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#include "datastructure/dynamic_li_chao_tree.hpp"
dynamic_li_chao_tree(min_index = -1e9, max_index = 1e9)
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add_line(a, b)
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add_segment(a, b, l, r)
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get(x)
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#include <algorithm> #include <limits> struct dynamic_li_chao_tree { public: dynamic_li_chao_tree(long long min_index = -1'000'000'000, long long max_index = 1'000'000'000) : min_index(min_index), max_index(max_index + 1), root(nullptr) { } void add_line(long long a, long long b) { Line line = Line{a, b}; add_line(root, min_index, max_index, line); } void add_segment(long long a, long long b, long long l_lim, long long r_lim) { Line line = Line{a, b}; add_segment(root, l_lim, r_lim, min_index, max_index, line); } long long get(long long x) { node* t = root; long long l = min_index, r = max_index; long long ret = std::numeric_limits<long long>::max(); while (r - l > 0 && t != nullptr) { long long m = (l + r) >> 1; ret = std::min(ret, t->line.f(x)); if (x < m) { r = m; t = t->left; } else { l = m; t = t->right; } } return ret; } private: struct Line { long long slope, intercept; Line() : slope(0), intercept(std::numeric_limits<long long>::max()) { } Line(long long a, long long b) : slope(a), intercept(b) { } long long f(long long x) { return slope * x + intercept; } }; struct node { Line line; node *left, *right; node(Line line) : line(line), left(nullptr), right(nullptr) { } }; const long long min_index, max_index; node* root; node* add_line(node*& t, long long l, long long r, Line line) const { if (l == r) return nullptr; if (!t) { t = new node(line); return t; } long long m = (l + r) >> 1; bool check_l = (line.f(l) <= t->line.f(l)); bool check_m = (line.f(m) <= t->line.f(m)); bool check_r = (line.f(r) <= t->line.f(r)); if (check_l && check_r) { t->line = line; return t; } if (!check_l && !check_r) { return t; } if (check_m) { std::swap(t->line, line); } if (check_l != check_m) { t->left = add_line(t->left, l, m, line); } else { t->right = add_line(t->right, m + 1, r, line); } return t; } node* add_segment(node*& t, long long l_lim, long long r_lim, long long l, long long r, Line line) { if (r <= l_lim || r_lim <= l) return t; if (l_lim <= l && r <= r_lim) return add_line(t, l, r, line); if (t == nullptr) t = new node(Line()); long long m = (l + r) >> 1; t->left = add_segment(t->left, l_lim, r_lim, l, m, line); t->right = add_segment(t->right, l_lim, r_lim, m, r, line); return t; } };
#line 1 "datastructure/dynamic_li_chao_tree.hpp" #include <algorithm> #include <limits> struct dynamic_li_chao_tree { public: dynamic_li_chao_tree(long long min_index = -1'000'000'000, long long max_index = 1'000'000'000) : min_index(min_index), max_index(max_index + 1), root(nullptr) { } void add_line(long long a, long long b) { Line line = Line{a, b}; add_line(root, min_index, max_index, line); } void add_segment(long long a, long long b, long long l_lim, long long r_lim) { Line line = Line{a, b}; add_segment(root, l_lim, r_lim, min_index, max_index, line); } long long get(long long x) { node* t = root; long long l = min_index, r = max_index; long long ret = std::numeric_limits<long long>::max(); while (r - l > 0 && t != nullptr) { long long m = (l + r) >> 1; ret = std::min(ret, t->line.f(x)); if (x < m) { r = m; t = t->left; } else { l = m; t = t->right; } } return ret; } private: struct Line { long long slope, intercept; Line() : slope(0), intercept(std::numeric_limits<long long>::max()) { } Line(long long a, long long b) : slope(a), intercept(b) { } long long f(long long x) { return slope * x + intercept; } }; struct node { Line line; node *left, *right; node(Line line) : line(line), left(nullptr), right(nullptr) { } }; const long long min_index, max_index; node* root; node* add_line(node*& t, long long l, long long r, Line line) const { if (l == r) return nullptr; if (!t) { t = new node(line); return t; } long long m = (l + r) >> 1; bool check_l = (line.f(l) <= t->line.f(l)); bool check_m = (line.f(m) <= t->line.f(m)); bool check_r = (line.f(r) <= t->line.f(r)); if (check_l && check_r) { t->line = line; return t; } if (!check_l && !check_r) { return t; } if (check_m) { std::swap(t->line, line); } if (check_l != check_m) { t->left = add_line(t->left, l, m, line); } else { t->right = add_line(t->right, m + 1, r, line); } return t; } node* add_segment(node*& t, long long l_lim, long long r_lim, long long l, long long r, Line line) { if (r <= l_lim || r_lim <= l) return t; if (l_lim <= l && r <= r_lim) return add_line(t, l, r, line); if (t == nullptr) t = new node(Line()); long long m = (l + r) >> 1; t->left = add_segment(t->left, l_lim, r_lim, l, m, line); t->right = add_segment(t->right, l_lim, r_lim, m, r, line); return t; } };