numberlab 0.1.9

A collection of numerical algorithms
Documentation 
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/// Calculates the nth Lucas number.
///
/// # Arguments
///
/// * `n` - A non-negative integer representing the position in the Lucas sequence.
///
/// # Returns
///
/// The nth Lucas number .
///
/// # Examples
///
/// ```
/// use numberlab::sequence::lucas::nth_lucas;
///
/// let result = nth_lucas(10);
/// assert_eq!(result, (123u128));
/// ```
pub fn nth_lucas(n: usize) -> u128 {
    match n {
        0 => 2u128,
        1 => 1u128,
        _ => nth_lucas(n - 1) + nth_lucas(n - 2),
    }
}

/// Calculates the nth Lucas number using memoization.
///
/// # Arguments
///
/// * `n` - A non-negative integer representing the position in the Lucas sequence.
///
/// # Returns
///
/// The nth Lucas number .
///
/// # Examples
///
/// ```
/// use numberlab::sequence::lucas::nth_lucas_memoized;
///
/// let result = nth_lucas_memoized(10);
/// assert_eq!(result, (123u128));
/// ```
pub fn nth_lucas_memoized(n: usize) -> u128 {
    let mut memoizer = vec![2, 1];
    nth_lucas_with_memoizer(n, &mut memoizer)
}

fn nth_lucas_with_memoizer(n: usize, memoizer: &mut Vec<u128>) -> u128 {
    if n < memoizer.len() {
        memoizer[n].clone()
    } else {
        let lth_lucas = nth_lucas_with_memoizer(n - 1, memoizer);
        let mth_lucas = nth_lucas_with_memoizer(n - 2, memoizer);
        let nth_lucas = lth_lucas + mth_lucas;
        memoizer.push(nth_lucas);
        memoizer[n].clone()
    }
}

/// Generates a sequence of Lucas numbers up to the given number `n`.
///
/// # Arguments
///
/// * `n` - A non-negative integer representing the number of terms in the Lucas sequence.
///
/// # Returns
///
/// A vector containing the Lucas sequence up to the given number `n`.
///
/// # Examples
///
/// ```
/// use numberlab::sequence::lucas::lucas_sequence;
///
/// let sequence = lucas_sequence(5);
/// assert_eq!(sequence, vec![2, 1, 3, 4, 7]);
/// ```
pub fn lucas_sequence(n: usize) -> Vec<u128> {
    if n == 0 {
        vec![]
    } else if n == 1 {
        vec![2]
    } else if n == 2 {
        vec![2, 1]
    } else {
        let mut sequence = vec![2, 1];
        (2..n).for_each(|i| sequence.push(sequence[i - 1] + sequence[i - 2]));
        sequence
    }
}