Tifa's CP Library

:heavy_check_mark: src/test_cpverifier/library-checker/min_plus_convolution_convex_arbitrary.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/min_plus_convolution_convex_arbitrary"

#include "../../code/conv/conv_minplus_ca.hpp"
#include "../../code/io/ios_container.hpp"

int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  u32 n, m;
  std::cin >> n >> m;
  vecu a(n), b(m);
  std::cin >> a >> b;
  std::cout << tifa_libs::math::conv_minplus_ca(a, b) << '\n';
  return 0;
}
#line 1 "src/test_cpverifier/library-checker/min_plus_convolution_convex_arbitrary.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/min_plus_convolution_convex_arbitrary"

#line 1 "src/code/conv/conv_minplus_ca.hpp"



#line 1 "src/code/opt/smawk.hpp"



#line 1 "src/code/util/util.hpp"



#include <bits/stdc++.h>

template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }

using i8 = int8_t;
using i16 = int16_t;
using i32 = int32_t;
using i64 = int64_t;
using i128 = __int128_t;
using isz = ptrdiff_t;

using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using u128 = __uint128_t;
using usz = size_t;

using f32 = float;
using f64 = double;
using f128 = long double;

template <class T>
using ptt = std::pair<T, T>;
template <class T>
using pt3 = std::tuple<T, T, T>;
template <class T>
using pt4 = std::tuple<T, T, T, T>;

template <class T, usz N>
using arr = std::array<T, N>;
template <class T>
using vec = std::vector<T>;
template <class T>
using vvec = vec<vec<T>>;
template <class T>
using v3ec = vec<vvec<T>>;
template <class U, class T>
using vecp = vec<std::pair<U, T>>;
template <class U, class T>
using vvecp = vvec<std::pair<U, T>>;
template <class T>
using vecpt = vec<ptt<T>>;
template <class T>
using vvecpt = vvec<ptt<T>>;

template <class T, class C = std::less<T>>
using pq = std::priority_queue<T, vec<T>, C>;
template <class T>
using pqg = std::priority_queue<T, vec<T>, std::greater<T>>;

using strn = std::string;
using strnv = std::string_view;

using vecu = vec<u32>;
using vvecu = vvec<u32>;
using v3ecu = v3ec<u32>;
using vecu64 = vec<u64>;
using vecb = vec<bool>;
using vvecb = vvec<bool>;

#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif

using namespace std::literals;

constexpr i8 operator""_i8(unsigned long long x) { return (i8)x; }
constexpr i16 operator""_i16(unsigned long long x) { return (i16)x; }
constexpr i32 operator""_i32(unsigned long long x) { return (i32)x; }
constexpr i64 operator""_i64(unsigned long long x) { return (i64)x; }
constexpr isz operator""_iz(unsigned long long x) { return (isz)x; }

constexpr u8 operator""_u8(unsigned long long x) { return (u8)x; }
constexpr u16 operator""_u16(unsigned long long x) { return (u16)x; }
constexpr u32 operator""_u32(unsigned long long x) { return (u32)x; }
constexpr u64 operator""_u64(unsigned long long x) { return (u64)x; }
constexpr usz operator""_uz(unsigned long long x) { return (usz)x; }

inline const auto fn_0 = [](auto&&...) {};


#line 5 "src/code/opt/smawk.hpp"

namespace tifa_libs::opt {

//! $h(r) = argmin_i a_{r,i}$ MUST be non-decreasing
// a: $[0, n) \times [0, m)$
// @param f: f(u32, u32, u32) -> bool
// f(r, x, y): $a_{r,x}\leq a_{r,y}$
template <class Ft>
constexpr vecu smawk(u32 n, u32 m, Ft&& f) {
  vecu ans(n);
  auto run = [&](auto&& run, u32 u, u32 d, u32 l, u32 r) -> void {
    if (u == d) return;
    assert(l < r);
    const u32 rmid = (u + d) / 2;
    u32 cm = l;
    for (u32 col = l + 1; col < r; ++col)
      if (!f(rmid, cm, col)) cm = col;
    ans[rmid] = cm;
    run(run, u, rmid, l, cm + 1);
    run(run, rmid + 1, d, cm, r);
  };
  run(run, 0, n, 0, m);
  return ans;
}

}  // namespace tifa_libs::opt


#line 5 "src/code/conv/conv_minplus_ca.hpp"

namespace tifa_libs::math {

//! assume a is convex, aka. $a_{i-1} - a_{i-2} \leq a_i - a_{i-1}$
//! assume b is arbitary, aka. $b_i = b_j \iff i = j$
template <class T>
constexpr vec<T> conv_minplus_ca(vec<T> const& a, vec<T> const& b) {
  u32 n = (u32)a.size(), m = (u32)b.size();
  vecu argmin = opt::smawk(
      n + m - 1, m,
      [&](u32 k, u32 j1, u32 j2) -> bool {
        i32 i1 = (i32)k - (i32)j1, i2 = (i32)k - (i32)j2;
        if (i2 < 0) return 1;
        if (i1 >= n) return 0;
        return a[i1] + b[j1] < a[i2] + b[j2];
      });
  vec<T> c(n + m - 1);
  for (u32 k = 0; k < n + m - 1; ++k) {
    u32 j = argmin[k];
    c[k] = a[k - j] + b[j];
  }
  return c;
}

}  // namespace tifa_libs::math


#line 1 "src/code/io/ios_container.hpp"



#line 1 "src/code/util/traits.hpp"



#line 5 "src/code/util/traits.hpp"

namespace tifa_libs {

template <class T>
concept iterable_c = requires(T v) {
  { v.begin() } -> std::same_as<typename T::iterator>;
  { v.end() } -> std::same_as<typename T::iterator>;
};

template <class T>
concept container_c = iterable_c<T> && !std::derived_from<T, std::basic_string<typename T::value_type>>;

template <class T>
constexpr bool is_char_v = std::is_same_v<T, char> || std::is_same_v<T, signed char> || std::is_same_v<T, unsigned char>;
template <class T>
concept char_c = is_char_v<T>;

template <class T>
constexpr bool is_s128_v = std::is_same_v<T, __int128_t> || std::is_same_v<T, __int128>;
template <class T>
concept s128_c = is_s128_v<T>;

template <class T>
constexpr bool is_u128_v = std::is_same_v<T, __uint128_t> || std::is_same_v<T, unsigned __int128>;
template <class T>
concept u128_c = is_u128_v<T>;

template <class T>
constexpr bool is_i128_v = is_s128_v<T> || is_u128_v<T>;
template <class T>
concept i128_c = is_u128_v<T>;

template <class T>
constexpr bool is_int_v = std::is_integral_v<T> || is_i128_v<T>;
template <class T>
concept int_c = is_int_v<T>;

template <class T>
constexpr bool is_sint_v = is_s128_v<T> || (is_int_v<T> && std::is_signed_v<T>);
template <class T>
concept sint_c = is_sint_v<T>;

template <class T>
constexpr bool is_uint_v = is_u128_v<T> || (is_int_v<T> && std::is_unsigned_v<T>);
template <class T>
concept uint_c = is_uint_v<T>;

template <class T>
concept mint_c = requires(T x) {
  { x.mod() } -> uint_c;
  { x.val() } -> uint_c;
};

template <class T>
constexpr bool is_arithm_v = std::is_arithmetic_v<T> || is_int_v<T>;
template <class T>
concept arithm_c = is_arithm_v<T>;

template <class T>
struct to_sint : std::make_signed<T> {};
template <>
struct to_sint<u128> {
  using type = u128;
};
template <>
struct to_sint<i128> {
  using type = u128;
};
template <class T>
using to_sint_t = typename to_sint<T>::type;

template <class T>
struct to_uint : std::make_unsigned<T> {};
template <>
struct to_uint<u128> {
  using type = u128;
};
template <>
struct to_uint<i128> {
  using type = u128;
};
template <class T>
using to_uint_t = typename to_uint<T>::type;

}  // namespace tifa_libs


#line 5 "src/code/io/ios_container.hpp"

template <tifa_libs::container_c T>
std::istream &operator>>(std::istream &is, T &x) {
  for (auto &i : x) is >> i;
  return is;
}
template <tifa_libs::container_c T>
std::ostream &operator<<(std::ostream &os, T const &x) {
  if (x.begin() == x.end()) return os;
  auto it = x.begin();
  os << *it++;
  for (; it != x.end(); ++it) os << ' ' << *it;
  return os;
}


#line 5 "src/test_cpverifier/library-checker/min_plus_convolution_convex_arbitrary.test.cpp"

int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  u32 n, m;
  std::cin >> n >> m;
  vecu a(n), b(m);
  std::cin >> a >> b;
  std::cout << tifa_libs::math::conv_minplus_ca(a, b) << '\n';
  return 0;
}

Test cases

Env Name Status Elapsed Memory
g++-12 example_00 :heavy_check_mark: AC 10 ms 4 MB
g++-12 max_random_00 :heavy_check_mark: AC 164 ms 15 MB
g++-12 max_random_01 :heavy_check_mark: AC 159 ms 15 MB
g++-12 max_random_02 :heavy_check_mark: AC 165 ms 15 MB
g++-12 med_random_00 :heavy_check_mark: AC 11 ms 4 MB
g++-12 med_random_01 :heavy_check_mark: AC 9 ms 4 MB
g++-12 med_random_02 :heavy_check_mark: AC 10 ms 4 MB
g++-12 monotone_00 :heavy_check_mark: AC 169 ms 15 MB
g++-12 monotone_01 :heavy_check_mark: AC 156 ms 15 MB
g++-12 monotone_02 :heavy_check_mark: AC 140 ms 15 MB
g++-12 monotone_03 :heavy_check_mark: AC 170 ms 15 MB
g++-12 near_power_of_2_00 :heavy_check_mark: AC 92 ms 9 MB
g++-12 near_power_of_2_01 :heavy_check_mark: AC 84 ms 9 MB
g++-12 near_power_of_2_02 :heavy_check_mark: AC 92 ms 9 MB
g++-12 near_power_of_2_03 :heavy_check_mark: AC 93 ms 9 MB
g++-12 near_power_of_2_04 :heavy_check_mark: AC 88 ms 9 MB
g++-12 near_power_of_2_05 :heavy_check_mark: AC 87 ms 9 MB
g++-12 near_power_of_2_06 :heavy_check_mark: AC 92 ms 9 MB
g++-12 near_power_of_2_07 :heavy_check_mark: AC 83 ms 9 MB
g++-12 near_power_of_2_08 :heavy_check_mark: AC 85 ms 9 MB
g++-12 random_00 :heavy_check_mark: AC 126 ms 13 MB
g++-12 random_01 :heavy_check_mark: AC 132 ms 14 MB
g++-12 random_02 :heavy_check_mark: AC 79 ms 8 MB
g++-12 small_00 :heavy_check_mark: AC 10 ms 4 MB
g++-12 small_01 :heavy_check_mark: AC 9 ms 4 MB
g++-12 small_02 :heavy_check_mark: AC 9 ms 4 MB
g++-12 small_03 :heavy_check_mark: AC 9 ms 4 MB
g++-12 small_04 :heavy_check_mark: AC 9 ms 4 MB
g++-12 small_05 :heavy_check_mark: AC 9 ms 4 MB
g++-12 small_06 :heavy_check_mark: AC 9 ms 4 MB
g++-12 small_07 :heavy_check_mark: AC 9 ms 4 MB
g++-12 small_08 :heavy_check_mark: AC 9 ms 4 MB
g++-12 small_slopes_00 :heavy_check_mark: AC 171 ms 15 MB
g++-12 small_slopes_01 :heavy_check_mark: AC 166 ms 15 MB
Back to top page