test/yukicoder/913.LiCT.test.cpp

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• Last update: 2024-09-01 14:21:07+09:00
• Problem: https://yukicoder.me/problems/no/913

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://yukicoder.me/problems/no/913
// competitive-verifier: TLE 1
// competitive-verifier: MLE 256
#include <iostream>
#include <vector>
#include "src/Optimization/LiChaoTree.hpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int N;
 cin >> N;
 long long A[N], sum[N + 1];
 sum[0]= 0;
 for (int i= 0; i < N; ++i) cin >> A[i], sum[i + 1]= sum[i] + A[i];
 auto f= [&](int i, int j) { return (long long)(j - i) * (j - i) + sum[j] - sum[i]; };
 auto g= [&](int i, int j) { return f(j, i); };
 LiChaoTree lct1(f, 0, N + 1);
 LiChaoTree lct2(g, 0, N + 1);
 static constexpr long long INF= 1e18;
 vector<long long> ans(N, INF);
 auto rec= [&](auto rec, int L, int R) -> void {
  if (L == R) return;
  int M= (L + R) / 2;
  {
   auto tree= lct1.make_tree<MINIMIZE>();
   for (int i= M + 1; i <= R; ++i) tree.insert(i);
   long long mn= INF;
   for (int i= L; i < M; ++i) {
    mn= min(mn, tree.query(i).first);
    ans[i]= min(ans[i], mn);
   }
  }
  {
   auto tree= lct2.make_tree<MINIMIZE>();
   for (int i= L; i <= M; ++i) tree.insert(i);
   long long mn= INF;
   for (int i= R; i-- > M;) {
    mn= min(mn, tree.query(i + 1).first);
    ans[i]= min(ans[i], mn);
   }
  }
  rec(rec, L, M), rec(rec, M + 1, R);
 };
 rec(rec, 0, N);
 for (int i= 0; i < N; ++i) cout << ans[i] << '\n';
 return 0;
}

#line 1 "test/yukicoder/913.LiCT.test.cpp"
// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/913
// competitive-verifier: TLE 1
// competitive-verifier: MLE 256
#include <iostream>
#include <vector>
#line 2 "src/Optimization/LiChaoTree.hpp"
#include <limits>
#include <algorithm>
#line 5 "src/Optimization/LiChaoTree.hpp"
#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 7 "test/yukicoder/913.LiCT.test.cpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int N;
 cin >> N;
 long long A[N], sum[N + 1];
 sum[0]= 0;
 for (int i= 0; i < N; ++i) cin >> A[i], sum[i + 1]= sum[i] + A[i];
 auto f= [&](int i, int j) { return (long long)(j - i) * (j - i) + sum[j] - sum[i]; };
 auto g= [&](int i, int j) { return f(j, i); };
 LiChaoTree lct1(f, 0, N + 1);
 LiChaoTree lct2(g, 0, N + 1);
 static constexpr long long INF= 1e18;
 vector<long long> ans(N, INF);
 auto rec= [&](auto rec, int L, int R) -> void {
  if (L == R) return;
  int M= (L + R) / 2;
  {
   auto tree= lct1.make_tree<MINIMIZE>();
   for (int i= M + 1; i <= R; ++i) tree.insert(i);
   long long mn= INF;
   for (int i= L; i < M; ++i) {
    mn= min(mn, tree.query(i).first);
    ans[i]= min(ans[i], mn);
   }
  }
  {
   auto tree= lct2.make_tree<MINIMIZE>();
   for (int i= L; i <= M; ++i) tree.insert(i);
   long long mn= INF;
   for (int i= R; i-- > M;) {
    mn= min(mn, tree.query(i + 1).first);
    ans[i]= min(ans[i], mn);
   }
  }
  rec(rec, L, M), rec(rec, M + 1, R);
 };
 rec(rec, 0, N);
 for (int i= 0; i < N; ++i) cout << ans[i] << '\n';
 return 0;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++-13	01_sample_01	AC	6 ms	4 MB
g++-13	01_sample_02	AC	5 ms	4 MB
g++-13	01_sample_03	AC	5 ms	4 MB
g++-13	02_random_01	AC	6 ms	4 MB
g++-13	02_random_02	AC	6 ms	4 MB
g++-13	02_random_03	AC	6 ms	4 MB
g++-13	02_random_04	AC	6 ms	4 MB
g++-13	02_random_05	AC	5 ms	4 MB
g++-13	03_random_01	AC	85 ms	34 MB
g++-13	03_random_02	AC	85 ms	36 MB
g++-13	03_random_03	AC	85 ms	36 MB
g++-13	03_random_04	AC	85 ms	34 MB
g++-13	03_random_05	AC	85 ms	35 MB
g++-13	04_random_01	AC	78 ms	36 MB
g++-13	04_random_02	AC	75 ms	33 MB
g++-13	04_random_03	AC	77 ms	36 MB
g++-13	05_random_01	AC	75 ms	34 MB
g++-13	05_random_02	AC	73 ms	35 MB
g++-13	05_random_03	AC	71 ms	32 MB
g++-13	06_random_01	AC	77 ms	35 MB
g++-13	06_random_02	AC	74 ms	34 MB
g++-13	06_random_03	AC	274 ms	61 MB
g++-13	06_random_04	AC	334 ms	66 MB
g++-13	06_random_05	AC	406 ms	86 MB
g++-13	06_random_06	AC	446 ms	115 MB
g++-13	06_random_07	AC	463 ms	133 MB
g++-13	06_random_08	AC	86 ms	34 MB
g++-13	06_random_09	AC	86 ms	35 MB
g++-13	07_random_01	AC	184 ms	54 MB
g++-13	07_random_02	AC	250 ms	61 MB
g++-13	07_random_03	AC	256 ms	62 MB
g++-13	08_random_01	AC	118 ms	45 MB
g++-13	08_random_02	AC	86 ms	36 MB
g++-13	08_random_03	AC	82 ms	35 MB
g++-13	09_random_01	AC	211 ms	55 MB
g++-13	09_random_02	AC	223 ms	57 MB
g++-13	09_random_03	AC	259 ms	62 MB
clang++-18	01_sample_01	AC	6 ms	4 MB
clang++-18	01_sample_02	AC	5 ms	4 MB
clang++-18	01_sample_03	AC	5 ms	4 MB
clang++-18	02_random_01	AC	6 ms	4 MB
clang++-18	02_random_02	AC	6 ms	4 MB
clang++-18	02_random_03	AC	6 ms	4 MB
clang++-18	02_random_04	AC	6 ms	4 MB
clang++-18	02_random_05	AC	5 ms	4 MB
clang++-18	03_random_01	AC	91 ms	34 MB
clang++-18	03_random_02	AC	89 ms	33 MB
clang++-18	03_random_03	AC	90 ms	33 MB
clang++-18	03_random_04	AC	92 ms	34 MB
clang++-18	03_random_05	AC	96 ms	35 MB
clang++-18	04_random_01	AC	89 ms	34 MB
clang++-18	04_random_02	AC	86 ms	34 MB
clang++-18	04_random_03	AC	87 ms	36 MB
clang++-18	05_random_01	AC	84 ms	34 MB
clang++-18	05_random_02	AC	82 ms	33 MB
clang++-18	05_random_03	AC	83 ms	34 MB
clang++-18	06_random_01	AC	86 ms	36 MB
clang++-18	06_random_02	AC	88 ms	34 MB
clang++-18	06_random_03	AC	310 ms	61 MB
clang++-18	06_random_04	AC	375 ms	67 MB
clang++-18	06_random_05	AC	460 ms	86 MB
clang++-18	06_random_06	AC	498 ms	114 MB
clang++-18	06_random_07	AC	517 ms	133 MB
clang++-18	06_random_08	AC	95 ms	35 MB
clang++-18	06_random_09	AC	95 ms	34 MB
clang++-18	07_random_01	AC	208 ms	52 MB
clang++-18	07_random_02	AC	280 ms	62 MB
clang++-18	07_random_03	AC	295 ms	60 MB
clang++-18	08_random_01	AC	134 ms	45 MB
clang++-18	08_random_02	AC	106 ms	37 MB
clang++-18	08_random_03	AC	100 ms	36 MB
clang++-18	09_random_01	AC	238 ms	54 MB
clang++-18	09_random_02	AC	255 ms	57 MB
clang++-18	09_random_03	AC	296 ms	63 MB

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