Tifa's CP Library

:warning: tsearch (src/code/opt/tsearch.hpp)

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Code

#ifndef TIFALIBS_OPT_TSEARCH
#define TIFALIBS_OPT_TSEARCH

#include "../util/fp_const.hpp"
#include "../util/traits.hpp"

namespace tifa_libs::opt {

// @return $\argmin_{l\leq x\leq r}\{f\}$
template <arithm_c I, class F>
constexpr auto tsearch(I l, I r, F&& f) {
  using T = decltype(f(l));
  assert(l <= r);
  I ml, mr;
  T fl = f(l), fr = f(r), fml, fmr;
  using PT = std::conditional_t<std::is_floating_point_v<I>, I, f64>;
  fml = f(ml = l + (r - l) * (1 - phi_v<PT>)), fmr = f(mr = r - (r - l) * (1 - phi_v<PT>));

  do {
    if constexpr (is_int_v<I>) {
      if (r - l < 8) {
        I x = l, fx = fl;
        if (fr < fx) x = r, fx = fr;
        if (fml < fx) x = ml, fx = fml;
        if (fmr < fx) x = mr, fx = fmr;
        for (I i = l + 1; i < r; ++i) {
          if (i == ml || i == mr) continue;
          if (T fi = f(i); fi < fx) x = i, fx = fi;
        }
        return std::make_pair(x, fx);
      }
    } else if ((r - l) / std::max({l, r, (I)1}) < eps_v<I>) return std::make_pair(l, fl);
    if (fml < fmr) {
      r = mr, fr = fmr;
      mr = ml, fmr = fml;
      fml = f(ml = l - mr + r);
    } else {
      l = ml, fl = fml;
      ml = mr, fml = fmr;
      fmr = f(mr = r - ml + l);
    }
  } while (1);
}

}  // namespace tifa_libs::opt

#endif
#line 1 "src/code/opt/tsearch.hpp"



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

namespace tifa_libs {

using namespace std::numbers;

// std::sqrt(std::numeric_limits<FP>::epsilon())
template <std::floating_point FP>
constexpr inline FP eps_v = FP(1e-8L);

}  // namespace tifa_libs


#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 6 "src/code/opt/tsearch.hpp"

namespace tifa_libs::opt {

// @return $\argmin_{l\leq x\leq r}\{f\}$
template <arithm_c I, class F>
constexpr auto tsearch(I l, I r, F&& f) {
  using T = decltype(f(l));
  assert(l <= r);
  I ml, mr;
  T fl = f(l), fr = f(r), fml, fmr;
  using PT = std::conditional_t<std::is_floating_point_v<I>, I, f64>;
  fml = f(ml = l + (r - l) * (1 - phi_v<PT>)), fmr = f(mr = r - (r - l) * (1 - phi_v<PT>));

  do {
    if constexpr (is_int_v<I>) {
      if (r - l < 8) {
        I x = l, fx = fl;
        if (fr < fx) x = r, fx = fr;
        if (fml < fx) x = ml, fx = fml;
        if (fmr < fx) x = mr, fx = fmr;
        for (I i = l + 1; i < r; ++i) {
          if (i == ml || i == mr) continue;
          if (T fi = f(i); fi < fx) x = i, fx = fi;
        }
        return std::make_pair(x, fx);
      }
    } else if ((r - l) / std::max({l, r, (I)1}) < eps_v<I>) return std::make_pair(l, fl);
    if (fml < fmr) {
      r = mr, fr = fmr;
      mr = ml, fmr = fml;
      fml = f(ml = l - mr + r);
    } else {
      l = ml, fl = fml;
      ml = mr, fml = fmr;
      fmr = f(mr = r - ml + l);
    }
  } while (1);
}

}  // namespace tifa_libs::opt


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