This documentation is automatically generated by online-judge-tools/verification-helper
View the Project on GitHub ebi-fly13/Library
#define PROBLEM "https://judge.yosupo.jp/problem/stern_brocot_tree" #include "../../math/stern_brocot_tree.hpp" #include "../../template/template.hpp" namespace ebi { void main_() { std::string type; std::cin >> type; if (type == "ENCODE_PATH") { i64 a, b; std::cin >> a >> b; auto path = stern_brocot_tree::encode_path({a, b}); stern_brocot_tree::print_path(path); } else if (type == "DECODE_PATH") { int k; std::cin >> k; std::vector<std::pair<char, i64>> path(k); for (auto &[c, n] : path) { std::cin >> c >> n; } auto lr = stern_brocot_tree::decode_path(path); auto f = stern_brocot_tree::val(lr); std::cout << f << '\n'; } else if (type == "LCA") { i64 a, b, c, d; std::cin >> a >> b >> c >> d; std::cout << stern_brocot_tree::lca({a, b}, {c, d}) << '\n'; } else if (type == "ANCESTOR") { i64 k, a, b; std::cin >> k >> a >> b; auto f = stern_brocot_tree::ancestor(k, {a, b}); if (f) { std::cout << f.value() << '\n'; } else { std::cout << "-1\n"; } } else if (type == "RANGE") { i64 a, b; std::cin >> a >> b; std::cout << stern_brocot_tree::range({a, b}) << '\n'; } } } // namespace ebi int main() { ebi::fast_io(); int t = 1; std::cin >> t; while (t--) { ebi::main_(); } return 0; }
#line 1 "test/math/Stern-Brocot_Tree.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/stern_brocot_tree" #line 2 "math/stern_brocot_tree.hpp" #include <algorithm> #include <cassert> #include <concepts> #include <cstdint> #include <iostream> #include <optional> #include <vector> /* reference: https://miscalc.hatenablog.com/entry/2023/12/22/213007 https://rsk0315.hatenablog.com/entry/2023/04/17/022705 https://atcoder.jp/contests/abc294/editorial/6017 */ namespace ebi { struct stern_brocot_tree { private: using value_type = std::int64_t; using T = value_type; using Fraction = std::pair<T, T>; static Fraction add(const Fraction &lhs, const Fraction &rhs) { return {lhs.first + rhs.first, lhs.second + rhs.second}; } static Fraction mul(const T k, const Fraction &a) { return {k * a.first, k * a.second}; } static bool compare(Fraction a, Fraction b) { return __int128_t(a.first) * b.second < __int128_t(a.second) * b.first; } static void euler_tour_order(std::vector<Fraction> &fs) { std::sort(fs.begin(), fs.end(), [&](Fraction a, Fraction b) -> bool { if (a == b) return false; if (in_subtree(a, b)) return false; if (in_subtree(b, a)) return true; return compare(a, b); }); } public: stern_brocot_tree() = default; static std::vector<T> encode_path(const Fraction &f) { auto [x, y] = f; std::vector<T> path; while (x != y) { T m = (x - 1) / y; path.emplace_back(m); x -= m * y; std::swap(x, y); } return path; } static std::pair<Fraction, Fraction> decode_path( const std::vector<T> &path) { T lx = 0, ly = 1, rx = 1, ry = 0; for (bool is_right = true; auto n : path) { if (is_right) { lx += rx * n; ly += ry * n; } else { rx += lx * n; ry += ly * n; } is_right = !is_right; } return {{lx, ly}, {rx, ry}}; } static std::pair<Fraction, Fraction> decode_path( const std::vector<std::pair<char, T>> &path) { if (path.empty()) { return {{0, 1}, {1, 0}}; } std::vector<T> p; bool is_right = true; if (path[0].first == 'L') { p.emplace_back(0); is_right = !is_right; } for (auto [c, n] : path) { assert(c == (is_right ? 'R' : 'L')); p.emplace_back(n); is_right = !is_right; } return decode_path(p); } static Fraction lca(Fraction f, Fraction g) { auto path_f = encode_path(f); auto path_g = encode_path(g); std::vector<T> path_h; for (int i = 0; i < (int)std::min(path_f.size(), path_g.size()); i++) { T k = std::min(path_f[i], path_g[i]); path_h.emplace_back(k); if (path_f[i] != path_g[i]) { break; } } return val(decode_path(path_h)); } static std::optional<Fraction> ancestor(T k, Fraction f) { std::vector<T> path; for (auto n : encode_path(f)) { T m = std::min(k, n); path.emplace_back(m); k -= m; if (k == 0) break; } if (k > 0) return std::nullopt; return val(decode_path(path)); } static std::pair<Fraction, Fraction> range(Fraction f) { return decode_path(encode_path(f)); } template <class F> static Fraction binary_search(const T max_value, F f) { Fraction l = {0, 1}, r = {1, 0}; while (true) { Fraction now = val({l, r}); bool flag = f(now); Fraction from = flag ? l : r; Fraction to = flag ? r : l; T ok = 1, ng = 2; while (f(add(from, mul(ng, to))) == flag) { ok <<= 1; ng <<= 1; auto nxt = add(from, mul(ok, to)); if (nxt.first > max_value || nxt.second > max_value) return to; } while (ng - ok > 1) { T mid = (ok + ng) >> 1; if (f(add(from, mul(mid, to))) == flag) { ok = mid; } else { ng = mid; } } (flag ? l : r) = add(from, mul(ok, to)); } assert(0); return l; } static std::pair<Fraction, Fraction> nearest_fraction(T max, Fraction f) { Fraction l = {0, 1}, r = {1, 0}; for (bool is_right = true; auto n : encode_path(f)) { Fraction nl = l, nr = r; if (is_right) { nl = add(l, mul(n, r)); } else { nr = add(r, mul(n, l)); } if (std::max(nl.second, nr.second) > max) { nl = l, nr = r; if (is_right) { T x = (max - l.second) / r.second; nl.first += r.first * x; nl.second += r.second * x; } else { T x = (max - r.second) / l.second; nr.first += l.first * x; nr.second += l.second * x; } std::swap(l, nl); std::swap(r, nr); break; } std::swap(l, nl); std::swap(r, nr); is_right = !is_right; } return {l, r}; } static Fraction best_rational_within_an_interval(Fraction l, Fraction r) { Fraction m = lca(l, r); if (l == m) { Fraction rch = childs(l).second; if (rch == r) { return childs(r).first; } else { return rch; } } else if (r == m) { Fraction lch = childs(r).first; if (lch == l) { return childs(l).second; } else { return lch; } } else { return m; } } static std::vector<std::pair<Fraction, int>> lca_based_auxiliary_tree_euler_tour_order(std::vector<Fraction> fs) { if (fs.empty()) return {}; euler_tour_order(fs); fs.erase(std::unique(fs.begin(), fs.end()), fs.end()); int n = (int)fs.size(); for (int i = 0; i < n - 1; i++) { fs.emplace_back(lca(fs[i], fs[i + 1])); } euler_tour_order(fs); fs.erase(std::unique(fs.begin(), fs.end()), fs.end()); n = (int)fs.size(); std::vector<std::pair<Fraction, int>> tree(n); std::vector<int> stack = {0}; tree[0] = {fs[0], -1}; for (int i = 1; i < n; i++) { while (!in_subtree(fs[i], fs[stack.back()])) { stack.pop_back(); } tree[i] = {fs[i], stack.back()}; stack.emplace_back(i); } return tree; } static std::pair<Fraction, Fraction> childs(Fraction f) { auto [l, r] = range(f); return {add(l, f), add(f, r)}; } static bool in_subtree(Fraction f, Fraction g) { auto [l, r] = range(g); return compare(l, f) && compare(f, r); } static T depth(Fraction f) { T d = 0; for (auto n : encode_path(f)) d += n; return d; } static Fraction val(const std::pair<Fraction, Fraction> &f) { return add(f.first, f.second); } static void print_path(const std::vector<T> &path) { if (path.empty()) { std::cout << "0\n"; return; } int k = (int)path.size() - int(path[0] == 0); std::cout << k; for (bool is_right = true; auto c : path) { if (c > 0) { std::cout << " " << (is_right ? 'R' : 'L') << " " << c; } is_right = !is_right; } std::cout << '\n'; return; } }; } // namespace ebi #line 1 "template/template.hpp" #include <bits/stdc++.h> #define rep(i, a, n) for (int i = (int)(a); i < (int)(n); i++) #define rrep(i, a, n) for (int i = ((int)(n)-1); i >= (int)(a); i--) #define Rep(i, a, n) for (i64 i = (i64)(a); i < (i64)(n); i++) #define RRep(i, a, n) for (i64 i = ((i64)(n)-i64(1)); i >= (i64)(a); i--) #define all(v) (v).begin(), (v).end() #define rall(v) (v).rbegin(), (v).rend() #line 2 "template/debug_template.hpp" #line 4 "template/debug_template.hpp" namespace ebi { #ifdef LOCAL #define debug(...) \ std::cerr << "LINE: " << __LINE__ << " [" << #__VA_ARGS__ << "]:", \ debug_out(__VA_ARGS__) #else #define debug(...) #endif void debug_out() { std::cerr << std::endl; } template <typename Head, typename... Tail> void debug_out(Head h, Tail... t) { std::cerr << " " << h; if (sizeof...(t) > 0) std::cerr << " :"; debug_out(t...); } } // namespace ebi #line 2 "template/int_alias.hpp" #line 4 "template/int_alias.hpp" namespace ebi { using ld = long double; using std::size_t; using i8 = std::int8_t; using u8 = std::uint8_t; using i16 = std::int16_t; using u16 = std::uint16_t; using i32 = std::int32_t; using u32 = std::uint32_t; using i64 = std::int64_t; using u64 = std::uint64_t; using i128 = __int128_t; using u128 = __uint128_t; } // namespace ebi #line 2 "template/io.hpp" #line 7 "template/io.hpp" namespace ebi { template <typename T1, typename T2> std::ostream &operator<<(std::ostream &os, const std::pair<T1, T2> &pa) { return os << pa.first << " " << pa.second; } template <typename T1, typename T2> std::istream &operator>>(std::istream &os, std::pair<T1, T2> &pa) { return os >> pa.first >> pa.second; } template <typename T> std::ostream &operator<<(std::ostream &os, const std::vector<T> &vec) { for (std::size_t i = 0; i < vec.size(); i++) os << vec[i] << (i + 1 == vec.size() ? "" : " "); return os; } template <typename T> std::istream &operator>>(std::istream &os, std::vector<T> &vec) { for (T &e : vec) std::cin >> e; return os; } template <typename T> std::ostream &operator<<(std::ostream &os, const std::optional<T> &opt) { if (opt) { os << opt.value(); } else { os << "invalid value"; } return os; } void fast_io() { std::cout << std::fixed << std::setprecision(15); std::cin.tie(nullptr); std::ios::sync_with_stdio(false); } } // namespace ebi #line 2 "template/utility.hpp" #line 5 "template/utility.hpp" #line 2 "graph/base.hpp" #line 5 "graph/base.hpp" #include <ranges> #line 7 "graph/base.hpp" #line 2 "data_structure/simple_csr.hpp" #line 6 "data_structure/simple_csr.hpp" namespace ebi { template <class E> struct simple_csr { simple_csr() = default; simple_csr(int n, const std::vector<std::pair<int, E>>& elements) : start(n + 1, 0), elist(elements.size()) { for (auto e : elements) { start[e.first + 1]++; } for (auto i : std::views::iota(0, n)) { start[i + 1] += start[i]; } auto counter = start; for (auto [i, e] : elements) { elist[counter[i]++] = e; } } simple_csr(const std::vector<std::vector<E>>& es) : start(es.size() + 1, 0) { int n = es.size(); for (auto i : std::views::iota(0, n)) { start[i + 1] = (int)es[i].size() + start[i]; } elist.resize(start.back()); for (auto i : std::views::iota(0, n)) { std::copy(es[i].begin(), es[i].end(), elist.begin() + start[i]); } } int size() const { return (int)start.size() - 1; } const auto operator[](int i) const { return std::ranges::subrange(elist.begin() + start[i], elist.begin() + start[i + 1]); } auto operator[](int i) { return std::ranges::subrange(elist.begin() + start[i], elist.begin() + start[i + 1]); } const auto operator()(int i, int l, int r) const { return std::ranges::subrange(elist.begin() + start[i] + l, elist.begin() + start[i + 1] + r); } auto operator()(int i, int l, int r) { return std::ranges::subrange(elist.begin() + start[i] + l, elist.begin() + start[i + 1] + r); } private: std::vector<int> start; std::vector<E> elist; }; } // namespace ebi #line 9 "graph/base.hpp" namespace ebi { template <class T> struct Edge { int from, to; T cost; int id; }; template <class E> struct Graph { using cost_type = E; using edge_type = Edge<cost_type>; Graph(int n_) : n(n_) {} Graph() = default; void add_edge(int u, int v, cost_type c) { buff.emplace_back(u, edge_type{u, v, c, m}); edges.emplace_back(edge_type{u, v, c, m++}); } void add_undirected_edge(int u, int v, cost_type c) { buff.emplace_back(u, edge_type{u, v, c, m}); buff.emplace_back(v, edge_type{v, u, c, m}); edges.emplace_back(edge_type{u, v, c, m}); m++; } void read_tree(int offset = 1, bool is_weighted = false) { read_graph(n - 1, offset, false, is_weighted); } void read_parents(int offset = 1) { for (auto i : std::views::iota(1, n)) { int p; std::cin >> p; p -= offset; add_undirected_edge(p, i, 1); } build(); } void read_graph(int e, int offset = 1, bool is_directed = false, bool is_weighted = false) { for (int i = 0; i < e; i++) { int u, v; std::cin >> u >> v; u -= offset; v -= offset; if (is_weighted) { cost_type c; std::cin >> c; if (is_directed) { add_edge(u, v, c); } else { add_undirected_edge(u, v, c); } } else { if (is_directed) { add_edge(u, v, 1); } else { add_undirected_edge(u, v, 1); } } } build(); } void build() { assert(!prepared); csr = simple_csr<edge_type>(n, buff); buff.clear(); prepared = true; } int size() const { return n; } int node_number() const { return n; } int edge_number() const { return m; } edge_type get_edge(int i) const { return edges[i]; } std::vector<edge_type> get_edges() const { return edges; } const auto operator[](int i) const { return csr[i]; } auto operator[](int i) { return csr[i]; } private: int n, m = 0; std::vector<std::pair<int,edge_type>> buff; std::vector<edge_type> edges; simple_csr<edge_type> csr; bool prepared = false; }; } // namespace ebi #line 8 "template/utility.hpp" namespace ebi { template <class T> inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; } return false; } template <class T> inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; } return false; } template <class T> T safe_ceil(T a, T b) { if (a % b == 0) return a / b; else if (a >= 0) return (a / b) + 1; else return -((-a) / b); } template <class T> T safe_floor(T a, T b) { if (a % b == 0) return a / b; else if (a >= 0) return a / b; else return -((-a) / b) - 1; } constexpr i64 LNF = std::numeric_limits<i64>::max() / 4; constexpr int INF = std::numeric_limits<int>::max() / 2; const std::vector<int> dy = {1, 0, -1, 0, 1, 1, -1, -1}; const std::vector<int> dx = {0, 1, 0, -1, 1, -1, 1, -1}; } // namespace ebi #line 5 "test/math/Stern-Brocot_Tree.test.cpp" namespace ebi { void main_() { std::string type; std::cin >> type; if (type == "ENCODE_PATH") { i64 a, b; std::cin >> a >> b; auto path = stern_brocot_tree::encode_path({a, b}); stern_brocot_tree::print_path(path); } else if (type == "DECODE_PATH") { int k; std::cin >> k; std::vector<std::pair<char, i64>> path(k); for (auto &[c, n] : path) { std::cin >> c >> n; } auto lr = stern_brocot_tree::decode_path(path); auto f = stern_brocot_tree::val(lr); std::cout << f << '\n'; } else if (type == "LCA") { i64 a, b, c, d; std::cin >> a >> b >> c >> d; std::cout << stern_brocot_tree::lca({a, b}, {c, d}) << '\n'; } else if (type == "ANCESTOR") { i64 k, a, b; std::cin >> k >> a >> b; auto f = stern_brocot_tree::ancestor(k, {a, b}); if (f) { std::cout << f.value() << '\n'; } else { std::cout << "-1\n"; } } else if (type == "RANGE") { i64 a, b; std::cin >> a >> b; std::cout << stern_brocot_tree::range({a, b}) << '\n'; } } } // namespace ebi int main() { ebi::fast_io(); int t = 1; std::cin >> t; while (t--) { ebi::main_(); } return 0; }