quadratic_residues/
lib.rs

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
/// Returns the quadratic residues of an integer
///
/// Examples:
///
/// use quadratic_residues::{ quadratic_residues, quadratic_non_residues, quadratic_residues_all };
///
/// quadratic_residues(7) => [1, 2, 4]
/// quadratic_non_residues(7) => [3, 5, 6]
/// quadratic_residues_all(7) => [1, 4, 2, 2, 4, 1]
use std::collections::HashSet;

/// Returns unique quadratic residues of an integer
pub fn quadratic_residues(number: i32) -> Vec<i32> {
    let mut quadratic_residues = quadratic_residues_all(number);
    quadratic_residues = get_unique(quadratic_residues);
    quadratic_residues.sort();
    quadratic_residues
}

/// Returns the quadratic non-residues of an integer
pub fn quadratic_non_residues(number: i32) -> Vec<i32> {
    let quadratic_residues = quadratic_residues_all(number);
    let mut quadratic_non_residues: Vec<i32> = vec![];

    for x in 1..number {
        if !quadratic_residues.contains(&x) {
            quadratic_non_residues.push(x);
        }
    }

    quadratic_non_residues
}

/// Returns the quadratic residues of an integer, including duplicates pub fn quadratic_residues_all(number: i32) -> Vec<i32> {
pub fn quadratic_residues_all(number: i32) -> Vec<i32> {
    let mut v = vec_of_smaller_ints(number);

    for x in v.iter_mut() {
        *x = (*x * *x) % number;
    }

    return v;
}

fn vec_of_smaller_ints(n: i32) -> Vec<i32> {
    (1..n).collect()
}

fn get_unique(vec: Vec<i32>) -> Vec<i32> {
    let unique_only: HashSet<_> = vec.clone().drain(..).collect();
    let mut unique_vec: Vec<_> = unique_only.into_iter().collect();
    unique_vec.sort();
    unique_vec
}

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

    #[test]
    fn test_quadratic_residues() {
        assert_eq!(quadratic_residues(7), vec![1, 2, 4]);
    }

    #[test]
    fn test_quadratic_non_residue() {
        assert_eq!(quadratic_non_residues(7), vec![3, 5, 6]);
    }

    #[test]
    fn test_quadratic_residues_all() {
        assert_eq!(quadratic_residues_all(7), vec![1, 4, 2, 2, 4, 1]);
    }

}