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#define PROBLEM "https://judge.yosupo.jp/problem/vertex_set_path_composite" #include "Mathematics/ModInt.hpp" #include "GraphTheory/HeavyLightDecomposition_Query.hpp" #include <cstdio> #include <vector> #include <utility> int main() { int N, Q; scanf("%d %d", &N, &Q); using mint = ModInt<998244353>; using P = std::pair<mint, mint>; using HLD = HeavyLightDecomposition_Query<P>; std::vector<P> init(N); for (int i = 0; i < N; ++i) { int a, b; scanf("%d %d", &a, &b); init[i] = {a, b}; } HLD::Graph g(N); for (int i = 0; i < N - 1; ++i) { int u, v; scanf("%d %d", &u, &v); g[u].emplace_back(v); g[v].emplace_back(u); } HLD hld(g, init, {1, 0}, [](auto && x, auto && y) -> P { return {x.first * y.first, x.second * y.first + y.second}; }); while (Q--) { int q; scanf("%d", &q); if (q == 0) { int p, c, d; scanf("%d %d %d", &p, &c, &d); hld.set(p, {c, d}); } else { int u, v, x; scanf("%d %d %d", &u, &v, &x); auto res = hld.fold(u, v); printf("%d\n", (res.first * x + res.second).val()); } } }
#line 1 "Test/HeavyLightDecomposition_Query.PathQuery.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/vertex_set_path_composite" #line 1 "Mathematics/ModInt.hpp" #include <cassert> #include <iostream> #include <cstdint> /** * @brief https://tkmst201.github.io/Library/Mathematics/ModInt.hpp */ template<int M> struct ModInt { static_assert(M > 0); using value_type = int; using calc_type = std::int_fast64_t; private: value_type val_; public: constexpr ModInt(calc_type val = 0) : val_(val % M + (val >= 0 ? 0 : M)) {} constexpr value_type val() const noexcept { return val_; } constexpr static decltype(M) mod() noexcept { return M; } explicit constexpr operator bool() const noexcept { return val_; } constexpr bool operator !() const noexcept { return !static_cast<bool>(*this); } constexpr ModInt operator +() const noexcept { return *this; } constexpr ModInt operator -() const noexcept { return ModInt(val_ == 0 ? 0 : M - val_); } constexpr ModInt operator ++(int) noexcept { ModInt res = *this; ++*this; return res; } constexpr ModInt operator --(int) noexcept { ModInt res = *this; --*this; return res; } constexpr ModInt & operator ++() noexcept { val_ = val_ + 1 == M ? 0 : val_ + 1; return *this; } constexpr ModInt & operator --() noexcept { val_ = val_ == 0 ? M - 1 : val_ - 1; return *this; } constexpr ModInt & operator +=(const ModInt & rhs) noexcept { val_ += val_ < M - rhs.val_ ? rhs.val_ : rhs.val_ - M; return *this; } constexpr ModInt & operator -=(const ModInt & rhs) noexcept { val_ += val_ >= rhs.val_ ? -rhs.val_ : M - rhs.val_; return *this; } constexpr ModInt & operator *=(const ModInt & rhs) noexcept { val_ = static_cast<calc_type>(val_) * rhs.val_ % M; return *this; } constexpr ModInt & operator /=(const ModInt & rhs) noexcept { return *this *= rhs.inv(); } friend constexpr ModInt operator +(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) += rhs; } friend constexpr ModInt operator -(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) -= rhs; } friend constexpr ModInt operator *(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) *= rhs; } friend constexpr ModInt operator /(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) /= rhs; } friend constexpr bool operator ==(const ModInt & lhs, const ModInt & rhs) noexcept { return lhs.val_ == rhs.val_; } friend constexpr bool operator !=(const ModInt & lhs, const ModInt & rhs) noexcept { return !(lhs == rhs); } friend std::ostream & operator <<(std::ostream & os, const ModInt & rhs) { return os << rhs.val_; } friend std::istream & operator >>(std::istream & is, ModInt & rhs) { calc_type x; is >> x; rhs = ModInt(x); return is; } constexpr ModInt pow(calc_type n) const noexcept { ModInt res = 1, x = val_; if (n < 0) { x = x.inv(); n = -n; } while (n) { if (n & 1) res *= x; x *= x; n >>= 1; } return res; } constexpr ModInt inv() const noexcept { value_type a = val_, a1 = 1, b = M, b1 = 0; while (b > 0) { const value_type q = a / b; value_type tmp = a - q * b; a = b; b = tmp; tmp = a1 - q * b1; a1 = b1; b1 = tmp; } assert(a == 1); if (a1 < 0) a1 += M; return a1; } }; #line 1 "GraphTheory/HeavyLightDecomposition_Query.hpp" #line 1 "DataStructure/SegmentTree.hpp" #include <vector> #include <algorithm> #line 7 "DataStructure/SegmentTree.hpp" #include <functional> /** * @brief https://tkmst201.github.io/Library/DataStructure/SegmentTree.hpp */ template<typename T> struct SegmentTree { using value_type = T; using const_reference = const value_type &; using F = std::function<value_type (const_reference, const_reference)>; using size_type = std::size_t; private: size_type n, n_; value_type id_elem; F f; std::vector<value_type> node; public: SegmentTree() = default; SegmentTree(size_type n, const_reference id_elem, const F & f) : n(n), id_elem(id_elem), f(f) { n_ = 1; while (n_ < n) n_ <<= 1; node.assign(2 * n_, id_elem); } SegmentTree(const std::vector<value_type> & v, const_reference id_elem, const F & f) : SegmentTree(v.size(), id_elem, f) { for (size_type i = 0; i < v.size(); ++i) node[i + n_] = v[i]; for (size_type i = n_ - 1; i > 0; --i) node[i] = f(node[i << 1], node[i << 1 | 1]); } size_type size() const noexcept { return n; } void set(size_type i, const_reference x) noexcept { assert(i < size()); node[i += n_] = x; while (i > 1) { i >>= 1; node[i] = f(node[i << 1], node[i << 1 | 1]); } } const_reference get(size_type i) const noexcept { assert(i < size()); return node[i + n_]; } value_type fold(size_type l, size_type r) const noexcept { assert(l <= r); assert(r <= size()); value_type lv = id_elem, rv = id_elem; for (l += n_, r += n_; l < r; l >>= 1, r >>= 1) { if (l & 1) lv = f(lv, node[l++]); if (r & 1) rv = f(node[r - 1], rv); } return f(lv, rv); } value_type fold_all() const noexcept { return node[1]; } size_type max_right(size_type l, std::function<bool (const_reference)> g) const noexcept { assert(l <= size()); assert(g(id_elem)); if (l == size()) return size(); l += n_; value_type sum = id_elem; while (true) { while (~l & 1) l >>= 1; const value_type nex_sum = f(sum, node[l]); if (g(nex_sum)) { sum = nex_sum; ++l; } else break; if ((l & -l) == l) return size(); } while (l < n_) { const value_type nex_sum = f(sum, node[l << 1]); l <<= 1; if (g(nex_sum)) { sum = nex_sum; l |= 1; } } return l - n_; } size_type min_left(size_type r, std::function<bool (const_reference)> g) const noexcept { assert(r <= size()); assert(g(id_elem)); if (r == 0) return 0; r += n_; value_type sum = id_elem; while (true) { --r; while (r > 1 && (r & 1)) r >>= 1; const value_type nex_sum = f(node[r], sum); if (g(nex_sum)) sum = nex_sum; else break; if ((r & -r) == r) return 0; } while (r < n_) { const value_type nex_sum = f(node[r << 1 | 1], sum); r <<= 1; if (!g(nex_sum)) r |= 1; else sum = nex_sum; } return r + 1 - n_; } }; #line 1 "GraphTheory/HeavyLightDecomposition.hpp" #line 6 "GraphTheory/HeavyLightDecomposition.hpp" #include <stack> #include <utility> #line 9 "GraphTheory/HeavyLightDecomposition.hpp" /** * @brief https://tkmst201.github.io/Library/GraphTheory/HeavyLightDecomposition.hpp */ struct HeavyLightDecomposition { using Graph = std::vector<std::vector<int>>; private: int n; std::vector<int> par_; std::vector<int> heavy_, head_, heavy_size_, heavy_depth_; std::vector<int> tree_id_, roots_; std::vector<int> in_, out_; std::vector<std::vector<int>> par_dblng_; bool LCA; public: HeavyLightDecomposition(const Graph & g, bool LCA = false) : HeavyLightDecomposition(g, -1, LCA) {} HeavyLightDecomposition(const Graph & g, int root, bool LCA) : n(g.size()), par_(n, -1), heavy_(n, -1), tree_id_(n, -1), in_(n, -1), out_(n, -1), LCA(LCA) { std::vector<int> sub_size(n, 0), next(n, -1); for (int i = 0; i < n; ++i) { if (tree_id_[i] != -1) continue; if (root != -1 && i != root) continue; tree_id_[i] = roots_.size(); std::stack<int> stk; stk.emplace(i); while (!stk.empty()) { const int u = stk.top(); stk.pop(); if (sub_size[u]) { int mx_size = 0; for (int v : g[u]) { if (v == par_[u]) continue; sub_size[u] += sub_size[v]; if (mx_size < sub_size[v]) mx_size = sub_size[v], next[u] = v; } continue; } sub_size[u] = 1; stk.emplace(u); for (int v : g[u]) { assert(0 <= v && v < n); assert(v != u); if (v == par_[u]) continue; par_[v] = u; tree_id_[v] = roots_.size(); stk.emplace(v); } } roots_.emplace_back(i); } int euc = 0; for (int r : roots_) { heavy_[r] = head_.size(); head_.emplace_back(r); heavy_size_.emplace_back(1); heavy_depth_.emplace_back(0); std::stack<std::pair<int, int>> stk; stk.emplace(r, 0); while (!stk.empty()) { const auto [u, i] = stk.top(); stk.pop(); if (i < static_cast<int>(g[u].size())) { stk.emplace(u, i + 1); const int v = g[u][i]; if (v != par_[u] && v != next[u]) { heavy_[v] = head_.size(); head_.emplace_back(v); heavy_size_.emplace_back(1); heavy_depth_.emplace_back(heavy_depth_[heavy_[u]] + 1); stk.emplace(v, 0); } } if (i == 0) { in_[u] = euc++; const int v = next[u]; if (v != -1) { heavy_[v] = heavy_[u]; ++heavy_size_[heavy_[u]]; stk.emplace(v, 0); } } if (i == static_cast<int>(g[u].size())) out_[u] = euc; } } if (!LCA) return; int max_depth = *std::max_element(begin(heavy_depth_), end(heavy_depth_)); int lglg_n = 0; while ((1 << lglg_n) <= max_depth) ++lglg_n; par_dblng_.assign(lglg_n + 1, std::vector<int>(heavy_size(), -1)); for (int i = 0; i < heavy_size(); ++i) par_dblng_[0][i] = par_[head_[i]] == -1 ? head_[i] : par_[head_[i]]; for (int i = 0; i < lglg_n; ++i) { for (int j = 0; j < heavy_size(); ++j) { par_dblng_[i + 1][j] = par_dblng_[i][heavy_[par_dblng_[i][j]]]; } } } int size() const noexcept { return n; } int par(int v) const noexcept { assert(0 <= v && v < size()); return par_[v]; } int tree_id(int v) const noexcept { assert(0 <= v && v < size()); return tree_id_[v]; } int tree_cnt() const noexcept { return roots_.size(); } const std::vector<int> & trees() const noexcept { return roots_; } int heavy(int v) const noexcept { assert(0 <= v && v < size()); return heavy_[v]; } int head(int k) const noexcept { assert(0 <= k && k < heavy_size()); return head_[k]; } int heavy_size() const noexcept { return head_.size(); } int heavy_size(int k) const noexcept { assert(0 <= k && k < heavy_size()); return heavy_size_[k]; } int heavy_depth(int k) const noexcept { assert(0 <= k && k < heavy_size()); return heavy_depth_[k]; } int in(int v) const noexcept { assert(0 <= v && v < size()); return in_[v]; } int out(int v) const noexcept { assert(0 <= v && v < size()); return out_[v]; } const std::vector<std::vector<int>> & par_dblng() const noexcept { assert(LCA); return par_dblng_; } std::pair<int, int> lca_heavy(int x, int y) const noexcept { assert(LCA); assert(0 <= x && x < size()); assert(0 <= y && y < size()); assert(tree_id_[x] == tree_id_[y]); if (heavy_[x] == heavy_[y]) return {x, y}; const bool isswap = heavy_depth_[heavy_[x]] < heavy_depth_[heavy_[y]]; if (isswap) std::swap(x, y); const int diff = heavy_depth_[heavy_[x]] - heavy_depth_[heavy_[y]]; for (int i = 0; i < static_cast<int>(par_dblng_.size()); ++i) if (diff >> i & 1) x = par_dblng_[i][heavy_[x]]; if (heavy_[x] == heavy_[y]) return isswap ? std::make_pair(y, x) : std::make_pair(x, y); for (int i = par_dblng_.size() - 1; i >= 0; --i) { const int p1 = par_dblng_[i][heavy_[x]], p2 = par_dblng_[i][heavy_[y]]; if (heavy_[p1] != heavy_[p2]) x = p1, y = p2; } x = par_dblng_[0][heavy_[x]]; y = par_dblng_[0][heavy_[y]]; return isswap ? std::make_pair(y, x) : std::make_pair(x, y); } int lca(int x, int y) { assert(LCA); assert(0 <= x && x < size()); assert(0 <= y && y < size()); assert(tree_id_[x] == tree_id_[y]); const auto [a, b] = lca_heavy(x, y); return in_[a] < in_[b] ? a : b; } }; #line 6 "GraphTheory/HeavyLightDecomposition_Query.hpp" #line 11 "GraphTheory/HeavyLightDecomposition_Query.hpp" /** * @brief https://tkmst201.github.io/Library/GraphTheory/HeavyLightDecomposition_Query.hpp */ template<typename T> struct HeavyLightDecomposition_Query { using value_type = T; using const_reference = const value_type &; using seg_type = SegmentTree<value_type>; using hld_type = HeavyLightDecomposition; using size_type = std::size_t; using Graph = typename hld_type::Graph; using F = std::function<value_type (const_reference, const_reference)>; private: bool VERTEX; value_type id_elem; F f; hld_type hld; seg_type seg, rseg; public: HeavyLightDecomposition_Query(const Graph & g, bool VERTEX, const value_type & id_elem, const F & f) : HeavyLightDecomposition_Query(g, VERTEX, -1, id_elem, f) {} HeavyLightDecomposition_Query(const Graph & g, bool VERTEX, int root, const value_type & id_elem, const F & f) : VERTEX(VERTEX), id_elem(id_elem), f(f), hld(g, root, false) { seg = seg_type{static_cast<size_type>(hld.size()), id_elem, f}; rseg = seg_type{static_cast<size_type>(hld.size()), id_elem, f}; } template<typename U> HeavyLightDecomposition_Query(const Graph & g, const std::vector<U> & v, const value_type & id_elem, const F & f) : HeavyLightDecomposition_Query(g, -1, v, id_elem, f) {} template<typename U> HeavyLightDecomposition_Query(const Graph & g, int root, const std::vector<U> & v, const value_type & id_elem, const F & f) : VERTEX(true), id_elem(id_elem), f(f), hld(g, root, false) { assert(hld.size() == v.size()); std::vector<value_type> init(hld.size()); for (int i = 0; i < hld.size(); ++i) init[hld.in(i)] = v[i]; seg = seg_type{init, id_elem, f}; for (int i = 0; i < hld.heavy_size(); ++i) { const int offset = hld.in(hld.head(i)); std::reverse(begin(init) + offset, begin(init) + offset + hld.heavy_size(i)); } rseg = seg_type{init, id_elem, f}; } const hld_type & get_hld() const noexcept { return get_hld; } void set(int v, const_reference x) noexcept { assert(VERTEX); assert(0 <= v && v < hld.size()); set_(v, x); } value_type get(int v) const noexcept { assert(VERTEX); assert(0 <= v && v < hld.size()); return get_(v); } void set(int u, int v, const_reference x) noexcept { assert(!VERTEX); assert(0 <= u && u < hld.size()); assert(0 <= v && v < hld.size()); assert(hld.par(u) == v || hld.par(v) == u); set_(hld.par(u) == v ? u : v, x); } value_type get(int u, int v) const noexcept { assert(!VERTEX); assert(0 <= u && u < hld.size()); assert(0 <= v && v < hld.size()); assert(hld.par(u) == v || hld.par(v) == u); return get_(hld.par(u) == v ? u : v); } private: void set_(int v, const_reference x) noexcept { seg.set(hld.in(v), x); rseg.set(reverse_idx(v), x); } value_type get_(int v) const noexcept { return seg.get(hld.in(v)); } int reverse_idx(int v) const noexcept { const int id = hld.heavy(v); return (hld.in(hld.head(id)) << 1) + hld.heavy_size(id) - hld.in(v) - 1; } public: value_type fold(int u, int v) const noexcept { assert(0 <= u && u < hld.size()); assert(0 <= v && v < hld.size()); assert(hld.tree_id(u) == hld.tree_id(v)); value_type lv = id_elem, rv = id_elem; while (hld.heavy(u) != hld.heavy(v)) { if (hld.heavy_depth(hld.heavy(u)) >= hld.heavy_depth(hld.heavy(v))) { const int head = hld.head(hld.heavy(u)); lv = f(lv, rseg.fold(reverse_idx(u), reverse_idx(head) + 1)); u = hld.par(head); } if (hld.heavy(u) == hld.heavy(v)) break; if (hld.heavy_depth(hld.heavy(u)) <= hld.heavy_depth(hld.heavy(v))) { const int head = hld.head(hld.heavy(v)); rv = f(seg.fold(hld.in(head), hld.in(v) + 1), rv); v = hld.par(head); } } if (hld.in(u) < hld.in(v)) rv = f(seg.fold(hld.in(u) + !VERTEX, hld.in(v) + 1), rv); else lv = f(lv, rseg.fold(reverse_idx(u), reverse_idx(v) + VERTEX)); return f(lv, rv); } value_type subtree_sum(int v) const noexcept { assert(0 <= v && v < hld.size()); return seg.fold(hld.in(v) + !VERTEX, hld.out(v)); } }; #line 5 "Test/HeavyLightDecomposition_Query.PathQuery.test.cpp" #include <cstdio> #line 9 "Test/HeavyLightDecomposition_Query.PathQuery.test.cpp" int main() { int N, Q; scanf("%d %d", &N, &Q); using mint = ModInt<998244353>; using P = std::pair<mint, mint>; using HLD = HeavyLightDecomposition_Query<P>; std::vector<P> init(N); for (int i = 0; i < N; ++i) { int a, b; scanf("%d %d", &a, &b); init[i] = {a, b}; } HLD::Graph g(N); for (int i = 0; i < N - 1; ++i) { int u, v; scanf("%d %d", &u, &v); g[u].emplace_back(v); g[v].emplace_back(u); } HLD hld(g, init, {1, 0}, [](auto && x, auto && y) -> P { return {x.first * y.first, x.second * y.first + y.second}; }); while (Q--) { int q; scanf("%d", &q); if (q == 0) { int p, c, d; scanf("%d %d %d", &p, &c, &d); hld.set(p, {c, d}); } else { int u, v, x; scanf("%d %d %d", &u, &v, &x); auto res = hld.fold(u, v); printf("%d\n", (res.first * x + res.second).val()); } } }