Tifa's CP Library

:heavy_check_mark: smawk (src/code/opt/smawk.hpp)

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#ifndef TIFALIBS_OPT_SMAWK
#define TIFALIBS_OPT_SMAWK

#include "../util/util.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>
CEXP vecu smawk(u32 n, u32 m, Ft&& f) {
  vecu ans(n);
  auto g = [&](auto&& g, 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;
    flt_ (u32, col, l + 1, r)
      if (!f(rmid, cm, col)) cm = col;
    ans[rmid] = cm, g(g, u, rmid, l, cm + 1), g(g, rmid + 1, d, cm, r);
  };
  g(g, 0, n, 0, m);
  return ans;
}

}  // namespace tifa_libs::opt

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



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



#include <bits/extc++.h>

#define CEXP constexpr
#define CEXPE constexpr explicit
#define TPN typename
#define CR const&

#define cT_(...) std::conditional_t<sizeof(__VA_ARGS__) <= sizeof(size_t), __VA_ARGS__, __VA_ARGS__ CR>
#define fle_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i <= i##e; ++i)
#define flt_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i < i##e; ++i)

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

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

// clang-format off
template <class T, T v> using ic = std::integral_constant<T, v>;
template <class T> using ptt = std::pair<T, T>;
template <class T> struct edge_t {
  T w; u32 u, v;
  CEXP auto operator<=>(edge_t CR) const = default;
};
template <class T> struct pt3 {
  T _0, _1, _2;
  CEXP auto operator<=>(pt3 CR) const = default;
};
template <class T> struct pt4 {
  T _0, _1, _2, _3;
  CEXP auto operator<=>(pt4 CR) const = default;
};
template <class E> using itl = std::initializer_list<E>;
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 T> using vecpt = vec<ptt<T>>;
template <class T> using vvecpt = vvec<ptt<T>>;
template <class T> using ptvec = ptt<vec<T>>;
template <class T> using ptvvec = ptt<vvec<T>>;

template <class T, usz ext = std::dynamic_extent> using spn = std::span<T const, ext>;
template <class T, usz N> using arr = std::array<T, N>;
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, 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>>;
// clang-format on

#define mk_(V, A, T) using V##A = V<T>;
#define mk(A, T) mk_(edge_t, A, T) mk_(ptt, A, T) mk_(pt3, A, T) mk_(pt4, A, T) mk_(vec, A, T) mk_(vvec, A, T) mk_(v3ec, A, T) mk_(vecpt, A, T) mk_(vvecpt, A, T) mk_(ptvec, A, T) mk_(ptvvec, A, T) mk_(spn, A, T) mk_(itl, A, T)
mk(b, bool) mk(i, i32) mk(u, u32) mk(ii, i64) mk(uu, u64);
#undef mk
#undef mk_

using namespace std::literals;
CEXP i8 operator""_i8(unsigned long long x) { return (i8)x; }
CEXP i16 operator""_i16(unsigned long long x) { return (i16)x; }
CEXP i32 operator""_i32(unsigned long long x) { return (i32)x; }
CEXP i64 operator""_i64(unsigned long long x) { return (i64)x; }
CEXP isz operator""_iz(unsigned long long x) { return (isz)x; }
CEXP u8 operator""_u8(unsigned long long x) { return (u8)x; }
CEXP u16 operator""_u16(unsigned long long x) { return (u16)x; }
CEXP u32 operator""_u32(unsigned long long x) { return (u32)x; }
CEXP u64 operator""_u64(unsigned long long x) { return (u64)x; }
CEXP usz operator""_uz(unsigned long long x) { return (usz)x; }

using std::numbers::pi_v;
template <std::floating_point FP>
inline FP eps_v = std::sqrt(std::numeric_limits<FP>::epsilon());
template <std::floating_point FP>
CEXP void set_eps(FP v) { eps_v<FP> = v; }

inline const auto fn_0 = [](auto&&...) {};
inline const auto fn_is0 = [](auto x) { return x == 0; };

namespace tifa_libs {
using std::min, std::max, std::swap;
template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }
}  // namespace tifa_libs


#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>
CEXP vecu smawk(u32 n, u32 m, Ft&& f) {
  vecu ans(n);
  auto g = [&](auto&& g, 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;
    flt_ (u32, col, l + 1, r)
      if (!f(rmid, cm, col)) cm = col;
    ans[rmid] = cm, g(g, u, rmid, l, cm + 1), g(g, rmid + 1, d, cm, r);
  };
  g(g, 0, n, 0, m);
  return ans;
}

}  // namespace tifa_libs::opt


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