Tifa's CP Library

:warning: interp_newton_n2 (src/code/math/interp_newton_n2.hpp)

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Code

#ifndef TIFALIBS_MATH_INTERP_NEWTON_N2
#define TIFALIBS_MATH_INTERP_NEWTON_N2

#include "../util/util.hpp"

namespace tifa_libs::math {

template <class T>
class interp_newton {
  // {(x_0,y_0),(x__1,y_1),...,(x_{n-1},y_{n-1})}
  vecpt<T> points;
  // diffs[r][l] = f[x_l,x_{l+1},...,x_r]
  vvec<T> diffs;
  // (x-x_0)(x-x_1)...(x-x_{n-1})
  vec<T> base;
  // f[x_0]+f[x_0,x_1](x-x_0)+...+f[x_0,x_1,...,x_n](x-x_0)(x-x_1)...(x-x_{n-1})
  vec<T> fit;

 public:
  explicit constexpr interp_newton() {}
  constexpr interp_newton &insert(T const &x, T const &y) {
    points.emplace_back(x, y);
    u32 n = (u32)points.size();
    if (n == 1) {
      base.push_back(1);
    } else {
      u32 m = (u32)base.size();
      base.push_back(0);
      for (u32 i = m; i; --i) base[i] = base[i - 1];
      base[0] = 0;
      for (u32 i = 0; i < m; ++i) base[i] = base[i] - points[n - 2].first * base[i + 1];
    }
    diffs.emplace_back(points.size());
    diffs[n - 1][n - 1] = y;
    if (n > 1)
      for (u32 i = n - 2; ~i; --i) diffs[n - 1][i] = (diffs[n - 2][i] - diffs[n - 1][i + 1]) / (points[i].first - points[n - 1].first);
    fit.push_back(0);
    for (u32 i = 0; i < n; ++i) fit[i] = fit[i] + diffs[n - 1][0] * base[i];
    return *this;
  }
  constexpr vec<T> coeffs() const { return fit; }
  constexpr T eval(T const &x) {
    T ans{};
    for (auto it = fit.rbegin(); it != fit.rend(); ++it) ans = ans * x + *it;
    return ans;
  }
};

}  // namespace tifa_libs::math

#endif
#line 1 "src/code/math/interp_newton_n2.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/math/interp_newton_n2.hpp"

namespace tifa_libs::math {

template <class T>
class interp_newton {
  // {(x_0,y_0),(x__1,y_1),...,(x_{n-1},y_{n-1})}
  vecpt<T> points;
  // diffs[r][l] = f[x_l,x_{l+1},...,x_r]
  vvec<T> diffs;
  // (x-x_0)(x-x_1)...(x-x_{n-1})
  vec<T> base;
  // f[x_0]+f[x_0,x_1](x-x_0)+...+f[x_0,x_1,...,x_n](x-x_0)(x-x_1)...(x-x_{n-1})
  vec<T> fit;

 public:
  explicit constexpr interp_newton() {}
  constexpr interp_newton &insert(T const &x, T const &y) {
    points.emplace_back(x, y);
    u32 n = (u32)points.size();
    if (n == 1) {
      base.push_back(1);
    } else {
      u32 m = (u32)base.size();
      base.push_back(0);
      for (u32 i = m; i; --i) base[i] = base[i - 1];
      base[0] = 0;
      for (u32 i = 0; i < m; ++i) base[i] = base[i] - points[n - 2].first * base[i + 1];
    }
    diffs.emplace_back(points.size());
    diffs[n - 1][n - 1] = y;
    if (n > 1)
      for (u32 i = n - 2; ~i; --i) diffs[n - 1][i] = (diffs[n - 2][i] - diffs[n - 1][i + 1]) / (points[i].first - points[n - 1].first);
    fit.push_back(0);
    for (u32 i = 0; i < n; ++i) fit[i] = fit[i] + diffs[n - 1][0] * base[i];
    return *this;
  }
  constexpr vec<T> coeffs() const { return fit; }
  constexpr T eval(T const &x) {
    T ans{};
    for (auto it = fit.rbegin(); it != fit.rend(); ++it) ans = ans * x + *it;
    return ans;
  }
};

}  // namespace tifa_libs::math


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