Tifa's CP Library

:heavy_check_mark: conv_minplus_ca (src/code/conv/conv_minplus_ca.hpp)

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#ifndef TIFALIBS_CONV_CONV_MINPLUS_CA
#define TIFALIBS_CONV_CONV_MINPLUS_CA

#include "../opt/smawk.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

#endif
#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


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