test/aoj/3086.LARSCH.test.cpp

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• Last update: 2024-10-11 11:35:48+09:00
• Problem: https://onlinejudge.u-aizu.ac.jp/problems/3086

Depends on

• Segment-Tree (src/DataStructure/SegmentTree.hpp)
• detection idiom (src/Internal/detection_idiom.hpp)
• 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)
• 簡易版LARSCH (src/Optimization/simplified_larsch_dp.hpp)

Code

// competitive-verifier: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/3086
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#include <vector>
#include <algorithm>
#include "src/DataStructure/SegmentTree.hpp"
#include "src/Optimization/simplified_larsch_dp.hpp"
using namespace std;
struct RMQ {
 using T= long long;
 static T ti() { return 1e18; }
 static T op(T l, T r) { return min(l, r); }
};
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int N, L;
 cin >> N >> L;
 vector<long long> a(N);
 for (int i= 0; i < N; ++i) cin >> a[i], a[i]= -a[i];
 SegmentTree<RMQ> seg(a);
 auto w= [&](int i, int j) -> long long {
  if (i - j < L) return 1e18;
  return seg.prod(j, i);
 };
 cout << -simplified_larsch_dp(N, w)[N] << '\n';
 return 0;
}

#line 1 "test/aoj/3086.LARSCH.test.cpp"
// competitive-verifier: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/3086
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#include <vector>
#include <algorithm>
#line 2 "src/DataStructure/SegmentTree.hpp"
#include <memory>
#include <cassert>
#line 2 "src/Internal/detection_idiom.hpp"
#include <type_traits>
#define _DETECT_BOOL(name, ...) \
 template <class, class= void> struct name: std::false_type {}; \
 template <class T> struct name<T, std::void_t<__VA_ARGS__>>: std::true_type {}; \
 template <class T> static constexpr bool name##_v= name<T>::value
#define _DETECT_TYPE(name, type1, type2, ...) \
 template <class T, class= void> struct name { \
  using type= type2; \
 }; \
 template <class T> struct name<T, std::void_t<__VA_ARGS__>> { \
  using type= type1; \
 }
#line 7 "src/DataStructure/SegmentTree.hpp"
template <class M> class SegmentTree {
 _DETECT_BOOL(monoid, typename T::T, decltype(&T::op), decltype(&T::ti));
 _DETECT_BOOL(dual, typename T::T, typename T::E, decltype(&T::mp), decltype(&T::cp));
 _DETECT_TYPE(nullptr_or_E, typename T::E, std::nullptr_t, typename T::E);
 using T= typename M::T;
 using E= typename nullptr_or_E<M>::type;
 int n;
 std::unique_ptr<T[]> dat;
 std::unique_ptr<E[]> laz;
 std::unique_ptr<bool[]> flg;
 inline void update(int k) { dat[k]= M::op(dat[k << 1], dat[k << 1 | 1]); }
 inline bool map(int k, E x, int sz) {
  if constexpr (std::is_invocable_r_v<bool, decltype(M::mp), T &, E, int>) return M::mp(dat[k], x, sz);
  else if constexpr (std::is_invocable_r_v<bool, decltype(M::mp), T &, E>) return M::mp(dat[k], x);
  else if constexpr (std::is_invocable_r_v<void, decltype(M::mp), T &, E, int>) return M::mp(dat[k], x, sz), true;
  else return M::mp(dat[k], x), true;
 }
 inline void prop(int k, E x, int sz) {
  if (k < n) {
   if (flg[k]) M::cp(laz[k], x);
   else laz[k]= x;
   flg[k]= true;
   if constexpr (monoid_v<M>)
    if (!map(k, x, sz)) push(k, sz), update(k);
  } else {
   if constexpr (monoid_v<M>) map(k, x, 1);
   else map(k - n, x, 1);
  }
 }
 inline void push(int k, int sz) {
  if (flg[k]) prop(k << 1, laz[k], sz >> 1), prop(k << 1 | 1, laz[k], sz >> 1), flg[k]= false;
 }
 inline bool valid(int k) const {
  int d= __builtin_clz(k) - __builtin_clz(n);
  return (n >> d) != k || ((n >> d) << d) == n;
 }
public:
 SegmentTree() {}
 SegmentTree(int n): n(n), dat(std::make_unique<T[]>(n << monoid_v<M>)) {
  if constexpr (monoid_v<M>) std::fill_n(dat.get(), n << 1, M::ti());
  if constexpr (dual_v<M>) laz= std::make_unique<E[]>(n), flg= std::make_unique<bool[]>(n), std::fill_n(flg.get(), n, false);
 }
 template <class F> SegmentTree(int n, const F &init): n(n), dat(std::make_unique<T[]>(n << monoid_v<M>)) {
  auto a= dat.get() + (n & -monoid_v<M>);
  for (int i= 0; i < n; ++i) a[i]= init(i);
  if constexpr (monoid_v<M>) build();
  if constexpr (dual_v<M>) laz= std::make_unique<E[]>(n), flg= std::make_unique<bool[]>(n), std::fill_n(flg.get(), n, false);
 }
 SegmentTree(int n, T x): SegmentTree(n, [x](int) { return x; }) {}
 SegmentTree(const std::vector<T> &v): SegmentTree(v.size(), [&v](int i) { return v[i]; }) {}
 SegmentTree(const T *bg, const T *ed): SegmentTree(ed - bg, [bg](int i) { return bg[i]; }) {}
 void build() {
  static_assert(monoid_v<M>, "\"build\" is not available\n");
  for (int i= n; --i;) update(i);
 }
 inline void unsafe_set(int i, T x) {
  static_assert(monoid_v<M>, "\"unsafe_set\" is not available\n");
  dat[i + n]= x;
 }
 inline void set(int i, T x) {
  get(i);
  if constexpr (monoid_v<M>)
   for (dat[i+= n]= x; i>>= 1;) update(i);
  else dat[i]= x;
 }
 inline void mul(int i, T x) {
  static_assert(monoid_v<M>, "\"mul\" is not available\n");
  set(i, M::op(get(i), x));
 }
 inline T get(int i) {
  i+= n;
  if constexpr (dual_v<M>)
   for (int j= 31 - __builtin_clz(i); j; --j) push(i >> j, 1 << j);
  if constexpr (monoid_v<M>) return dat[i];
  else return dat[i - n];
 }
 inline T operator[](int i) { return get(i); }
 inline T prod(int l, int r) {
  static_assert(monoid_v<M>, "\"prod\" is not available\n");
  l+= n, r+= n;
  if constexpr (dual_v<M>) {
   for (int j= 31 - __builtin_clz(l); ((l >> j) << j) != l; --j) push(l >> j, 1 << j);
   for (int j= 31 - __builtin_clz(r); ((r >> j) << j) != r; --j) push(r >> j, 1 << j);
  }
  T s1= M::ti(), s2= M::ti();
  for (; l < r; l>>= 1, r>>= 1) {
   if (l & 1) s1= M::op(s1, dat[l++]);
   if (r & 1) s2= M::op(dat[--r], s2);
  }
  return M::op(s1, s2);
 }
 inline void apply(int l, int r, E x) {
  static_assert(dual_v<M>, "\"apply\" is not available\n");
  l+= n, r+= n;
  for (int j= 31 - __builtin_clz(l); ((l >> j) << j) != l; j--) push(l >> j, 1 << j);
  for (int j= 31 - __builtin_clz(r); ((r >> j) << j) != r; j--) push(r >> j, 1 << j);
  for (int a= l, b= r, sz= 1; a < b; a>>= 1, b>>= 1, sz<<= 1) {
   if (a & 1) prop(a++, x, sz);
   if (b & 1) prop(--b, x, sz);
  }
  if constexpr (monoid_v<M>) {
   for (int j= __builtin_ctz(l) + 1; l >> j; ++j) update(l >> j);
   for (int j= __builtin_ctz(r) + 1; r >> j; ++j) update(r >> j);
  }
 }
 template <class C> int max_right(int l, const C &check) {
  static_assert(monoid_v<M>, "\"max_right\" is not available\n");
  assert(check(M::ti()));
  if (check(prod(l, n))) return n;
  T s= M::ti(), t;
  int sz= 1;
  for (get(l), l+= n;; s= t, ++l) {
   while (!(l & 1) && valid(l >> 1)) l>>= 1, sz<<= 1;
   if (!check(t= M::op(s, dat[l]))) {
    while (l < n) {
     if constexpr (dual_v<M>) push(l, sz);
     l<<= 1, sz>>= 1;
     if (check(t= M::op(s, dat[l]))) s= t, ++l;
    }
    return l - n;
   }
  }
 }
 template <class C> int min_left(int r, const C &check) {
  static_assert(monoid_v<M>, "\"min_left\" is not available\n");
  assert(check(M::ti()));
  if (check(prod(0, r))) return 0;
  T s= M::ti(), t;
  int sz= 1;
  for (get(--r), r+= n;; s= t, --r) {
   while (!valid(r)) r= r << 1 | 1, sz>>= 1;
   while ((r & 1) && valid(r >> 1)) r>>= 1, sz<<= 1;
   if (!check(t= M::op(dat[r], s))) {
    while (r < n) {
     if constexpr (dual_v<M>) push(r, sz);
     r= r << 1 | 1, sz>>= 1;
     if (check(t= M::op(dat[r], s))) s= t, --r;
    }
    return r + 1 - n;
   }
  }
 }
};
#line 3 "src/Optimization/simplified_larsch_dp.hpp"
#include <limits>
#line 3 "src/Internal/function_traits.hpp"
// 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 5 "src/Optimization/simplified_larsch_dp.hpp"
// dp[i] = min_{j<i} (dp[j] + w(i,j))
// w(i,j) -> monge cost
template <class F> std::vector<result_type_t<F>> simplified_larsch_dp(int n, const F &w) {
 using T= result_type_t<F>;
 std::vector<T> dp(n + 1, std::numeric_limits<T>::max());
 std::vector<int> x(n + 1);
 auto check= [&](int i, int j) {
  if (T cost= dp[j] + w(i, j); dp[i] > cost) dp[i]= cost, x[i]= j;
 };
 auto rec= [&](auto &rec, int l, int r) {
  if (r - l <= 1) return;
  int m= (l + r) / 2;
  for (int i= x[l]; i <= x[r]; ++i) check(m, i);
  rec(rec, l, m);
  for (int i= l + 1; i <= m; ++i) check(r, i);
  rec(rec, m, r);
 };
 return dp[0]= 0, check(n, 0), rec(rec, 0, n), dp;
}
#line 9 "test/aoj/3086.LARSCH.test.cpp"
using namespace std;
struct RMQ {
 using T= long long;
 static T ti() { return 1e18; }
 static T op(T l, T r) { return min(l, r); }
};
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int N, L;
 cin >> N >> L;
 vector<long long> a(N);
 for (int i= 0; i < N; ++i) cin >> a[i], a[i]= -a[i];
 SegmentTree<RMQ> seg(a);
 auto w= [&](int i, int j) -> long long {
  if (i - j < L) return 1e18;
  return seg.prod(j, i);
 };
 cout << -simplified_larsch_dp(N, w)[N] << '\n';
 return 0;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++-13	00_sample_01.in	AC	5 ms	4 MB
g++-13	00_sample_02.in	AC	5 ms	4 MB
g++-13	00_sample_03.in	AC	5 ms	4 MB
g++-13	00_sample_04.in	AC	4 ms	4 MB
g++-13	10_small_01.in	AC	4 ms	4 MB
g++-13	10_small_02.in	AC	5 ms	4 MB
g++-13	10_small_03.in	AC	5 ms	3 MB
g++-13	10_small_04.in	AC	5 ms	4 MB
g++-13	10_small_05.in	AC	5 ms	4 MB
g++-13	10_small_06.in	AC	5 ms	4 MB
g++-13	10_small_07.in	AC	4 ms	4 MB
g++-13	10_small_08.in	AC	4 ms	4 MB
g++-13	10_small_09.in	AC	5 ms	4 MB
g++-13	10_small_10.in	AC	4 ms	4 MB
g++-13	10_small_11.in	AC	4 ms	4 MB
g++-13	10_small_12.in	AC	4 ms	3 MB
g++-13	10_small_13.in	AC	4 ms	4 MB
g++-13	10_small_14.in	AC	4 ms	4 MB
g++-13	10_small_15.in	AC	4 ms	4 MB
g++-13	10_small_16.in	AC	4 ms	4 MB
g++-13	10_small_17.in	AC	4 ms	4 MB
g++-13	10_small_18.in	AC	4 ms	4 MB
g++-13	10_small_19.in	AC	4 ms	4 MB
g++-13	10_small_20.in	AC	4 ms	4 MB
g++-13	20_random_01.in	AC	5 ms	4 MB
g++-13	20_random_02.in	AC	7 ms	4 MB
g++-13	20_random_03.in	AC	5 ms	4 MB
g++-13	20_random_04.in	AC	5 ms	4 MB
g++-13	20_random_05.in	AC	6 ms	4 MB
g++-13	20_random_06.in	AC	5 ms	4 MB
g++-13	20_random_07.in	AC	6 ms	4 MB
g++-13	20_random_08.in	AC	5 ms	4 MB
g++-13	20_random_09.in	AC	7 ms	4 MB
g++-13	20_random_10.in	AC	5 ms	4 MB
g++-13	30_large_01.in	AC	148 ms	10 MB
g++-13	30_large_02.in	AC	115 ms	9 MB
g++-13	30_large_03.in	AC	20 ms	9 MB
g++-13	31_large_allneg_01.in	AC	40 ms	10 MB
g++-13	31_large_allneg_02.in	AC	42 ms	9 MB
g++-13	31_large_allneg_03.in	AC	21 ms	9 MB
g++-13	32_large_allpos_01.in	AC	143 ms	10 MB
g++-13	32_large_allpos_02.in	AC	118 ms	9 MB
g++-13	32_large_allpos_03.in	AC	19 ms	9 MB
g++-13	40_long_01.in	AC	123 ms	10 MB
g++-13	40_long_02.in	AC	104 ms	9 MB
g++-13	40_long_03.in	AC	127 ms	9 MB
g++-13	41_short_01.in	AC	131 ms	10 MB
g++-13	41_short_02.in	AC	108 ms	9 MB
g++-13	41_short_03.in	AC	113 ms	9 MB
clang++-18	00_sample_01.in	AC	5 ms	4 MB
clang++-18	00_sample_02.in	AC	5 ms	4 MB
clang++-18	00_sample_03.in	AC	4 ms	4 MB
clang++-18	00_sample_04.in	AC	4 ms	4 MB
clang++-18	10_small_01.in	AC	4 ms	4 MB
clang++-18	10_small_02.in	AC	5 ms	4 MB
clang++-18	10_small_03.in	AC	4 ms	4 MB
clang++-18	10_small_04.in	AC	5 ms	4 MB
clang++-18	10_small_05.in	AC	4 ms	4 MB
clang++-18	10_small_06.in	AC	4 ms	4 MB
clang++-18	10_small_07.in	AC	5 ms	4 MB
clang++-18	10_small_08.in	AC	4 ms	4 MB
clang++-18	10_small_09.in	AC	5 ms	4 MB
clang++-18	10_small_10.in	AC	4 ms	4 MB
clang++-18	10_small_11.in	AC	4 ms	4 MB
clang++-18	10_small_12.in	AC	4 ms	4 MB
clang++-18	10_small_13.in	AC	4 ms	4 MB
clang++-18	10_small_14.in	AC	4 ms	4 MB
clang++-18	10_small_15.in	AC	4 ms	4 MB
clang++-18	10_small_16.in	AC	5 ms	4 MB
clang++-18	10_small_17.in	AC	5 ms	4 MB
clang++-18	10_small_18.in	AC	4 ms	4 MB
clang++-18	10_small_19.in	AC	4 ms	4 MB
clang++-18	10_small_20.in	AC	5 ms	4 MB
clang++-18	20_random_01.in	AC	5 ms	4 MB
clang++-18	20_random_02.in	AC	7 ms	4 MB
clang++-18	20_random_03.in	AC	5 ms	4 MB
clang++-18	20_random_04.in	AC	5 ms	4 MB
clang++-18	20_random_05.in	AC	6 ms	4 MB
clang++-18	20_random_06.in	AC	5 ms	4 MB
clang++-18	20_random_07.in	AC	6 ms	4 MB
clang++-18	20_random_08.in	AC	5 ms	4 MB
clang++-18	20_random_09.in	AC	7 ms	4 MB
clang++-18	20_random_10.in	AC	5 ms	4 MB
clang++-18	30_large_01.in	AC	143 ms	10 MB
clang++-18	30_large_02.in	AC	111 ms	9 MB
clang++-18	30_large_03.in	AC	20 ms	9 MB
clang++-18	31_large_allneg_01.in	AC	38 ms	10 MB
clang++-18	31_large_allneg_02.in	AC	41 ms	9 MB
clang++-18	31_large_allneg_03.in	AC	21 ms	9 MB
clang++-18	32_large_allpos_01.in	AC	138 ms	10 MB
clang++-18	32_large_allpos_02.in	AC	111 ms	9 MB
clang++-18	32_large_allpos_03.in	AC	19 ms	9 MB
clang++-18	40_long_01.in	AC	121 ms	10 MB
clang++-18	40_long_02.in	AC	102 ms	9 MB
clang++-18	40_long_03.in	AC	120 ms	9 MB
clang++-18	41_short_01.in	AC	127 ms	10 MB
clang++-18	41_short_02.in	AC	104 ms	9 MB
clang++-18	41_short_03.in	AC	110 ms	9 MB

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