#### Ternary Search Min Max Recursive

```/// Recursive ternary search algorithm for finding maximum of unimodal function
pub fn ternary_search_max_rec(
f: fn(f32) -> f32,
start: f32,
end: f32,
absolute_precision: f32,
) -> f32 {
if (end - start).abs() >= absolute_precision {
let mid1 = start + (end - start) / 3.0;
let mid2 = end - (end - start) / 3.0;

let r1 = f(mid1);
let r2 = f(mid2);

if r1 < r2 {
return ternary_search_max_rec(f, mid1, end, absolute_precision);
} else if r1 > r2 {
return ternary_search_max_rec(f, start, mid2, absolute_precision);
} else {
return ternary_search_max_rec(f, mid1, mid2, absolute_precision);
}
}
f(start)
}

/// Recursive ternary search algorithm for finding minimum of unimodal function
pub fn ternary_search_min_rec(
f: fn(f32) -> f32,
start: f32,
end: f32,
absolute_precision: f32,
) -> f32 {
if (end - start).abs() >= absolute_precision {
let mid1 = start + (end - start) / 3.0;
let mid2 = end - (end - start) / 3.0;

let r1 = f(mid1);
let r2 = f(mid2);

if r1 < r2 {
return ternary_search_min_rec(f, start, mid2, absolute_precision);
} else if r1 > r2 {
return ternary_search_min_rec(f, mid1, end, absolute_precision);
} else {
return ternary_search_min_rec(f, mid1, mid2, absolute_precision);
}
}
f(start)
}

#[cfg(test)]
mod tests {
use super::*;

#[test]
fn finds_max_value() {
let expected = 4.0;
let f = |x: f32| -x * x - 2.0 * x + 3.0;

let start: f32 = -10000000000.0;
let end: f32 = 10000000000.0;
let absolute_precision = 0.0000001;

let result = ternary_search_max_rec(f, start, end, absolute_precision);

assert_eq!(result, expected);
}

#[test]
fn finds_min_value() {
let expected = 2.0;
let f = |x: f32| x * x - 2.0 * x + 3.0;

let start: f32 = -10000000000.0;
let end: f32 = 10000000000.0;
let absolute_precision = 0.0000001;

let result = ternary_search_min_rec(f, start, end, absolute_precision);

assert_eq!(result, expected);
}

#[test]
fn finds_max_value_2() {
let expected = 7.25;
let f = |x: f32| -x.powi(2) + 3.0 * x + 5.0;

let start: f32 = -10000000000.0;
let end: f32 = 10000000000.0;
let absolute_precision = 0.000001;

let result = ternary_search_max_rec(f, start, end, absolute_precision);

assert_eq!(result, expected);
}

#[test]
fn finds_min_value_2() {
let expected = 2.75;
let f = |x: f32| x.powi(2) + 3.0 * x + 5.0;

let start: f32 = -10000000000.0;
let end: f32 = 10000000000.0;
let absolute_precision = 0.000001;

let result = ternary_search_min_rec(f, start, end, absolute_precision);

assert_eq!(result, expected);
}
}
```