# competitive-programming-library

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# old/ternary-search.inc.cpp

## Code

/**
* @arg f must be a downward-convex function
* @retrun argmin f
* @note f is called (iteration + 1) times
*/
template <class Function>
double golden_section_search(double l, double r, int iteration, Function f) {
static const double GOLDEN_RATIO = (1 + sqrt(5)) / 2;
double m1 = l + (r - l) / (GOLDEN_RATIO + 1);
double m2 = l + (r - l) / GOLDEN_RATIO;  // NOTE: this equals to GOLDEN_RATIO / (GOLDEN_RATIO + 1.0)
double f1 = f(m1);
double f2 = f(m2);
while (iteration --) {
if (f1 < f2){
r = m2;
m2 = m1;
f2 = f1;
m1 = l + (r - l) / (GOLDEN_RATIO + 1);
f1 = f(m1);
} else {
l = m1;
m1 = m2;
f1 = f2;
m2 = l + (r - l) / GOLDEN_RATIO;
f2 = f(m2);
}
}
return (l + r) / 2;
}



#line 1 "old/ternary-search.inc.cpp"
/**
* @arg f must be a downward-convex function
* @retrun argmin f
* @note f is called (iteration + 1) times
*/
template <class Function>
double golden_section_search(double l, double r, int iteration, Function f) {
static const double GOLDEN_RATIO = (1 + sqrt(5)) / 2;
double m1 = l + (r - l) / (GOLDEN_RATIO + 1);
double m2 = l + (r - l) / GOLDEN_RATIO;  // NOTE: this equals to GOLDEN_RATIO / (GOLDEN_RATIO + 1.0)
double f1 = f(m1);
double f2 = f(m2);
while (iteration --) {
if (f1 < f2){
r = m2;
m2 = m1;
f2 = f1;
m1 = l + (r - l) / (GOLDEN_RATIO + 1);
f1 = f(m1);
} else {
l = m1;
m1 = m2;
f1 = f2;
m2 = l + (r - l) / GOLDEN_RATIO;
f2 = f(m2);
}
}
return (l + r) / 2;
}