other/fibonacci_search.hpp

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• Last update: 2024-01-01 07:01:30+09:00
• Include: #include "other/fibonacci_search.hpp"

Required by

• convex/monge.hpp

Verified with

• test/mytest/fibonacci_search.test.cpp
• test/yukicoder/2276.test.cpp
• test/yukicoder/2627.test.cpp
• test/yukicoder/705.test.cpp

Code

// returns: {fx, x}
// [L, R) での極小値をひとつ求める、単峰は不要
template <typename T, bool MINIMIZE, typename F>
pair<T, ll> fibonacci_search(F f, ll L, ll R) {
  assert(L < R);
  --R;
  ll a = L, b = L + 1, c = L + 2, d = L + 3;
  int n = 0;
  while (d < R) { b = c, c = d, d = b + c - a, ++n; }
  auto get = [&](ll x) -> T {
    if (R < x) return infty<T>;
    return (MINIMIZE ? f(x) : -f(x));
  };
  T ya = get(a), yb = get(b), yc = get(c), yd = get(d);
  // この中で極小ならば全体でも極小、を維持する
  FOR(n) {
    if (yb <= yc) {
      d = c, c = b, b = a + d - c;
      yd = yc, yc = yb, yb = get(b);
    } else {
      a = b, b = c, c = a + d - b;
      ya = yb, yb = yc, yc = get(c);
    }
  }
  ll x = a;
  T y = ya;
  if (chmin(y, yb)) x = b;
  if (chmin(y, yc)) x = c;
  if (chmin(y, yd)) x = d;
  if (MINIMIZE) return {y, x};
  return {-y, x};
}

#line 1 "other/fibonacci_search.hpp"
// returns: {fx, x}
// [L, R) での極小値をひとつ求める、単峰は不要
template <typename T, bool MINIMIZE, typename F>
pair<T, ll> fibonacci_search(F f, ll L, ll R) {
  assert(L < R);
  --R;
  ll a = L, b = L + 1, c = L + 2, d = L + 3;
  int n = 0;
  while (d < R) { b = c, c = d, d = b + c - a, ++n; }
  auto get = [&](ll x) -> T {
    if (R < x) return infty<T>;
    return (MINIMIZE ? f(x) : -f(x));
  };
  T ya = get(a), yb = get(b), yc = get(c), yd = get(d);
  // この中で極小ならば全体でも極小、を維持する
  FOR(n) {
    if (yb <= yc) {
      d = c, c = b, b = a + d - c;
      yd = yc, yc = yb, yb = get(b);
    } else {
      a = b, b = c, c = a + d - b;
      ya = yb, yb = yc, yc = get(c);
    }
  }
  ll x = a;
  T y = ya;
  if (chmin(y, yb)) x = b;
  if (chmin(y, yc)) x = c;
  if (chmin(y, yd)) x = d;
  if (MINIMIZE) return {y, x};
  return {-y, x};
}

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