sotanishy's code snippets for competitive programming
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#define PROBLEM "https://judge.yosupo.jp/problem/vertex_set_path_composite" #include <bits/stdc++.h> #include "../../data-structure/segtree/segment_tree.hpp" #include "../../math/modint.hpp" #include "../../tree/hld.hpp" using namespace std; using ll = long long; using mint = Modint<998244353>; struct AffineMonoid { using T = pair<pair<mint, mint>, pair<mint, mint>>; static T id() { return {{1, 0}, {1, 0}}; } static T op(T a, T b) { return { {a.first.first * b.first.first, a.first.second * b.first.first + b.first.second}, {b.second.first * a.second.first, b.second.second * a.second.first + a.second.second}, }; } }; int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); int N, Q; cin >> N >> Q; vector<pair<pair<mint, mint>, pair<mint, mint>>> ab(N); for (int i = 0; i < N; ++i) { mint a, b; cin >> a >> b; ab[i] = {{a, b}, {a, b}}; } vector<vector<int>> G(N); for (int i = 0; i < N - 1; ++i) { int u, v; cin >> u >> v; G[u].push_back(v); G[v].push_back(u); } HLD<AffineMonoid> hld(G, false); SegmentTree<AffineMonoid> st(N); auto update = [&](int k, const AffineMonoid::T& p) { st.update(k, p); }; auto fold = [&](int l, int r) { return st.fold(l, r); }; auto flip = [&](AffineMonoid::T& a) { return make_pair(a.second, a.first); }; for (int i = 0; i < N; ++i) hld.update(i, ab[i], update); for (int i = 0; i < Q; ++i) { int t; cin >> t; if (t == 0) { int p, c, d; cin >> p >> c >> d; hld.update(p, {{c, d}, {c, d}}, update); } else { int u, v, x; cin >> u >> v >> x; auto a = hld.path_fold(u, v, fold, flip).first; cout << a.first * x + a.second << "\n"; } } }
#line 1 "test/yosupo/vertex_set_path_composite.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/vertex_set_path_composite" #include <bits/stdc++.h> #line 3 "data-structure/segtree/segment_tree.hpp" #include <bit> #line 5 "data-structure/segtree/segment_tree.hpp" template <typename M> class SegmentTree { using T = M::T; public: SegmentTree() = default; explicit SegmentTree(int n) : SegmentTree(std::vector<T>(n, M::id())) {} explicit SegmentTree(const std::vector<T>& v) : size(std::bit_ceil(v.size())), node(2 * size, M::id()) { std::ranges::copy(v, node.begin() + size); for (int i = size - 1; i > 0; --i) { node[i] = M::op(node[2 * i], node[2 * i + 1]); } } T operator[](int k) const { return node[k + size]; } void update(int k, const T& x) { k += size; node[k] = x; while (k >>= 1) node[k] = M::op(node[2 * k], node[2 * k + 1]); } T fold(int l, int r) const { T vl = M::id(), vr = M::id(); for (l += size, r += size; l < r; l >>= 1, r >>= 1) { if (l & 1) vl = M::op(vl, node[l++]); if (r & 1) vr = M::op(node[--r], vr); } return M::op(vl, vr); } template <typename F> int find_first(int l, F cond) const { T v = M::id(); for (l += size; l > 0; l >>= 1) { if (l & 1) { T nv = M::op(v, node[l]); if (cond(nv)) { while (l < size) { nv = M::op(v, node[2 * l]); if (cond(nv)) { l = 2 * l; } else { v = nv, l = 2 * l + 1; } } return l + 1 - size; } v = nv; ++l; } } return -1; } template <typename F> int find_last(int r, F cond) const { T v = M::id(); for (r += size; r > 0; r >>= 1) { if (r & 1) { --r; T nv = M::op(node[r], v); if (cond(nv)) { while (r < size) { nv = M::op(node[2 * r + 1], v); if (cond(nv)) { r = 2 * r + 1; } else { v = nv, r = 2 * r; } } return r - size; } v = nv; } } return -1; } private: int size; std::vector<T> node; }; #line 4 "math/modint.hpp" /** * @brief Mod int */ template <int m> class Modint { using mint = Modint; static_assert(m > 0, "Modulus must be positive"); public: static constexpr int mod() { return m; } constexpr Modint(long long y = 0) : x(y >= 0 ? y % m : (y % m + m) % m) {} constexpr int val() const { return x; } constexpr mint& operator+=(const mint& r) { if ((x += r.x) >= m) x -= m; return *this; } constexpr mint& operator-=(const mint& r) { if ((x += m - r.x) >= m) x -= m; return *this; } constexpr mint& operator*=(const mint& r) { x = static_cast<int>(1LL * x * r.x % m); return *this; } constexpr mint& operator/=(const mint& r) { return *this *= r.inv(); } constexpr bool operator==(const mint& r) const { return x == r.x; } constexpr mint operator+() const { return *this; } constexpr mint operator-() const { return mint(-x); } constexpr friend mint operator+(const mint& l, const mint& r) { return mint(l) += r; } constexpr friend mint operator-(const mint& l, const mint& r) { return mint(l) -= r; } constexpr friend mint operator*(const mint& l, const mint& r) { return mint(l) *= r; } constexpr friend mint operator/(const mint& l, const mint& r) { return mint(l) /= r; } constexpr mint inv() const { int a = x, b = m, u = 1, v = 0; while (b > 0) { int t = a / b; std::swap(a -= t * b, b); std::swap(u -= t * v, v); } return mint(u); } constexpr mint pow(long long n) const { mint ret(1), mul(x); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend std::ostream& operator<<(std::ostream& os, const mint& r) { return os << r.x; } friend std::istream& operator>>(std::istream& is, mint& r) { long long t; is >> t; r = mint(t); return is; } private: int x; }; #line 4 "tree/hld.hpp" template <typename M> class HLD { using T = M::T; public: HLD() = default; HLD(const std::vector<std::vector<int>>& G, bool edge) : G(G), size(G.size()), depth(G.size()), par(G.size(), -1), in(G.size()), out(G.size()), head(G.size()), heavy(G.size(), -1), edge(edge) { dfs(0); decompose(0, 0); } template <typename F> void update(int v, const T& x, const F& f) const { f(in[v], x); } template <typename F> void update_edge(int u, int v, const T& x, const F& f) const { if (in[u] > in[v]) std::swap(u, v); f(in[v], x); } template <typename E, typename F> void update(int u, int v, const E& x, const F& f) const { while (head[u] != head[v]) { if (in[head[u]] > in[head[v]]) std::swap(u, v); f(in[head[v]], in[v] + 1, x); v = par[head[v]]; } if (in[u] > in[v]) std::swap(u, v); f(in[u] + edge, in[v] + 1, x); } template <typename F, typename Flip> T path_fold(int u, int v, const F& f, const Flip& flip) const { bool flipped = false; T resu = M::id(), resv = M::id(); while (head[u] != head[v]) { if (in[head[u]] > in[head[v]]) { std::swap(u, v); std::swap(resu, resv); flipped ^= true; } T val = f(in[head[v]], in[v] + 1); resv = M::op(val, resv); v = par[head[v]]; } if (in[u] > in[v]) { std::swap(u, v); std::swap(resu, resv); flipped ^= true; } T val = f(in[u] + edge, in[v] + 1); resv = M::op(val, resv); resv = M::op(flip(resu), resv); if (flipped) { resv = flip(resv); } return resv; } template <typename F> T path_fold(int u, int v, const F& f) const { return path_fold(u, v, f, [&](auto& v) { return v; }); } template <typename F> T subtree_fold(int v, const F& f) const { return f(in[v] + edge, out[v]); } int lca(int u, int v) const { while (true) { if (in[u] > in[v]) std::swap(u, v); if (head[u] == head[v]) return u; v = par[head[v]]; } } int dist(int u, int v) const { return depth[u] + depth[v] - 2 * depth[lca(u, v)]; } private: std::vector<std::vector<int>> G; std::vector<int> size, depth, par, in, out, head, heavy; bool edge; int cur_pos = 0; void dfs(int v) { size[v] = 1; int max_size = 0; for (int c : G[v]) { if (c == par[v]) continue; par[c] = v; depth[c] = depth[v] + 1; dfs(c); size[v] += size[c]; if (size[c] > max_size) { max_size = size[c]; heavy[v] = c; } } } void decompose(int v, int h) { head[v] = h; in[v] = cur_pos++; if (heavy[v] != -1) decompose(heavy[v], h); for (int c : G[v]) { if (c != par[v] && c != heavy[v]) decompose(c, c); } out[v] = cur_pos; } }; #line 8 "test/yosupo/vertex_set_path_composite.test.cpp" using namespace std; using ll = long long; using mint = Modint<998244353>; struct AffineMonoid { using T = pair<pair<mint, mint>, pair<mint, mint>>; static T id() { return {{1, 0}, {1, 0}}; } static T op(T a, T b) { return { {a.first.first * b.first.first, a.first.second * b.first.first + b.first.second}, {b.second.first * a.second.first, b.second.second * a.second.first + a.second.second}, }; } }; int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); int N, Q; cin >> N >> Q; vector<pair<pair<mint, mint>, pair<mint, mint>>> ab(N); for (int i = 0; i < N; ++i) { mint a, b; cin >> a >> b; ab[i] = {{a, b}, {a, b}}; } vector<vector<int>> G(N); for (int i = 0; i < N - 1; ++i) { int u, v; cin >> u >> v; G[u].push_back(v); G[v].push_back(u); } HLD<AffineMonoid> hld(G, false); SegmentTree<AffineMonoid> st(N); auto update = [&](int k, const AffineMonoid::T& p) { st.update(k, p); }; auto fold = [&](int l, int r) { return st.fold(l, r); }; auto flip = [&](AffineMonoid::T& a) { return make_pair(a.second, a.first); }; for (int i = 0; i < N; ++i) hld.update(i, ab[i], update); for (int i = 0; i < Q; ++i) { int t; cin >> t; if (t == 0) { int p, c, d; cin >> p >> c >> d; hld.update(p, {{c, d}, {c, d}}, update); } else { int u, v, x; cin >> u >> v >> x; auto a = hld.path_fold(u, v, fold, flip).first; cout << a.first * x + a.second << "\n"; } } }