test/yosupo/min_plus_convolution_convex_arbitrary.LiCT.test.cpp

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• Last update: 2024-09-01 12:11:12+09:00
• Problem: https://judge.yosupo.jp/problem/min_plus_convolution_convex_arbitrary

Depends on

• 関数型や関数オブジェクトに関するテンプレート (src/Internal/function_traits.hpp)
• Li-Chao-Tree (src/Optimization/LiChaoTree.hpp)
• 最大最小を指定するための列挙型 (src/Optimization/MinMaxEnum.hpp)

Code

// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/min_plus_convolution_convex_arbitrary
// competitive-verifier: TLE 1
// competitive-verifier: MLE 64
#include <iostream>
#include "src/Optimization/LiChaoTree.hpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int N, M;
 cin >> N >> M;
 long long a[N], b[M];
 for (int i= 0; i < N; ++i) cin >> a[i];
 for (int j= 0; j < M; ++j) cin >> b[j];
 LiChaoTree lct([&](int i, int j) { return a[i - j] + b[j]; }, 0, N + M - 1);
 auto tree= lct.make_tree<MINIMIZE>();
 for (int j= 0; j < M; ++j) tree.insert(j, j, N + j);
 for (int i= 0; i < N + M - 1; ++i) cout << tree.query(i).first << " \n"[i == N + M - 2];
 return 0;
}

#line 1 "test/yosupo/min_plus_convolution_convex_arbitrary.LiCT.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/min_plus_convolution_convex_arbitrary
// competitive-verifier: TLE 1
// competitive-verifier: MLE 64
#include <iostream>
#line 2 "src/Optimization/LiChaoTree.hpp"
#include <limits>
#include <algorithm>
#include <vector>
#include <tuple>
#include <cassert>
#line 2 "src/Internal/function_traits.hpp"
#include <type_traits>
// clang-format off
namespace function_template_internal{
template<class C>struct is_function_object{
 template<class U,int dummy=(&U::operator(),0)> static std::true_type check(U *);
 static std::false_type check(...);
 static C *m;
 static constexpr bool value= decltype(check(m))::value;
};
template<class F,bool,bool>struct function_type_impl{using type= void;};
template<class F>struct function_type_impl<F,true,false>{using type= F *;};
template<class F>struct function_type_impl<F,false,true>{using type= decltype(&F::operator());};
template<class F> using function_type_t= typename function_type_impl<F,std::is_function_v<F>,is_function_object<F>::value>::type;
template<class... Args>struct result_type_impl{using type= void;};
template<class R,class... Args>struct result_type_impl<R(*)(Args...)>{using type= R;};
template<class C,class R,class... Args>struct result_type_impl<R(C::*)(Args...)>{using type= R;};
template<class C,class R,class... Args>struct result_type_impl<R(C::*)(Args...)const>{using type= R;};
template<class F> using result_type_t= typename result_type_impl<function_type_t<F>>::type;
template<class... Args>struct argument_type_impl{using type= void;};
template<class R,class... Args>struct argument_type_impl<R(*)(Args...)>{using type= std::tuple<Args...>;};
template<class C,class R,class... Args>struct argument_type_impl<R(C::*)(Args...)>{using type= std::tuple<Args...>;};
template<class C,class R,class... Args>struct argument_type_impl<R(C::*)(Args...)const>{using type= std::tuple<Args...>;};
template<class F> using argument_type_t= typename argument_type_impl<function_type_t<F>>::type;
}
using function_template_internal::result_type_t,function_template_internal::argument_type_t;
// clang-format on
#line 2 "src/Optimization/MinMaxEnum.hpp"
enum MinMaxEnum { MAXIMIZE= -1, MINIMIZE= 1 };
#line 9 "src/Optimization/LiChaoTree.hpp"
template <class F, class T> class LiChaoTree {};
template <class F, class T, class... Prms> class LiChaoTree<F, std::tuple<T, Prms...>> {
 using R= result_type_t<F>;
 F f;
 const T LB, UB;
 std::vector<std::tuple<Prms...>> ps;
 template <MinMaxEnum sgn, bool persistent> class LiChaoTreeInterface {
  LiChaoTree *ins;
  struct Node {
   int id= -1;
   Node *ch[2]= {nullptr, nullptr};
  } *root;
  inline R eval(int id, T x) const { return std::apply(ins->f, std::tuple_cat(std::make_tuple(x), ins->ps[id])); }
  static inline bool cmp(const R &p, const R &n, int pi, int ni) {
   if constexpr (sgn == MINIMIZE) return p > n || (p == n && pi > ni);
   else return p < n || (p == n && pi > ni);
  }
  inline bool cmp(T x, int pi, int ni) const {
   if (ni == -1) return false;
   if (pi == -1) return true;
   return cmp(eval(pi, x), eval(ni, x), pi, ni);
  }
  static inline T ub(T r) {
   if constexpr (std::is_floating_point_v<T>) return r;
   else return r - 1;
  }
  inline void addl(Node *&t, int id, T xl, T xr) {
   if (!t) return t= new Node{id}, void();
   bool bl= cmp(xl, t->id, id), br= cmp(ub(xr), t->id, id);
   if (!bl && !br) return;
   if constexpr (persistent) t= new Node(*t);
   if (bl && br) return t->id= id, void();
   T xm= (xl + xr) / 2;
   if (cmp(xm, t->id, id)) std::swap(t->id, id), bl= !bl;
   if constexpr (std::is_floating_point_v<T>)
    if (xr - xl < 1e-9) return;
   bl ? addl(t->ch[0], id, xl, xm) : addl(t->ch[1], id, xm, xr);
  }
  inline void adds(Node *&t, int id, T l, T r, T xl, T xr) {
   if (r <= xl || xr <= l) return;
   if (l <= xl && xr <= r) return addl(t, id, xl, xr);
   if (!t) t= new Node;
   else if constexpr (persistent) t= new Node(*t);
   T xm= (xl + xr) / 2;
   adds(t->ch[0], id, l, r, xl, xm), adds(t->ch[1], id, l, r, xm, xr);
  }
  inline std::pair<R, int> query(const Node *t, T x, T xl, T xr) const {
   if (!t) return {R(), -1};
   T xm= (xl + xr) / 2;
   auto b= x < xm ? query(t->ch[0], x, xl, xm) : query(t->ch[1], x, xm, xr);
   if (t->id == -1) return b;
   R a= eval(t->id, x);
   return b.second != -1 && cmp(a, b.first, t->id, b.second) ? b : std::make_pair(a, t->id);
  }
 public:
  LiChaoTreeInterface()= default;
  LiChaoTreeInterface(LiChaoTree *ins): ins(ins), root(nullptr) {}
  void insert(const Prms &...args) { ins->ps.emplace_back(args...), addl(root, ins->ps.size() - 1, ins->LB, ins->UB); }
  // [l, r)
  void insert(const Prms &...args, T l, T r) {
   l= std::max(l, ins->LB), r= std::min(r, ins->UB);
   if (l < r) ins->ps.emplace_back(args...), adds(root, ins->ps.size() - 1, l, r, ins->LB, ins->UB);
  }
  // [l, UB)
  void insert(const Prms &...args, T l) { insert(args..., l, ins->UB); }
  std::pair<R, int> query(T x) const { return assert(ins->LB <= x && x < ins->UB), query(root, x, ins->LB, ins->UB); }
  const std::tuple<Prms...> &params(int id) const { return ins->ps[id]; }
 };
public:
 LiChaoTree(const F &f, T LB= -2e9, T UB= 2e9): f(f), LB(LB), UB(UB) {}
 template <MinMaxEnum sgn= MINIMIZE, bool persistent= false> LiChaoTreeInterface<sgn, persistent> make_tree() { return this; }
};
template <class F, class T, class U> LiChaoTree(F, T, U) -> LiChaoTree<F, argument_type_t<F>>;
template <class F, class T> LiChaoTree(F, T) -> LiChaoTree<F, argument_type_t<F>>;
template <class F> LiChaoTree(F) -> LiChaoTree<F, argument_type_t<F>>;
#line 6 "test/yosupo/min_plus_convolution_convex_arbitrary.LiCT.test.cpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int N, M;
 cin >> N >> M;
 long long a[N], b[M];
 for (int i= 0; i < N; ++i) cin >> a[i];
 for (int j= 0; j < M; ++j) cin >> b[j];
 LiChaoTree lct([&](int i, int j) { return a[i - j] + b[j]; }, 0, N + M - 1);
 auto tree= lct.make_tree<MINIMIZE>();
 for (int j= 0; j < M; ++j) tree.insert(j, j, N + j);
 for (int i= 0; i < N + M - 1; ++i) cout << tree.query(i).first << " \n"[i == N + M - 2];
 return 0;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++-13	example_00	AC	5 ms	4 MB
g++-13	hack_00	AC	4 ms	4 MB
g++-13	large_small_00	AC	66 ms	8 MB
g++-13	large_small_01	AC	62 ms	8 MB
g++-13	large_small_02	AC	181 ms	42 MB
g++-13	large_small_03	AC	192 ms	42 MB
g++-13	max_random_00	AC	416 ms	63 MB
g++-13	max_random_01	AC	420 ms	63 MB
g++-13	max_random_02	AC	412 ms	63 MB
g++-13	med_random_00	AC	5 ms	4 MB
g++-13	med_random_01	AC	4 ms	4 MB
g++-13	med_random_02	AC	4 ms	4 MB
g++-13	monotone_00	AC	424 ms	63 MB
g++-13	monotone_01	AC	422 ms	63 MB
g++-13	monotone_02	AC	412 ms	63 MB
g++-13	monotone_03	AC	425 ms	63 MB
g++-13	near_power_of_2_00	AC	213 ms	33 MB
g++-13	near_power_of_2_01	AC	203 ms	33 MB
g++-13	near_power_of_2_02	AC	204 ms	35 MB
g++-13	near_power_of_2_03	AC	205 ms	33 MB
g++-13	near_power_of_2_04	AC	203 ms	33 MB
g++-13	near_power_of_2_05	AC	205 ms	34 MB
g++-13	near_power_of_2_06	AC	204 ms	33 MB
g++-13	near_power_of_2_07	AC	203 ms	33 MB
g++-13	near_power_of_2_08	AC	206 ms	35 MB
g++-13	only_first_small_00	AC	415 ms	63 MB
g++-13	only_first_small_01	AC	414 ms	63 MB
g++-13	random_00	AC	325 ms	49 MB
g++-13	random_01	AC	329 ms	51 MB
g++-13	random_02	AC	225 ms	34 MB
g++-13	small_00	AC	5 ms	4 MB
g++-13	small_01	AC	4 ms	4 MB
g++-13	small_02	AC	4 ms	4 MB
g++-13	small_03	AC	4 ms	4 MB
g++-13	small_04	AC	4 ms	4 MB
g++-13	small_05	AC	4 ms	4 MB
g++-13	small_06	AC	4 ms	4 MB
g++-13	small_07	AC	4 ms	4 MB
g++-13	small_08	AC	4 ms	4 MB
g++-13	small_slopes_00	AC	410 ms	63 MB
g++-13	small_slopes_01	AC	421 ms	63 MB
clang++-18	example_00	AC	5 ms	4 MB
clang++-18	hack_00	AC	4 ms	4 MB
clang++-18	large_small_00	AC	60 ms	8 MB
clang++-18	large_small_01	AC	63 ms	8 MB
clang++-18	large_small_02	AC	195 ms	42 MB
clang++-18	large_small_03	AC	192 ms	42 MB
clang++-18	max_random_00	AC	425 ms	63 MB
clang++-18	max_random_01	AC	437 ms	63 MB
clang++-18	max_random_02	AC	439 ms	63 MB
clang++-18	med_random_00	AC	5 ms	4 MB
clang++-18	med_random_01	AC	4 ms	4 MB
clang++-18	med_random_02	AC	4 ms	4 MB
clang++-18	monotone_00	AC	435 ms	63 MB
clang++-18	monotone_01	AC	417 ms	63 MB
clang++-18	monotone_02	AC	415 ms	63 MB
clang++-18	monotone_03	AC	442 ms	63 MB
clang++-18	near_power_of_2_00	AC	211 ms	33 MB
clang++-18	near_power_of_2_01	AC	214 ms	33 MB
clang++-18	near_power_of_2_02	AC	219 ms	34 MB
clang++-18	near_power_of_2_03	AC	212 ms	33 MB
clang++-18	near_power_of_2_04	AC	214 ms	33 MB
clang++-18	near_power_of_2_05	AC	214 ms	35 MB
clang++-18	near_power_of_2_06	AC	220 ms	33 MB
clang++-18	near_power_of_2_07	AC	217 ms	33 MB
clang++-18	near_power_of_2_08	AC	215 ms	34 MB
clang++-18	only_first_small_00	AC	439 ms	63 MB
clang++-18	only_first_small_01	AC	439 ms	63 MB
clang++-18	random_00	AC	324 ms	49 MB
clang++-18	random_01	AC	338 ms	51 MB
clang++-18	random_02	AC	239 ms	34 MB
clang++-18	small_00	AC	5 ms	4 MB
clang++-18	small_01	AC	4 ms	4 MB
clang++-18	small_02	AC	4 ms	4 MB
clang++-18	small_03	AC	4 ms	4 MB
clang++-18	small_04	AC	4 ms	4 MB
clang++-18	small_05	AC	4 ms	4 MB
clang++-18	small_06	AC	4 ms	4 MB
clang++-18	small_07	AC	4 ms	4 MB
clang++-18	small_08	AC	4 ms	4 MB
clang++-18	small_slopes_00	AC	438 ms	63 MB
clang++-18	small_slopes_01	AC	443 ms	63 MB

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