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

/// Factorial
///
/// # Type
/// : `usize -> usize`
///
/// # Usage
///
/// ```
/// extern crate peroxide;
/// use peroxide::*;
///
/// assert_eq!(factorial(5), 120);
/// ```
pub fn factorial(n: usize) -> usize {
    let mut p = 1usize;
    for i in 1..(n + 1) {
        p *= i;
    }
    p
}

/// Permutation
///
/// # Usage
///
/// ```
/// extern crate peroxide;
/// use peroxide::*;
///
/// assert_eq!(P(5,3), 60);
/// ```
#[allow(non_snake_case)]
pub fn P(n: usize, r: usize) -> usize {
    let mut p = 1usize;
    for i in 0..r {
        p *= n - i;
    }
    p
}

/// Combination
///
/// # Usage
///
/// ```
/// extern crate peroxide;
/// use peroxide::*;
///
/// assert_eq!(C(10, 9), 10);
/// ```
#[allow(non_snake_case)]
pub fn C(n: usize, r: usize) -> usize {
    if r > n / 2 {
        return C(n, n - r);
    }

    P(n, r) / factorial(r)
}

/// Combination with Repetition
///
/// # Usage
///
/// ```
/// extern crate peroxide;
/// use peroxide::*;
///
/// assert_eq!(H(5,3), C(7,3));
/// ```
#[allow(non_snake_case)]
pub fn H(n: usize, r: usize) -> usize {
    C(n + r - 1, r)
}