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:heavy_check_mark: Test/LC/vertex_add_path_sum.test.cpp

Depends on

Code

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

#include "../../Src/Template/IOSetting.hpp"
#include "../../Src/DataStructure/FenwickTree/FenwickTree.hpp"
#include "../../Src/Algebra/Group/AdditiveGroup.hpp"
#include "../../Src/Graph/Tree/HeavyLightDecomposition.hpp"

#include <cassert>
#include <iostream>
#include <utility>
#include <vector>

int main() {
    using namespace zawa; 
    SetFastIO();

    int N, Q;
    std::cin >> N >> Q;
    std::vector<int> A(N);
    for (int& a : A) std::cin >> a;
    std::vector<std::vector<int>> T(N);
    for (int _{} ; _ < N - 1 ; _++) {
        int u, v;
        std::cin >> u >> v;
        T[u].push_back(v);
        T[v].push_back(u);
        // AddEdge(T, u, v);
    }
    HeavyLightDecomposition hld(T);
    std::vector<long long> init(N);
    for (int v{} ; v < N ; v++) {
        init[hld[v]] = A[v];
    }
    FenwickTree<AdditiveGroup<long long>> fen{init};
    while (Q--) {
        int t;
        std::cin >> t;
        if (t == 0) {
            int p, x;
            std::cin >> p >> x;
            fen.operation(hld[p], x);
        }
        else if (t == 1) {
            int u, v;
            std::cin >> u >> v;
            long long ans{};
            for (auto [u, v] : hld(u, v)) {
                u = hld[u];
                v = hld[v];
                if (u > v) std::swap(u, v);
                ans += fen.product(u, v + 1);
            }
            std::cout << ans << '\n';
        }
        else {
            assert(false);
        }
    }
}
#line 1 "Test/LC/vertex_add_path_sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_add_path_sum"

#line 2 "Src/Template/IOSetting.hpp"

#line 2 "Src/Template/TypeAlias.hpp"

#include <cstdint>
#include <cstddef>

namespace zawa {

using i16 = std::int16_t;
using i32 = std::int32_t;
using i64 = std::int64_t;
using i128 = __int128_t;

using u8 = std::uint8_t;
using u16 = std::uint16_t;
using u32 = std::uint32_t;
using u64 = std::uint64_t;

using usize = std::size_t;

} // namespace zawa
#line 4 "Src/Template/IOSetting.hpp"

#include <iostream>
#include <iomanip>

namespace zawa {

void SetFastIO() {
    std::cin.tie(nullptr)->sync_with_stdio(false);
}

void SetPrecision(u32 dig) {
    std::cout << std::fixed << std::setprecision(dig);
}

} // namespace zawa
#line 2 "Src/DataStructure/FenwickTree/FenwickTree.hpp"

#line 2 "Src/Algebra/Group/GroupConcept.hpp"

#line 2 "Src/Algebra/Monoid/MonoidConcept.hpp"

#line 2 "Src/Algebra/Semigroup/SemigroupConcept.hpp"

#include <concepts>

namespace zawa {

namespace concepts {

template <class T>
concept Semigroup = requires {
    typename T::Element;
    { T::operation(std::declval<typename T::Element>(), std::declval<typename T::Element>()) } -> std::same_as<typename T::Element>;
};

} // namespace concepts

} // namespace zawa
#line 4 "Src/Algebra/Monoid/MonoidConcept.hpp"

#line 6 "Src/Algebra/Monoid/MonoidConcept.hpp"

namespace zawa {

namespace concepts {

template <class T>
concept Identitiable = requires {
    typename T::Element;
    { T::identity() } -> std::same_as<typename T::Element>;
};

template <class T>
concept Monoid = Semigroup<T> and Identitiable<T>;

} // namespace

} // namespace zawa
#line 4 "Src/Algebra/Group/GroupConcept.hpp"

namespace zawa {

namespace concepts {

template <class T>
concept Inversible = requires {
    typename T::Element;
    { T::inverse(std::declval<typename T::Element>()) } -> std::same_as<typename T::Element>;
};

template <class T>
concept Group = Monoid<T> and Inversible<T>;

} // namespace Concept

} // namespace zawa
#line 5 "Src/DataStructure/FenwickTree/FenwickTree.hpp"

#include <vector>
#include <cassert>
#include <ostream>
#include <functional>
#include <type_traits>

namespace zawa {

template <concepts::Group Group>
class FenwickTree {
public:

    using VM = Group;
    
    using V = typename VM::Element;

    FenwickTree() = default;

    explicit FenwickTree(usize n) : m_n{ n }, m_bitwidth{ std::__lg(n) + 1 }, m_a(n), m_dat(n + 1, VM::identity()) {
        m_dat.shrink_to_fit();
        m_a.shrink_to_fit();
    }

    explicit FenwickTree(const std::vector<V>& a) : m_n{ a.size() }, m_bitwidth{ std::__lg(a.size()) + 1 }, m_a(a), m_dat(a.size() + 1, VM::identity()) {
        m_dat.shrink_to_fit();  
        m_a.shrink_to_fit();
        for (i32 i{} ; i < static_cast<i32>(m_n) ; i++) {
            addDat(i, a[i]);
        }
    }

    inline usize size() const noexcept {
        return m_n;
    }

    // return a[i]
    const V& get(usize i) const noexcept {
        assert(i < size());
        return m_a[i];
    }

    // return a[i]
    const V& operator[](usize i) const noexcept {
        assert(i < size());
        return m_a[i];
    }

    // a[i] <- a[i] + v
    void operation(usize i, const V& v) {
        assert(i < size());
        addDat(i, v);
        m_a[i] = VM::operation(m_a[i], v);
    }

    // a[i] <- v
    void assign(usize i, const V& v) {
        assert(i < size());
        addDat(i, VM::operation(VM::inverse(m_a[i]), v));
        m_a[i] = v;
    }

    // return a[0] + a[1] + ... + a[r - 1]
    V prefixProduct(usize r) const {
        assert(r <= size());
        return product(r);
    }

    // return a[l] + a[l + 1] ... + a[r - 1]
    V product(usize l, usize r) const {
        assert(l <= r and r <= size());
        return VM::operation(VM::inverse(product(l)), product(r));
    }

    template <class Function>
    usize maxRight(usize l, const Function& f) const {
        static_assert(std::is_convertible_v<decltype(f), std::function<bool(V)>>, "maxRight's argument f must be function bool(T)");
        assert(l < size());
        V sum{ VM::inverse(product(l)) }; 
        usize r{};
        for (usize bit{ m_bitwidth } ; bit ; ) {
            bit--;
            usize nxt{ r | (1u << bit) };
            if (nxt < m_dat.size() and f(VM::operation(sum, m_dat[nxt]))) {
                sum = VM::operation(sum, m_dat[nxt]);
                r = std::move(nxt);
            }
        }
        assert(l <= r);
        return r;
    }

    template <class Function>
    usize minLeft(usize r, const Function& f) const {
        static_assert(std::is_convertible_v<decltype(f), std::function<bool(V)>>, "minLeft's argument f must be function bool(T)");
        assert(r <= size());
        V sum{ product(r) };
        usize l{};
        for (usize bit{ m_bitwidth } ; bit ; ) {
            bit--;
            usize nxt{ l | (1u << bit) };
            if (nxt <= r and not f(VM::operation(VM::inverse(m_dat[nxt]), sum))) {
                sum = VM::operation(VM::inverse(m_dat[nxt]), sum);
                l = std::move(nxt);
            }
        }
        assert(l <= r);
        return l;
    }

    // debug print
    friend std::ostream& operator<<(std::ostream& os, const FenwickTree& ft) {
        for (usize i{} ; i <= ft.size() ; i++) {
            os << ft.prefixProduct(i) << (i == ft.size() ? "" : " ");
        }
        return os;
    }

private:

    usize m_n{};

    usize m_bitwidth{};

    std::vector<V> m_a, m_dat;

    constexpr i32 lsb(i32 x) const noexcept {
        return x & -x;
    }
    
    // a[i] <- a[i] + v
    void addDat(i32 i, const V& v) {
        assert(0 <= i and i < static_cast<i32>(m_n));
        for ( i++ ; i < static_cast<i32>(m_dat.size()) ; i += lsb(i)) {
            m_dat[i] = VM::operation(m_dat[i], v);
        }
    }

    // return a[0] + a[1] + .. + a[i - 1]
    V product(i32 i) const {
        assert(0 <= i and i <= static_cast<i32>(m_n));
        V res{ VM::identity() };
        for ( ; i > 0 ; i -= lsb(i)) {
            res = VM::operation(res, m_dat[i]);
        }
        return res;
    }

};

} // namespace zawa
#line 2 "Src/Algebra/Group/AdditiveGroup.hpp"

namespace zawa {

template <class T>
class AdditiveGroup {
public:
    using Element = T;
    static constexpr T identity() noexcept {
        return T{};
    }
    static constexpr T operation(const T& l, const T& r) noexcept {
        return l + r;
    }
    static constexpr T inverse(const T& v) noexcept {
        return -v;
    }
};

} // namespace zawa
#line 2 "Src/Graph/Tree/HeavyLightDecomposition.hpp"

#line 4 "Src/Graph/Tree/HeavyLightDecomposition.hpp"

#include <algorithm>
#line 7 "Src/Graph/Tree/HeavyLightDecomposition.hpp"
#include <cmath>
#include <limits>
#include <utility>
#line 11 "Src/Graph/Tree/HeavyLightDecomposition.hpp"

namespace zawa {

template <class V>
class HeavyLightDecomposition {
public:

    static constexpr V Invalid() noexcept {
        return INVALID;
    }

    HeavyLightDecomposition() = default;

    HeavyLightDecomposition(std::vector<std::vector<V>> T, V root = 0u) 
        : n_{T.size()}, par_(n_), top_(n_), idx_(n_), 
        inv_(n_), size_(n_, usize{1}), dep_(n_) {

            auto dfs1{[&](auto dfs, V v, V p, usize d) -> usize {
                par_[v] = p;
                dep_[v] = d;
                if (p != INVALID) {
                    for (u32 i{} ; i + 1 < T[v].size() ; i++) if (T[v][i] == p) {
                        std::swap(T[v][i], T[v].back());
                        break;
                    }
                    assert(T[v].back() == p);
                    T[v].pop_back();
                }
                for (V x : T[v]) {
                    size_[v] += dfs(dfs, x, v, d + 1);
                }
                for (u32 i{1} ; i < T[v].size() ; i++) if (size_[T[v][0]] < size_[T[v][i]]) {
                    std::swap(T[v][0], T[v][i]);
                }
                return size_[v];
            }};

            auto dfs2{[&](auto dfs, V v, V idx, V top) -> V {
                idx_[v] = idx++;
                inv_[idx_[v]] = v;
                top_[v] = top;
                if (T[v].size()) {
                    idx = dfs(dfs, T[v][0], idx, top);
                    for (u32 i{1} ; i < T[v].size() ; i++) {
                        idx = dfs(dfs, T[v][i], idx, T[v][i]);
                    }
                }
                return idx;
            }};

            dfs1(dfs1, root, INVALID, 0u);
            dfs2(dfs2, root, 0u, root);
        }

    inline usize size() const noexcept {
        return n_;
    }

    usize size(V v) const noexcept {
        assert(v < (V)size());
        return size_[v];
    }

    usize depth(V v) const noexcept {
        assert(v < (V)size());
        return dep_[v];
    }

    V parent(V v) const noexcept {
        assert(v < (V)size());
        return par_[v];
    }

    V index(V v) const noexcept {
        assert(v < (V)size());
        return idx_[v];
    }

    V operator[](V v) const noexcept {
        assert(v < (V)size());
        return idx_[v];
    }

    std::vector<std::pair<V, V>> decomp(V s, V t) const {
        assert(s < (V)size());
        assert(t < (V)size());
        std::vector<std::pair<V, V>> res, ser;
        while (top_[s] != top_[t]) {
            if (dep_[top_[s]] >= dep_[top_[t]]) {
                res.emplace_back(s, top_[s]);
                s = top_[s];
                if (par_[s] != INVALID) s = par_[s];
            }
            else {
                ser.emplace_back(top_[t], t);
                t = top_[t];
                if (par_[t] != INVALID) t = par_[t];
            }
        }
        res.emplace_back(s, t);
        std::reverse(ser.begin(), ser.end());
        res.insert(res.end(), ser.begin(), ser.end()); 
        return res;
    }

    std::vector<std::pair<V, V>> operator()(V s, V t) const {
        return decomp(s, t);
    }

    V lca(V u, V v) const {
        assert(u < (V)size());
        assert(v < (V)size());
        while (top_[u] != top_[v]) {
            if (dep_[top_[u]] >= dep_[top_[v]]) {
                u = top_[u];
                if (par_[u] != INVALID) u = par_[u];
            }
            else {
                v = top_[v];
                if (par_[v] != INVALID) v = par_[v];
            }
        }
        return (dep_[u] <= dep_[v] ? u : v);
    }

    // pはvの祖先か？
    bool isAncestor(V v, V p) {
        assert(v < size());
        assert(p < size());
        if (dep_[v] < dep_[p]) return false;
        while (v != INVALID and top_[v] != top_[p]) {
            v = par_[top_[v]];
        }
        return v != INVALID;
    }

    V levelAncestor(V v, usize step) const {
        assert(v < (V)size());
        if (step > dep_[v]) return INVALID;
        while (true) {
            usize dist{dep_[v] - dep_[top_[v]]};
            if (dist >= step) break;
            step -= dist + 1;
            v = par_[top_[v]];
        }
        step = (dep_[v] - dep_[top_[v]]) - step;
        return inv_[idx_[top_[v]] + step];
    }

    V jump(V s, V t, usize step) const {
        assert(s < (V)size());
        assert(t < (V)size());
        V uu{INVALID}, vv{INVALID};
        usize d{};
        for (auto [u, v] : decomp(s, t)) {
            usize dist{std::max(dep_[u], dep_[v]) - std::min(dep_[u], dep_[v])};
            if (dist >= step) {
                uu = u;
                vv = v;
                d = dist;
                break;
            }
            step -= dist + 1;
        }
        if (uu == INVALID) return INVALID;
        if (dep_[uu] <= dep_[vv]) {
            return inv_[idx_[uu] + step];
        }
        else {
            return inv_[idx_[vv] + (d - step)];
        }
    }

    usize distance(V s, V t) const {
        assert(s < (V)size());
        assert(t < (V)size());
        usize res{};
        for (auto [u, v] : decomp(s, t)) {
            if (dep_[u] > dep_[v]) std::swap(u, v);
            res += dep_[v] - dep_[u];
        }
        return res;
    }

private:
    static constexpr V INVALID{static_cast<V>(-1)};
    usize n_{};
    std::vector<V> par_{}, top_{}, idx_{}, inv_{};
    std::vector<usize> size_{}, dep_{};
};

} // namespace zawa
#line 7 "Test/LC/vertex_add_path_sum.test.cpp"

#line 12 "Test/LC/vertex_add_path_sum.test.cpp"

int main() {
    using namespace zawa; 
    SetFastIO();

    int N, Q;
    std::cin >> N >> Q;
    std::vector<int> A(N);
    for (int& a : A) std::cin >> a;
    std::vector<std::vector<int>> T(N);
    for (int _{} ; _ < N - 1 ; _++) {
        int u, v;
        std::cin >> u >> v;
        T[u].push_back(v);
        T[v].push_back(u);
        // AddEdge(T, u, v);
    }
    HeavyLightDecomposition hld(T);
    std::vector<long long> init(N);
    for (int v{} ; v < N ; v++) {
        init[hld[v]] = A[v];
    }
    FenwickTree<AdditiveGroup<long long>> fen{init};
    while (Q--) {
        int t;
        std::cin >> t;
        if (t == 0) {
            int p, x;
            std::cin >> p >> x;
            fen.operation(hld[p], x);
        }
        else if (t == 1) {
            int u, v;
            std::cin >> u >> v;
            long long ans{};
            for (auto [u, v] : hld(u, v)) {
                u = hld[u];
                v = hld[v];
                if (u > v) std::swap(u, v);
                ans += fen.product(u, v + 1);
            }
            std::cout << ans << '\n';
        }
        else {
            assert(false);
        }
    }
}
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