# unit1.rs - source
Source of the Rust file `src/pre_algebra/unit1.rs`.

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    use std::collections::HashSet;

    /// Finds all factor pairs for a positive integer `n`.
    ///
    /// This function calculates and returns a `HashSet<(u32, u32)>` containing all unique factor pairs
    /// of the input positive integer `n`. A factor pair is a pair of positive integers
    /// `(a, b)` where `a` and `b` are both factors of `n` (i.e., `a * b == n`).
    ///
    /// # Examples
    ///
    /// ```rust
    /// use std::collections::HashSet;
    /// use ladderz::pre_algebra::get_factor_pairs;
    ///
    /// fn main() {
    ///     let result_pairs = get_factor_pairs(12);
    ///     let expected_pairs: HashSet<(u32, u32)> = [(1, 12), (2, 6), (3, 4)].into();
    ///     assert_eq!(result_pairs, expected_pairs);
    /// }
    /// ```
    ///
    /// # Note
    ///
    /// This function calculates factor pairs by iterating through positive integers from 1 to `n`
    /// (inclusive) and checking if they divide `n` evenly. If they do, a factor pair `(a, b)` is
    /// added to the `HashSet`. The function ensures that factor pairs are unique, so `(a, b)` and
    /// `(b, a)` will not both appear in the set.
    pub fn get_factor_pairs(n: u32) -> HashSet<(u32, u32)> {
        let mut factor_pairs: HashSet<(u32, u32)> = HashSet::new();

        for num in 1..n + 1 {
            let dividend: u32 = n;
            let divisor: u32 = num;
            let quotient: u32 = dividend / num;
            let remainder: u32 = dividend % num;
            if remainder == 0 && !factor_pairs.contains(&(quotient, divisor)) {
                factor_pairs.insert((divisor, quotient));
            }
        }

        factor_pairs
    }

    /// Finds all factors of a positive integer `n`.
    ///
    /// This function calculates and returns a `HashSet<u32>` containing all unique factors
    /// of the input positive integer `n`. A factor of `n` is a positive integer `a` where
    /// `n` is evenly divisible by `a` (i.e., `n % a == 0`).
    ///
    /// # Examples
    ///
    /// ```rust
    /// use std::collections::HashSet;
    /// use ladderz::pre_algebra::get_factors;
    ///
    /// fn main() {
    ///     let result_factors = get_factors(16);
    ///     let expected_factors: HashSet<u32> = [1, 2, 4, 8, 16].into();
    ///     assert_eq!(result_factors, expected_factors);
    /// }
    /// ```
    ///
    /// # Note
    ///
    /// This function calculates factors by iterating through positive integers from 1 to `n`
    /// (inclusive) and checking if they divide `n` evenly. If they do, the factor is added to
    /// the `HashSet`. The function ensures that factors are unique, so duplicates are not added.
    pub fn get_factors(n: u32) -> HashSet<u32> {
        let mut factors: HashSet<u32> = HashSet::new();

        for num in 1..n + 1 {
            if n % num == 0 {
                factors.insert(num);
            }
        }
        factors
    }

    /// Checks if a positive integer `x` is a factor of another positive integer `y`.
    ///
    /// A factor of `y` is a positive integer `x` where `y` is evenly divisible by `x` (i.e., `y % x == 0`).
    ///
    /// # Examples
    ///
    /// ```rust
    /// use ladderz::pre_algebra::is_factor;
    ///
    /// fn main() {
    ///     assert!(is_factor(2, 16)); // 2 is a factor of 16
    ///     assert!(!is_factor(3, 16)); // 3 is not a factor of 16
    /// }
    /// ```
    ///
    /// # Note
    ///
    /// This function determines if `x` is a factor of `y` by checking if `y` is evenly divisible by `x`
    /// (i.e., `y % x == 0`).
    pub fn is_factor(x: u32, y: u32) -> bool {
        y % x == 0
    }

    /// Checks if a positive integer `x` is a multiple of another positive integer `y`.
    ///
    /// A multiple of `y` is a positive integer `x` where `x` is evenly divisible by `y` (i.e., `x % y == 0`).
    ///
    /// # Examples
    ///
    /// ```rust
    /// use ladderz::pre_algebra::is_multiple;
    ///
    /// fn main() {
    ///     assert!(is_multiple(16, 2)); // 16 is a multiple of 2
    ///     assert!(!is_multiple(16, 3)); // 16 is not a multiple of 3
    /// }
    /// ```
    pub fn is_multiple(x: u32, y: u32) -> bool {
        x % y == 0
    }

    /// Finds all the multiples of a positive integer `n` up to and including `end` (in the range [n, end]).
    ///
    /// Returns a `HashSet<u32>` containing all the multiples of a positive integer `n` in the range [n, end].
    ///
    /// A multiple of `n` is a positive integer `num` where `num` is evenly divisible by `n` (i.e., `num % n == 0`).
    ///
    /// # Examples
    ///
    /// ```rust
    /// use ladderz::pre_algebra::get_multiples_in_range;
    /// use std::collections::HashSet;
    ///
    /// fn main() {
    ///     let result: HashSet<u32> = get_multiples_in_range(2, 10);
    ///     let expected: HashSet<u32> = [2, 4, 6, 8, 10].into();
    ///     assert_eq!(result, expected);
    ///
    ///     let result: HashSet<u32> = get_multiples_in_range(3, 15);
    ///     let expected: HashSet<u32> = [3, 6, 9, 12, 15].into();
    ///     assert_eq!(result, expected);
    /// }
    /// ```
    pub fn get_multiples_in_range(n: u32, end: u32) -> HashSet<u32> {
        let mut multiples: HashSet<u32> = HashSet::new();

        for num in n..end + 1 {
            if num % n == 0 {
                multiples.insert(num);
            }
        }
        multiples
    }

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

        #[test]
        fn test_get_factor_pairs() {
            let result: HashSet<(u32, u32)> = get_factor_pairs(1);
            let expected: HashSet<(u32, u32)> = [(1, 1)].into();
            assert_eq!(result, expected);

            let result_2: HashSet<(u32, u32)> = get_factor_pairs(16);
            let expected_2: HashSet<(u32, u32)> = [(1, 16), (2, 8), (4, 4)].into();
            assert_eq!(result_2, expected_2);
        }

        #[test]
        fn test_get_factors() {
            let result: HashSet<u32> = get_factors(1);
            let expected: HashSet<u32> = [1].into();
            assert_eq!(result, expected);

            let result_2: HashSet<u32> = get_factors(16);
            let expected_2: HashSet<u32> = [1, 2, 4, 8, 16].into();
            assert_eq!(result_2, expected_2);
        }

        #[test]
        fn test_is_factor() {
            let result: bool = true;
            let expected: bool = is_factor(2, 10);
            assert_eq!(result, expected);

            let result_2: bool = false;
            let expected_2: bool = is_factor(3, 10);
            assert_eq!(result_2, expected_2);
        }

        #[test]
        fn test_is_multiple() {
            let result: bool = true;
            let expected: bool = is_multiple(10, 2);
            assert_eq!(result, expected);

            let result_2: bool = false;
            let expected_2: bool = is_multiple(11, 2);
            assert_eq!(result_2, expected_2);
        }

        #[test]
        fn test_get_multiples_in_range() {
            let result: HashSet<u32> = get_multiples_in_range(2, 20);
            let expected: HashSet<u32> = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20].into();
            assert_eq!(result, expected);

            let result_2: HashSet<u32> = get_multiples_in_range(5, 34);
            let expected_2: HashSet<u32> = [5, 10, 15, 20, 25, 30].into();
            assert_eq!(result_2, expected_2);
        }
    }