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
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
use bools::random::{weighted_random_bools, WeightedRandomBools};
use itertools::Itertools;
use num::basic::traits::Zero;
use random::Seed;
use std::collections::{HashSet, VecDeque};
use std::fmt::Display;
use std::hash::Hash;
use vecs::{random_values_from_vec, RandomValuesFromVec};

/// Generates all the nonzero values of a provided iterator.
///
/// This `struct` is created by [`nonzero_values`]; see its documentation for more.
#[derive(Clone, Debug)]
pub struct NonzeroValues<I: Iterator>(I)
where
    I::Item: PartialEq<I::Item> + Zero;

impl<I: Iterator> Iterator for NonzeroValues<I>
where
    I::Item: PartialEq<I::Item> + Zero,
{
    type Item = I::Item;

    #[inline]
    fn next(&mut self) -> Option<I::Item> {
        loop {
            let x = self.0.next();
            if x != Some(I::Item::ZERO) {
                return x;
            }
        }
    }
}

impl<I: DoubleEndedIterator> DoubleEndedIterator for NonzeroValues<I>
where
    I::Item: PartialEq<I::Item> + Zero,
{
    #[inline]
    fn next_back(&mut self) -> Option<I::Item> {
        loop {
            let x = self.0.next_back();
            if x != Some(I::Item::ZERO) {
                return x;
            }
        }
    }
}

/// Returns an iterator that generates all the nonzero values of a provided iterator.
///
/// `nonzero_values(xs)` generates the same values as `xs.filter(|x| x != I::Item::ZERO)`, but its
/// type is easier to work with.
///
/// This iterator will hang if given an iterator that produces an infinite suffix of zeros.
///
/// The output length is the number of nonzero values produced by `xs`.
///
/// # Examples
/// ```
/// extern crate itertools;
///
/// use itertools::Itertools;
/// use malachite_base::iterators::nonzero_values;
///
/// assert_eq!(
///     nonzero_values([-3i8, -2, -1, 0, 1, 2, 3].iter().cloned()).collect_vec(),
///     &[-3, -2, -1, 1, 2, 3]
/// )
/// ```
#[inline]
pub const fn nonzero_values<I: Iterator>(xs: I) -> NonzeroValues<I>
where
    I::Item: PartialEq<I::Item> + Zero,
{
    NonzeroValues(xs)
}

/// Returns whether all of the values generated by an iterator are equal.
///
/// `is_constant(xs)` is equivalent to `xs.unique().count() == 1` for finite nonempty iterators,
/// but is more efficient, doesn't require [`Clone`] or [`Hash`] implementations, and doesn't hang
/// if provided an infinite non-constant iterator.
///
/// This function will hang if given an infinite constant iterator.
///
/// # Examples
/// ```
/// use malachite_base::iterators::is_constant;
///
/// assert_eq!(is_constant([1; 4].iter()), true);
/// assert_eq!(is_constant([1, 2, 3, 4].iter()), false);
/// ```
pub fn is_constant<I: Iterator>(xs: I) -> bool
where
    I::Item: Eq,
{
    let mut first = None;
    for x in xs {
        if let Some(ref first) = first {
            if x != *first {
                return false;
            }
        } else {
            first = Some(x);
        }
    }
    true
}

/// Returns whether an iterator returns at least some number of values.
///
/// `count_is_at_least(xs, n)` is equivalent to `xs.count() >= n` for finite iterators, but doesn't
/// hang if provided an infinite iterator.
///
/// # Examples
/// ```
/// use malachite_base::iterators::count_is_at_least;
///
/// assert_eq!(count_is_at_least([1, 2, 3, 4].iter(), 3), true);
/// assert_eq!(count_is_at_least([1, 2, 3, 4].iter(), 4), true);
/// assert_eq!(count_is_at_least([1, 2, 3, 4].iter(), 5), false);
/// ```
#[inline]
pub fn count_is_at_least<I: Iterator>(xs: I, n: usize) -> bool {
    xs.take(n).count() == n
}

/// Returns whether an iterator returns at most some number of values.
///
/// `count_is_at_most(xs, n)` is equivalent to `xs.count() <= n` for finite iterators, but doesn't
/// hang if provided an infinite iterator.
///
/// # Examples
/// ```
/// use malachite_base::iterators::count_is_at_most;
///
/// assert_eq!(count_is_at_most([1, 2, 3, 4].iter(), 3), false);
/// assert_eq!(count_is_at_most([1, 2, 3, 4].iter(), 4), true);
/// assert_eq!(count_is_at_most([1, 2, 3, 4].iter(), 5), true);
/// ```
#[inline]
pub fn count_is_at_most<I: Iterator>(xs: I, n: usize) -> bool {
    xs.take(n + 1).count() <= n
}

/// Returns whether an iterator never returns the same value twice.
///
/// `is_unique(xs)` is equivalent to `xs.unique().count() <= 1` for finite iterators, but is more
/// efficient and doesn't hang if provided a non-unique infinite iterator.
///
/// This iterator will hang if given an infinite unique iterator.
///
/// # Examples
/// ```
/// use malachite_base::iterators::is_unique;
///
/// let empty: [u32; 0] = [];
/// assert_eq!(is_unique(empty.iter()), true);
/// assert_eq!(is_unique([1, 2, 3, 4].iter()), true);
/// assert_eq!(is_unique([1, 2, 3, 1].iter()), false);
/// ```
#[inline]
pub fn is_unique<I: Iterator>(xs: I) -> bool
where
    I::Item: Eq + Hash,
{
    let mut set = HashSet::new();
    for x in xs {
        if !set.insert(x) {
            return false;
        }
    }
    true
}

/// Returns the first and last elements of an iterator, or `None` if it is empty.
///
/// The iterator's elements must be cloneable, since if the iterator consists of a single element
/// `x`, the result will be `(x, x)`.
///
/// This iterator will hang if given an infinite iterator.
///
/// # Examples
/// ```
/// use malachite_base::iterators::first_and_last;
///
/// let empty: [u32; 0] = [];
/// assert_eq!(first_and_last(&mut empty.iter()), None);
/// assert_eq!(first_and_last(&mut [1].iter().cloned()), Some((1, 1)));
/// assert_eq!(first_and_last(&mut [1, 2, 3].iter().cloned()), Some((1, 3)));
/// ```
pub fn first_and_last<I: Iterator>(xs: &mut I) -> Option<(I::Item, I::Item)>
where
    I::Item: Clone,
{
    xs.next().map(|first| {
        if let Some(last) = xs.last() {
            (first, last)
        } else {
            (first.clone(), first)
        }
    })
}

/// Groups elements of an iterator into intervals of adjacent elements that match a predicate. The
/// endpoints of each interval are returned.
///
/// The intervals are inclusive.
///
/// This iterator will hang if given an infinite iterator.
///
/// # Examples
/// ```
/// use malachite_base::iterators::matching_intervals_in_iterator;
///
/// let xs = &[1, 2, 10, 11, 12, 7, 8, 16, 5];
/// assert_eq!(
///     matching_intervals_in_iterator(xs.iter().cloned(), |&x| x >= 10).as_slice(),
///     &[(10, 12), (16, 16)]
/// );
/// assert_eq!(
///     matching_intervals_in_iterator(xs.iter().cloned(), |&x| x < 10).as_slice(),
///     &[(1, 2), (7, 8), (5, 5)]
/// );
/// ```
pub fn matching_intervals_in_iterator<I: Iterator, F: Fn(&I::Item) -> bool>(
    xs: I,
    predicate: F,
) -> Vec<(I::Item, I::Item)>
where
    I::Item: Clone,
{
    xs.group_by(predicate)
        .into_iter()
        .filter_map(|(b, mut group)| if b { first_and_last(&mut group) } else { None })
        .collect()
}

/// An iterator that randomly produces another iterator's values, or produces a special value.
///
/// This `struct` is created by [`with_special_value`]; see its documentation for more.
#[derive(Clone, Debug)]
pub struct WithSpecialValue<I: Iterator>
where
    I::Item: Clone,
{
    bs: WeightedRandomBools,
    special_value: I::Item,
    xs: I,
}

impl<I: Iterator> Iterator for WithSpecialValue<I>
where
    I::Item: Clone,
{
    type Item = I::Item;

    fn next(&mut self) -> Option<I::Item> {
        if self.bs.next().unwrap() {
            Some(self.special_value.clone())
        } else {
            self.xs.next()
        }
    }
}

/// An iterator that randomly produces another iterator's values, or produces a special value.
///
/// Let $n_p$ be `p_numerator`, $d_p$ be `p_denominator`, and let $p=n_p/d_p$.
///
/// Every time a value is to be generated, the iterator returns the special value with probability
/// $p$, or else returns a value from the inner iterator.
///
/// If $p > 0$, the output length is infinite. Otherwise, it is the same as the length of `xs`.
///
/// # Panics
/// Panics if `p_denominator` is 0 or `p_numerator` is greater than `p_denominator`.
///
/// # Examples
/// ```
/// extern crate itertools;
///
/// use itertools::Itertools;
/// use malachite_base::iterators::{prefix_to_string, with_special_value};
/// use malachite_base::num::random::random_primitive_ints;
/// use malachite_base::random::EXAMPLE_SEED;
///
/// assert_eq!(
///     prefix_to_string(
///         with_special_value(EXAMPLE_SEED, -1i16, 1, 2, &random_primitive_ints::<i16>),
///         20
///     ),
///     "[-1, -1, -1, 2901, -1, -14200, -1, -1, -1, -30997, -8245, -5338, -1, -1, -20007, -1, -1, \
///     -1, -1, -1, ...]"
/// );
/// ```
pub fn with_special_value<I: Iterator>(
    seed: Seed,
    special_value: I::Item,
    p_numerator: u64,
    p_denominator: u64,
    xs_gen: &dyn Fn(Seed) -> I,
) -> WithSpecialValue<I>
where
    I::Item: Clone,
{
    WithSpecialValue {
        bs: weighted_random_bools(seed.fork("bs"), p_numerator, p_denominator),
        special_value,
        xs: xs_gen(seed.fork("xs")),
    }
}

/// An iterator that randomly produces another iterator's values, or samples from a [`Vec`] of
/// special values.
///
/// This `struct` is created by [`with_special_values`]; see its documentation for more.
#[derive(Clone, Debug)]
pub struct WithSpecialValues<I: Iterator>
where
    I::Item: Clone,
{
    bs: WeightedRandomBools,
    special_values: RandomValuesFromVec<I::Item>,
    xs: I,
}

impl<I: Iterator> Iterator for WithSpecialValues<I>
where
    I::Item: Clone,
{
    type Item = I::Item;

    fn next(&mut self) -> Option<I::Item> {
        if self.bs.next().unwrap() {
            self.special_values.next()
        } else {
            self.xs.next()
        }
    }
}

/// An iterator that randomly produces another iterator's values, or produces a random special
/// value from a [`Vec`].
///
/// Let $n_p$ be `p_numerator`, $d_p$ be `p_denominator`, and let $p=n_p/d_p$.
///
/// Every time a value is to be generated, the iterator uniformly samples the special values
/// [`Vec`] with probability $p$, or else returns a value from the inner iterator.
///
/// If $p > 0$, the output length is infinite. Otherwise, it is the same as the length of `xs`.
///
/// # Worst-case complexity per iteration
/// Constant time and additional memory.
///
/// # Panics
/// Panics if `special_values` is empty, `p_denominator` is 0, or if `p_numerator` is greater than
/// `p_denominator`.
///
/// # Examples
/// ```
/// use malachite_base::iterators::{prefix_to_string, with_special_values};
/// use malachite_base::num::random::random_primitive_ints;
/// use malachite_base::random::EXAMPLE_SEED;
///
/// assert_eq!(
///     prefix_to_string(
///         with_special_values(EXAMPLE_SEED, vec![1, 2, 3], 1, 2, &random_primitive_ints::<i16>),
///         20,
///     ),
///     "[3, 1, 3, 2901, 1, -14200, 2, 3, 1, -30997, -8245, -5338, 1, 1, -20007, 3, 1, 1, 1, 1, \
///     ...]"
/// );
/// ```
pub fn with_special_values<I: Iterator>(
    seed: Seed,
    special_values: Vec<I::Item>,
    p_numerator: u64,
    p_denominator: u64,
    xs_gen: &dyn Fn(Seed) -> I,
) -> WithSpecialValues<I>
where
    I::Item: Clone,
{
    WithSpecialValues {
        bs: weighted_random_bools(seed.fork("bs"), p_numerator, p_denominator),
        special_values: random_values_from_vec(seed.fork("special_values"), special_values),
        xs: xs_gen(seed.fork("xs")),
    }
}

/// Generates sliding windows of elements from an iterator.
///
/// This `struct` is created by [`iter_windows`]; see its documentation for more.
#[derive(Clone, Debug)]
pub struct IterWindows<I: Iterator>
where
    I::Item: Clone,
{
    xs: I,
    window: VecDeque<I::Item>,
    window_size: usize,
}

impl<I: Iterator> Iterator for IterWindows<I>
where
    I::Item: Clone,
{
    type Item = VecDeque<I::Item>;

    fn next(&mut self) -> Option<VecDeque<I::Item>> {
        if self.window.len() < self.window_size {
            self.window = (&mut self.xs).take(self.window_size).collect();
            if self.window.len() < self.window_size {
                None
            } else {
                Some(self.window.clone())
            }
        } else {
            let x = self.xs.next()?;
            self.window.pop_front();
            self.window.push_back(x);
            Some(self.window.clone())
        }
    }
}

/// Returns windows of $n$ adjacent elements of an iterator, advancing the window by 1 in each
/// iteration. The values are cloned each time a new window is generated.
///
/// The output length is $n - k + 1$, where $n$ is `xs.count()` and $k$ is `window_size`.
///
/// # Panics
/// Panics if `window_size` is 0.
///
/// # Examples
/// ```
/// extern crate itertools;
///
/// use itertools::Itertools;
/// use malachite_base::iterators::iter_windows;
///
/// let xs = 0..=5;
/// let windows = iter_windows(3, xs).map(|ws| ws.iter().cloned().collect_vec()).collect_vec();
/// assert_eq!(
///     windows.iter().map(Vec::as_slice).collect_vec().as_slice(),
///     &[&[0, 1, 2], &[1, 2, 3], &[2, 3, 4], &[3, 4, 5]]
/// );
/// ```
pub fn iter_windows<I: Iterator>(window_size: usize, xs: I) -> IterWindows<I>
where
    I::Item: Clone,
{
    assert_ne!(window_size, 0);
    IterWindows {
        xs,
        window: VecDeque::with_capacity(window_size),
        window_size,
    }
}

/// Converts a prefix of an iterator to a string.
///
/// Suppose the iterator generates $(a, b, c, d)$. If `max_len` is 3, this function will return the
/// string `"[a, b, c, ...]"`. If `max_len` is 4 or more, this function will return `[a, b, c, d]`.
///
/// This function will attempt to advance the iterator `max_len + 1` times. The extra time is used
/// determine whether the output string should contain an ellipsis.
///
/// # Panics
/// Panics if `max_len` is 0.
///
/// # Examples
/// ```
/// extern crate itertools;
///
/// use itertools::Itertools;
/// use malachite_base::iterators::prefix_to_string;
///
/// assert_eq!(prefix_to_string(0..10, 3), "[0, 1, 2, ...]");
/// assert_eq!(prefix_to_string(0..4, 5), "[0, 1, 2, 3]");
/// ```
pub fn prefix_to_string<I: Iterator>(mut xs: I, max_len: usize) -> String
where
    I::Item: Display,
{
    assert_ne!(max_len, 0);
    let mut s = String::new();
    s.push('[');
    let mut first = true;
    let mut done = false;
    for _ in 0..max_len {
        if let Some(x) = xs.next() {
            if first {
                first = false;
            } else {
                s.push_str(", ");
            }
            s.push_str(&x.to_string());
        } else {
            done = true;
            break;
        }
    }
    if !done && xs.next().is_some() {
        s.push_str(", ...");
    }
    s.push(']');
    s
}

/// Contains [`BitDistributor`](bit_distributor::BitDistributor), which helps generate tuples
/// exhaustively.
pub mod bit_distributor;
/// Functions that compare adjacent iterator elements.
pub mod comparison;
/// Contains [`IteratorCache`](iterator_cache::IteratorCache), which remembers values produced by
/// an iterator.
pub mod iterator_cache;