num/float/convex.hpp

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• Last update: 2024-11-09 00:49:07+00:00
• Include: #include "num/float/convex.hpp"

Depends on

• prelude.hpp

Code

#pragma once
#include "prelude.hpp"

// Returns (min f, argmin f)
template <class F>
auto convex_min(double l, double r, double e, F f) {
  const double PHI = 1.6180339887498948;
  int k = log((r - l) / e) / log(PHI) + 2;
  double x = (PHI * l + r) / (1 + PHI);
  double y = (l + PHI * r) / (1 + PHI);
  double fx = f(x);
  double fy = f(y);
  rep(i, k) {
    if (fx < fy) {
      l = x;
      tie(x, fx) = make_pair(y, fy);
      y = (l + PHI * r) / (1 + PHI);
      fy = f(y);
    } else {
      r = y;
      tie(y, fy) = make_pair(x, fx);
      x = (PHI * l + r) / (1 + PHI);
      fx = f(x);
    }
  }
  return make_pair(fx, x);
}

#line 2 "prelude.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using vi = vector<int>;
using vvi = vector<vector<int>>;
using vll = vector<ll>;
using vvll = vector<vector<ll>>;
using vc = vector<char>;
#define rep2(i, m, n) for (auto i = (m); i < (n); i++)
#define rep(i, n) rep2(i, 0, n)
#define repr2(i, m, n) for (auto i = (n); i-- > (m);)
#define repr(i, n) repr2(i, 0, n)
#define all(x) begin(x), end(x)
auto ndvec(int n, auto e) { return vector(n, e); }
auto ndvec(int n, auto ...e) { return vector(n, ndvec(e...)); }
auto comp_key(auto&& f) { return [&](auto&& a, auto&& b) { return f(a) < f(b); }; }
auto& max(const auto& a, const auto& b) { return a < b ? b : a; }
auto& min(const auto& a, const auto& b) { return b < a ? b : a; }
#if __cpp_lib_ranges
namespace R = std::ranges;
namespace V = std::views;
#endif
#line 3 "num/float/convex.hpp"

// Returns (min f, argmin f)
template <class F>
auto convex_min(double l, double r, double e, F f) {
  const double PHI = 1.6180339887498948;
  int k = log((r - l) / e) / log(PHI) + 2;
  double x = (PHI * l + r) / (1 + PHI);
  double y = (l + PHI * r) / (1 + PHI);
  double fx = f(x);
  double fy = f(y);
  rep(i, k) {
    if (fx < fy) {
      l = x;
      tie(x, fx) = make_pair(y, fy);
      y = (l + PHI * r) / (1 + PHI);
      fy = f(y);
    } else {
      r = y;
      tie(y, fy) = make_pair(x, fx);
      x = (PHI * l + r) / (1 + PHI);
      fx = f(x);
    }
  }
  return make_pair(fx, x);
}

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