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
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129

use bools::random::{weighted_random_bools, WeightedRandomBools};
use random::Seed;

/// Generates random [`Option`]s except `None`, with values from a given random iterator.
///
/// This `struct` is created by [`random_somes`]; see its documentation for more.
#[derive(Clone, Debug)]
pub struct RandomSomes<I: Iterator> {
    xs: I,
}

impl<I: Iterator> Iterator for RandomSomes<I> {
    type Item = Option<I::Item>;

    #[inline]
    fn next(&mut self) -> Option<Option<I::Item>> {
        Some(self.xs.next())
    }
}

/// Generates random [`Option`]s except `None`, with values from a given random iterator.
///
/// The values have the same distribution as the values generated by the given iterator: If $Q(x)$
/// is the probability of $x$ being generated by `xs`, then
///
/// $P(\operatorname{Some}(x)) = Q(x)$.
///
/// `xs` must be infinite.
///
/// The output length is infinite.
///
/// # Examples
/// ```
/// use malachite_base::iterators::prefix_to_string;
/// use malachite_base::num::random::random_primitive_ints;
/// use malachite_base::options::random::random_somes;
/// use malachite_base::random::EXAMPLE_SEED;
/// use malachite_base::strings::ToDebugString;
///
/// assert_eq!(
///     prefix_to_string(
///         random_somes(random_primitive_ints::<u8>(EXAMPLE_SEED)).map(|x| x.to_debug_string()),
///         5
///     ),
///     "[Some(113), Some(239), Some(69), Some(108), Some(228), ...]",
/// )
/// ```
pub const fn random_somes<I: Iterator>(xs: I) -> RandomSomes<I> {
    RandomSomes { xs }
}

/// Generates random [`Option`]s with values from a given random iterator.
///
/// We don't use [`WithSpecialValue`](crate::iterators::WithSpecialValue) here because that
/// requires `I::Item` to be cloneable. The "special value" in this case, `None`, can be produced
/// on demand without any cloning.
///
/// This `struct` is created by [`random_options`]; see its documentation for more.
#[derive(Clone, Debug)]
pub struct RandomOptions<I: Iterator> {
    bs: WeightedRandomBools,
    xs: I,
}

impl<I: Iterator> Iterator for RandomOptions<I> {
    type Item = Option<I::Item>;

    #[inline]
    fn next(&mut self) -> Option<Option<I::Item>> {
        Some(if self.bs.next().unwrap() {
            self.xs.next()
        } else {
            None
        })
    }
}

/// Generates random [`Option`]s with values from a given random iterator.
///
/// The probability of generating `None` is specified by $p$ =
/// `none_p_numerator / none_p_denominator`. If a `Some` is generated, its values have the same
/// distribution as the values generated by the given iterator.
///
/// If $Q(x)$ is the probability of $x$ being generated by `xs`, then
///
/// $P(\text{None}) = p$
///
/// $P(\operatorname{Some}(x)) = (1-p)Q(x)$
///
/// `xs` must be infinite.
///
/// The output length is infinite.
///
/// # Panics
/// Panics if `none_p_denominator` is 0 or `none_p_numerator > none_p_denominator`.
///
/// # Examples
/// ```
/// use malachite_base::iterators::prefix_to_string;
/// use malachite_base::num::random::random_primitive_ints;
/// use malachite_base::options::random::random_options;
/// use malachite_base::random::EXAMPLE_SEED;
/// use malachite_base::strings::ToDebugString;
///
/// assert_eq!(
///     prefix_to_string(
///         random_options(EXAMPLE_SEED, 1, 2, &random_primitive_ints::<u8>)
///                 .map(|x| x.to_debug_string()),
///         10
///     ),
///     "[Some(85), Some(11), Some(136), None, Some(200), None, Some(235), Some(134), Some(203), \
///     None, ...]"
/// )
/// ```
pub fn random_options<I: Iterator>(
    seed: Seed,
    none_p_numerator: u64,
    none_p_denominator: u64,
    xs_gen: &dyn Fn(Seed) -> I,
) -> RandomOptions<I> {
    RandomOptions {
        bs: weighted_random_bools(
            seed.fork("bs"),
            none_p_denominator - none_p_numerator,
            none_p_denominator,
        ),
        xs: xs_gen(seed.fork("xs")),
    }
}