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
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
#![cfg(feature = "use_alloc")]

use crate::size_hint;
use crate::Itertools;

use alloc::vec::Vec;

#[derive(Clone)]
/// An iterator adaptor that iterates over the cartesian product of
/// multiple iterators of type `I`.
///
/// An iterator element type is `Vec<I>`.
///
/// See [`.multi_cartesian_product()`](crate::Itertools::multi_cartesian_product)
/// for more information.
#[must_use = "iterator adaptors are lazy and do nothing unless consumed"]
pub struct MultiProduct<I>(Vec<MultiProductIter<I>>)
    where I: Iterator + Clone,
          I::Item: Clone;

impl<I> std::fmt::Debug for MultiProduct<I>
where
    I: Iterator + Clone + std::fmt::Debug,
    I::Item: Clone + std::fmt::Debug,
{
    debug_fmt_fields!(CoalesceBy, 0);
}

/// Create a new cartesian product iterator over an arbitrary number
/// of iterators of the same type.
///
/// Iterator element is of type `Vec<H::Item::Item>`.
pub fn multi_cartesian_product<H>(iters: H) -> MultiProduct<<H::Item as IntoIterator>::IntoIter>
    where H: Iterator,
          H::Item: IntoIterator,
          <H::Item as IntoIterator>::IntoIter: Clone,
          <H::Item as IntoIterator>::Item: Clone
{
    MultiProduct(iters.map(|i| MultiProductIter::new(i.into_iter())).collect())
}

#[derive(Clone, Debug)]
/// Holds the state of a single iterator within a MultiProduct.
struct MultiProductIter<I>
    where I: Iterator + Clone,
          I::Item: Clone
{
    cur: Option<I::Item>,
    iter: I,
    iter_orig: I,
}

/// Holds the current state during an iteration of a MultiProduct.
#[derive(Debug)]
enum MultiProductIterState {
    StartOfIter,
    MidIter { on_first_iter: bool },
}

impl<I> MultiProduct<I>
    where I: Iterator + Clone,
          I::Item: Clone
{
    /// Iterates the rightmost iterator, then recursively iterates iterators
    /// to the left if necessary.
    ///
    /// Returns true if the iteration succeeded, else false.
    fn iterate_last(
        multi_iters: &mut [MultiProductIter<I>],
        mut state: MultiProductIterState
    ) -> bool {
        use self::MultiProductIterState::*;

        if let Some((last, rest)) = multi_iters.split_last_mut() {
            let on_first_iter = match state {
                StartOfIter => {
                    let on_first_iter = !last.in_progress();
                    state = MidIter { on_first_iter };
                    on_first_iter
                },
                MidIter { on_first_iter } => on_first_iter
            };

            if !on_first_iter {
                last.iterate();
            }

            if last.in_progress() {
                true
            } else if MultiProduct::iterate_last(rest, state) {
                last.reset();
                last.iterate();
                // If iterator is None twice consecutively, then iterator is
                // empty; whole product is empty.
                last.in_progress()
            } else {
                false
            }
        } else {
            // Reached end of iterator list. On initialisation, return true.
            // At end of iteration (final iterator finishes), finish.
            match state {
                StartOfIter => false,
                MidIter { on_first_iter } => on_first_iter
            }
        }
    }

    /// Returns the unwrapped value of the next iteration.
    fn curr_iterator(&self) -> Vec<I::Item> {
        self.0.iter().map(|multi_iter| {
            multi_iter.cur.clone().unwrap()
        }).collect()
    }

    /// Returns true if iteration has started and has not yet finished; false
    /// otherwise.
    fn in_progress(&self) -> bool {
        if let Some(last) = self.0.last() {
            last.in_progress()
        } else {
            false
        }
    }
}

impl<I> MultiProductIter<I>
    where I: Iterator + Clone,
          I::Item: Clone
{
    fn new(iter: I) -> Self {
        MultiProductIter {
            cur: None,
            iter: iter.clone(),
            iter_orig: iter
        }
    }

    /// Iterate the managed iterator.
    fn iterate(&mut self) {
        self.cur = self.iter.next();
    }

    /// Reset the managed iterator.
    fn reset(&mut self) {
        self.iter = self.iter_orig.clone();
    }

    /// Returns true if the current iterator has been started and has not yet
    /// finished; false otherwise.
    fn in_progress(&self) -> bool {
        self.cur.is_some()
    }
}

impl<I> Iterator for MultiProduct<I>
    where I: Iterator + Clone,
          I::Item: Clone
{
    type Item = Vec<I::Item>;

    fn next(&mut self) -> Option<Self::Item> {
        if MultiProduct::iterate_last(
            &mut self.0,
            MultiProductIterState::StartOfIter
        ) {
            Some(self.curr_iterator())
        } else {
            None
        }
    }

    fn count(self) -> usize {
        if self.0.is_empty() {
            return 0;
        }

        if !self.in_progress() {
            return self.0.into_iter().fold(1, |acc, multi_iter| {
                acc * multi_iter.iter.count()
            });
        }

        self.0.into_iter().fold(
            0,
            |acc, MultiProductIter { iter, iter_orig, cur: _ }| {
                let total_count = iter_orig.count();
                let cur_count = iter.count();
                acc * total_count + cur_count
            }
        )
    }

    fn size_hint(&self) -> (usize, Option<usize>) {
        // Not ExactSizeIterator because size may be larger than usize
        if self.0.is_empty() {
            return (0, Some(0));
        }

        if !self.in_progress() {
            return self.0.iter().fold((1, Some(1)), |acc, multi_iter| {
                size_hint::mul(acc, multi_iter.iter.size_hint())
            });
        }

        self.0.iter().fold(
            (0, Some(0)),
            |acc, &MultiProductIter { ref iter, ref iter_orig, cur: _ }| {
                let cur_size = iter.size_hint();
                let total_size = iter_orig.size_hint();
                size_hint::add(size_hint::mul(acc, total_size), cur_size)
            }
        )
    }

    fn last(self) -> Option<Self::Item> {
        let iter_count = self.0.len();

        let lasts: Self::Item = self.0.into_iter()
            .map(|multi_iter| multi_iter.iter.last())
            .while_some()
            .collect();

        if lasts.len() == iter_count {
            Some(lasts)
        } else {
            None
        }
    }
}