n - 1; ++i) {
        int u, v;
        std::cin >> u >> v;
        g[u].emplace_back(v);
        g[v].emplace_back(u);
    }
    lib::HeavyLightDecomposition hld(g);
    lib::segtree<i64, op, e> seg(n);
    i64 ans = e();
    auto set = [&](int u, i64 x) {
        int idx = hld.idx(u);
        seg.set(idx, seg.get(idx) + x);
    };
    auto f = [&](int l, int r) {
        if (l <= r)
            ans = op(ans, seg.prod(l, r));
        else
            ans = op(ans, seg.prod(r, l));
    };
    for (int i = 0; i < n; i++) {
        set(i, a[i]);
    }
    while (q--) {
        int flag;
        std::cin >> flag;
        if (flag == 0) {
            int p;
            i64 x;
            std::cin >> p >> x;
            set(p, x);
        } else {
            int u, v;
            std::cin >> u >> v;
            ans = e();
            hld.path_noncommutative_query(u, v, true, f);
            std::cout << ans << '\n';
        }
    }
}

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