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
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
// This Source Code Form is subject to the terms of the Mozilla Public
// License, v. 2.0. If a copy of the MPL was not distributed with this
// file, You can obtain one at http://mozilla.org/MPL/2.0/.

use std::borrow::Borrow;
use std::cmp::Ordering;
use std::mem;

use typenum::{Add1, Unsigned};

use config::OrdChunkSize as NodeSize;
use nodes::sized_chunk::Chunk;
use util::{clone_ref, Ref};

use self::Insert::*;
use self::InsertAction::*;

const NODE_SIZE: usize = NodeSize::USIZE;
const MEDIAN: usize = (NODE_SIZE + 1) >> 1;

pub trait BTreeValue: Clone {
    type Key;
    fn ptr_eq(&self, other: &Self) -> bool;
    fn search_key<BK>(slice: &[Self], key: &BK) -> Result<usize, usize>
    where
        BK: Ord + ?Sized,
        Self::Key: Borrow<BK>;
    fn search_value(slice: &[Self], value: &Self) -> Result<usize, usize>;
    fn cmp_keys<BK>(&self, other: &BK) -> Ordering
    where
        BK: Ord + ?Sized,
        Self::Key: Borrow<BK>;
    fn cmp_values(&self, other: &Self) -> Ordering;
}

pub struct Node<A> {
    keys: Chunk<A, NodeSize>,
    children: Chunk<Option<Ref<Node<A>>>, Add1<NodeSize>>,
}

pub enum Insert<A> {
    Added,
    Replaced(A),
    Update(Node<A>),
    Split(Node<A>, A, Node<A>),
}

enum InsertAction<A> {
    AddedAction,
    ReplacedAction(A),
    InsertAt,
    InsertSplit(Node<A>, A, Node<A>),
}

pub enum Remove<A> {
    NoChange,
    Removed(A),
    Update(A, Node<A>),
}

enum RemoveAction {
    DeleteAt(usize),
    PullUp(usize, usize, usize),
    Merge(usize),
    StealFromLeft(usize),
    StealFromRight(usize),
    MergeFirst(usize),
    ContinueDown(usize),
}

impl<A> Clone for Node<A>
where
    A: Clone,
{
    fn clone(&self) -> Self {
        Node {
            keys: self.keys.clone(),
            children: self.children.clone(),
        }
    }
}

impl<A> Default for Node<A> {
    fn default() -> Self {
        Node {
            keys: Chunk::new(),
            children: Chunk::unit(None),
        }
    }
}

impl<A> Node<A>
where
    A: Clone,
{
    #[inline]
    fn has_room(&self) -> bool {
        self.keys.len() < NODE_SIZE
    }

    #[inline]
    fn too_small(&self) -> bool {
        self.keys.len() < MEDIAN
    }

    #[inline]
    fn is_leaf(&self) -> bool {
        self.children[0].is_none()
    }

    #[inline]
    pub fn new() -> Self {
        Self::default()
    }

    #[inline]
    pub fn unit(value: A) -> Self {
        Node {
            keys: Chunk::unit(value),
            children: Chunk::pair(None, None),
        }
    }

    #[inline]
    pub fn from_split(left: Node<A>, median: A, right: Node<A>) -> Self {
        Node {
            keys: Chunk::unit(median),
            children: Chunk::pair(Some(Ref::from(left)), Some(Ref::from(right))),
        }
    }

    pub fn min(&self) -> Option<&A> {
        match self.children.first().unwrap() {
            None => self.keys.first(),
            Some(ref child) => child.min(),
        }
    }

    pub fn max(&self) -> Option<&A> {
        match self.children.last().unwrap() {
            None => self.keys.last(),
            Some(ref child) => child.max(),
        }
    }
}

impl<A: BTreeValue> Node<A> {
    fn child_contains<BK>(&self, index: usize, key: &BK) -> bool
    where
        BK: Ord + ?Sized,
        A::Key: Borrow<BK>,
    {
        if let Some(Some(ref child)) = self.children.get(index) {
            child.lookup(key).is_some()
        } else {
            false
        }
    }

    pub fn lookup<BK>(&self, key: &BK) -> Option<&A>
    where
        BK: Ord + ?Sized,
        A::Key: Borrow<BK>,
    {
        if self.keys.is_empty() {
            return None;
        }
        // Perform a binary search, resulting in either a match or
        // the index of the first higher key, meaning we search the
        // child to the left of it.
        match A::search_key(&self.keys, key) {
            Ok(index) => Some(&self.keys[index]),
            Err(index) => match self.children[index] {
                None => None,
                Some(ref node) => node.lookup(key),
            },
        }
    }

    pub fn lookup_mut<BK>(&mut self, key: &BK) -> Option<&mut A>
    where
        BK: Ord + ?Sized,
        A::Key: Borrow<BK>,
    {
        if self.keys.is_empty() {
            return None;
        }
        // Perform a binary search, resulting in either a match or
        // the index of the first higher key, meaning we search the
        // child to the left of it.
        match A::search_key(&self.keys, key) {
            Ok(index) => Some(&mut self.keys[index]),
            Err(index) => match self.children[index] {
                None => None,
                Some(ref mut child_ref) => {
                    let child = Ref::make_mut(child_ref);
                    child.lookup_mut(key)
                }
            },
        }
    }

    fn split(
        &mut self,
        value: A,
        ins_left: Option<Node<A>>,
        ins_right: Option<Node<A>>,
    ) -> Insert<A> {
        let left_child = ins_left.map(Ref::from);
        let right_child = ins_right.map(Ref::from);
        let index = A::search_value(&self.keys, &value).unwrap_err();
        let mut left_keys;
        let mut left_children;
        let mut right_keys;
        let mut right_children;
        let median;
        if index < MEDIAN {
            self.children[index] = left_child;

            left_keys = Chunk::from_front(&mut self.keys, index);
            left_keys.push_back(value);
            left_keys.drain_from_front(&mut self.keys, MEDIAN - index - 1);

            left_children = Chunk::from_front(&mut self.children, index + 1);
            left_children.push_back(right_child);
            left_children.drain_from_front(&mut self.children, MEDIAN - index - 1);

            median = self.keys.pop_front();

            right_keys = Chunk::drain_from(&mut self.keys);
            right_children = Chunk::drain_from(&mut self.children);
        } else if index > MEDIAN {
            self.children[index] = left_child;

            left_keys = Chunk::from_front(&mut self.keys, MEDIAN);
            left_children = Chunk::from_front(&mut self.children, MEDIAN + 1);

            median = self.keys.pop_front();

            right_keys = Chunk::from_front(&mut self.keys, index - MEDIAN - 1);
            right_keys.push_back(value);
            right_keys.append(&mut self.keys);

            right_children = Chunk::from_front(&mut self.children, index - MEDIAN);
            right_children.push_back(right_child);
            right_children.append(&mut self.children);
        } else {
            left_keys = Chunk::from_front(&mut self.keys, MEDIAN);
            left_children = Chunk::from_front(&mut self.children, MEDIAN);
            left_children.push_back(left_child);

            median = value;

            right_keys = Chunk::drain_from(&mut self.keys);
            right_children = Chunk::drain_from(&mut self.children);
            right_children[0] = right_child;
        }

        debug_assert!(left_keys.len() == MEDIAN);
        debug_assert!(left_children.len() == MEDIAN + 1);
        debug_assert!(right_keys.len() == MEDIAN);
        debug_assert!(right_children.len() == MEDIAN + 1);

        Split(
            Node {
                keys: left_keys,
                children: left_children,
            },
            median,
            Node {
                keys: right_keys,
                children: right_children,
            },
        )
    }

    fn merge(middle: A, left: Node<A>, mut right: Node<A>) -> Node<A> {
        let mut keys = left.keys;
        keys.push_back(middle);
        keys.append(&mut right.keys);
        let mut children = left.children;
        children.append(&mut right.children);
        Node { keys, children }
    }

    fn pop_min(&mut self) -> (A, Option<Ref<Node<A>>>) {
        let value = self.keys.pop_front();
        let child = self.children.pop_front();
        (value, child)
    }

    fn pop_max(&mut self) -> (A, Option<Ref<Node<A>>>) {
        let value = self.keys.pop_back();
        let child = self.children.pop_back();
        (value, child)
    }

    fn push_min(&mut self, child: Option<Ref<Node<A>>>, value: A) {
        self.keys.push_front(value);
        self.children.push_front(child);
    }

    fn push_max(&mut self, child: Option<Ref<Node<A>>>, value: A) {
        self.keys.push_back(value);
        self.children.push_back(child);
    }

    pub fn insert(&mut self, value: A) -> Insert<A> {
        if self.keys.is_empty() {
            self.keys.push_back(value);
            self.children.push_back(None);
            return Insert::Added;
        }
        let (median, left, right) = match A::search_value(&self.keys, &value) {
            // Key exists in node
            Ok(index) => {
                return Insert::Replaced(mem::replace(&mut self.keys[index], value));
            }
            // Key is adjacent to some key in node
            Err(index) => {
                let mut has_room = self.has_room();
                let action = match self.children[index] {
                    // No child at location, this is the target node.
                    None => InsertAt,
                    // Child at location, pass it on.
                    Some(ref mut child_ref) => {
                        let child = Ref::make_mut(child_ref);
                        match child.insert(value.clone()) {
                            Insert::Added => AddedAction,
                            Insert::Replaced(value) => ReplacedAction(value),
                            Insert::Update(_) => unreachable!(),
                            Insert::Split(left, median, right) => InsertSplit(left, median, right),
                        }
                    }
                };
                match action {
                    ReplacedAction(value) => return Insert::Replaced(value),
                    AddedAction => {
                        return Insert::Added;
                    }
                    InsertAt => {
                        if has_room {
                            self.keys.insert(index, value);
                            self.children.insert(index + 1, None);
                            return Insert::Added;
                        } else {
                            (value, None, None)
                        }
                    }
                    InsertSplit(left, median, right) => {
                        if has_room {
                            self.children[index] = Some(Ref::from(left));
                            self.keys.insert(index, median);
                            self.children.insert(index + 1, Some(Ref::from(right)));
                            return Insert::Added;
                        } else {
                            (median, Some(left), Some(right))
                        }
                    }
                }
            }
        };
        self.split(median, left, right)
    }

    pub fn remove<BK>(&mut self, key: &BK) -> Remove<A>
    where
        BK: Ord + ?Sized,
        A::Key: Borrow<BK>,
    {
        let index = A::search_key(&self.keys, key);
        self.remove_index(index, key)
    }

    fn remove_index<BK>(&mut self, index: Result<usize, usize>, key: &BK) -> Remove<A>
    where
        BK: Ord + ?Sized,
        A::Key: Borrow<BK>,
    {
        let action = match index {
            // Key exists in node, remove it.
            Ok(index) => {
                match (&self.children[index], &self.children[index + 1]) {
                    // If we're a leaf, just delete the entry.
                    (&None, &None) => RemoveAction::DeleteAt(index),
                    // If the left hand child has capacity, pull the predecessor up.
                    (&Some(ref left), _) if !left.too_small() => {
                        if left.is_leaf() {
                            RemoveAction::PullUp(left.keys.len() - 1, index, index)
                        } else {
                            RemoveAction::StealFromLeft(index + 1)
                        }
                    }
                    // If the right hand child has capacity, pull the successor up.
                    (_, &Some(ref right)) if !right.too_small() => {
                        if right.is_leaf() {
                            RemoveAction::PullUp(0, index, index + 1)
                        } else {
                            RemoveAction::StealFromRight(index)
                        }
                    }
                    // If neither child has capacity, we'll have to merge them.
                    (&Some(_), &Some(_)) => RemoveAction::Merge(index),
                    // If one child exists and the other doesn't, we're in a bad state.
                    _ => unreachable!(),
                }
            }
            // Key is adjacent to some key in node
            Err(index) => match self.children[index] {
                // No child at location means key isn't in map.
                None => return Remove::NoChange,
                // Child at location, but it's at minimum capacity.
                Some(ref child) if child.too_small() => {
                    let left = if index > 0 {
                        self.children.get(index - 1)
                    } else {
                        None
                    }; // index is usize and can't be negative, best make sure it never is.
                    match (left, self.children.get(index + 1)) {
                        // If it has a left sibling with capacity, steal a key from it.
                        (Some(&Some(ref old_left)), _) if !old_left.too_small() => {
                            RemoveAction::StealFromLeft(index)
                        }
                        // If it has a right sibling with capacity, same as above.
                        (_, Some(&Some(ref old_right))) if !old_right.too_small() => {
                            RemoveAction::StealFromRight(index)
                        }
                        // If it has neither, we'll have to merge it with a sibling.
                        // If we have a right sibling, we'll merge with that.
                        (_, Some(&Some(_))) => RemoveAction::MergeFirst(index),
                        // If we have a left sibling, we'll merge with that.
                        (Some(&Some(_)), _) => RemoveAction::MergeFirst(index - 1),
                        // If none of the above, we're in a bad state.
                        _ => unreachable!(),
                    }
                }
                // Child at location, and it's big enough, we can recurse down.
                Some(_) => RemoveAction::ContinueDown(index),
            },
        };
        match action {
            RemoveAction::DeleteAt(index) => {
                let pair = self.keys.remove(index);
                self.children.remove(index);
                Remove::Removed(pair)
            }
            RemoveAction::PullUp(target_index, pull_to, child_index) => {
                let mut children = &mut self.children;
                let mut update = None;
                let mut value;
                if let Some(&mut Some(ref mut child_ref)) = children.get_mut(child_index) {
                    let child = Ref::make_mut(child_ref);
                    match child.remove_index(Ok(target_index), key) {
                        Remove::NoChange => unreachable!(),
                        Remove::Removed(pulled_value) => {
                            value = self.keys.set(pull_to, pulled_value);
                        }
                        Remove::Update(pulled_value, new_child) => {
                            value = self.keys.set(pull_to, pulled_value);
                            update = Some(new_child);
                        }
                    }
                } else {
                    unreachable!()
                }
                if let Some(new_child) = update {
                    children[child_index] = Some(Ref::from(new_child));
                }
                Remove::Removed(value)
            }
            RemoveAction::Merge(index) => {
                let left = self.children.remove(index).unwrap();
                let right = mem::replace(&mut self.children[index], None).unwrap();
                let value = self.keys.remove(index);
                let mut merged_child = Node::merge(value, clone_ref(left), clone_ref(right));
                let (removed, new_child) = match merged_child.remove(key) {
                    Remove::NoChange => unreachable!(),
                    Remove::Removed(removed) => (removed, merged_child),
                    Remove::Update(removed, updated_child) => (removed, updated_child),
                };
                if self.keys.is_empty() {
                    // If we've depleted the root node, the merged child becomes the root.
                    Remove::Update(removed, new_child)
                } else {
                    self.children[index] = Some(Ref::from(new_child));
                    Remove::Removed(removed)
                }
            }
            RemoveAction::StealFromLeft(index) => {
                let mut update = None;
                let mut out_value;
                {
                    let mut children = self.children.as_mut_slice()[index - 1..=index]
                        .iter_mut()
                        .map(|n| {
                            if let Some(ref mut o) = *n {
                                o
                            } else {
                                unreachable!()
                            }
                        });
                    let mut left = Ref::make_mut(children.next().unwrap());
                    let mut child = Ref::make_mut(children.next().unwrap());
                    // Prepare the rebalanced node.
                    child.push_min(
                        left.children.last().unwrap().clone(),
                        self.keys[index - 1].clone(),
                    );
                    match child.remove(key) {
                        Remove::NoChange => {
                            // Key wasn't there, we need to revert the steal.
                            child.pop_min();
                            return Remove::NoChange;
                        }
                        Remove::Removed(value) => {
                            // If we did remove something, we complete the rebalancing.
                            let (left_value, _) = left.pop_max();
                            self.keys[index - 1] = left_value;
                            out_value = value;
                        }
                        Remove::Update(value, new_child) => {
                            // If we did remove something, we complete the rebalancing.
                            let (left_value, _) = left.pop_max();
                            self.keys[index - 1] = left_value;
                            update = Some(new_child);
                            out_value = value;
                        }
                    }
                }
                if let Some(new_child) = update {
                    self.children[index] = Some(Ref::from(new_child));
                }
                Remove::Removed(out_value)
            }
            RemoveAction::StealFromRight(index) => {
                let mut update = None;
                let mut out_value;
                {
                    let mut children = self.children.as_mut_slice()[index..index + 2]
                        .iter_mut()
                        .map(|n| {
                            if let Some(ref mut o) = *n {
                                o
                            } else {
                                unreachable!()
                            }
                        });
                    let mut child = Ref::make_mut(children.next().unwrap());
                    let mut right = Ref::make_mut(children.next().unwrap());
                    // Prepare the rebalanced node.
                    child.push_max(right.children[0].clone(), self.keys[index].clone());
                    match child.remove(key) {
                        Remove::NoChange => {
                            // Key wasn't there, we need to revert the steal.
                            child.pop_max();
                            return Remove::NoChange;
                        }
                        Remove::Removed(value) => {
                            // If we did remove something, we complete the rebalancing.
                            let (right_value, _) = right.pop_min();
                            self.keys[index] = right_value;
                            out_value = value;
                        }
                        Remove::Update(value, new_child) => {
                            // If we did remove something, we complete the rebalancing.
                            let (right_value, _) = right.pop_min();
                            self.keys[index] = right_value;
                            update = Some(new_child);
                            out_value = value;
                        }
                    }
                }
                if let Some(new_child) = update {
                    self.children[index] = Some(Ref::from(new_child));
                }
                Remove::Removed(out_value)
            }
            RemoveAction::MergeFirst(index) => {
                if self.keys[index].cmp_keys(key) != Ordering::Equal
                    && !self.child_contains(index, key)
                    && !self.child_contains(index + 1, key)
                {
                    return Remove::NoChange;
                }
                let left = self.children.remove(index).unwrap();
                let right = mem::replace(&mut self.children[index], None).unwrap();
                let middle = self.keys.remove(index);
                let mut merged = Node::merge(middle, clone_ref(left), clone_ref(right));
                let mut update;
                let mut out_value;
                match merged.remove(key) {
                    Remove::NoChange => {
                        panic!("nodes::btree::Node::remove: caught an absent key too late while merging");
                    }
                    Remove::Removed(value) => {
                        if self.keys.is_empty() {
                            return Remove::Update(value, merged);
                        }
                        update = merged;
                        out_value = value;
                    }
                    Remove::Update(value, new_child) => {
                        if self.keys.is_empty() {
                            return Remove::Update(value, new_child);
                        }
                        update = new_child;
                        out_value = value;
                    }
                }
                self.children[index] = Some(Ref::from(update));
                Remove::Removed(out_value)
            }
            RemoveAction::ContinueDown(index) => {
                let mut update = None;
                let mut out_value;
                if let Some(&mut Some(ref mut child_ref)) = self.children.get_mut(index) {
                    let child = Ref::make_mut(child_ref);
                    match child.remove(key) {
                        Remove::NoChange => return Remove::NoChange,
                        Remove::Removed(value) => {
                            out_value = value;
                        }
                        Remove::Update(value, new_child) => {
                            update = Some(new_child);
                            out_value = value;
                        }
                    }
                } else {
                    unreachable!()
                }
                if let Some(new_child) = update {
                    self.children[index] = Some(Ref::from(new_child));
                }
                Remove::Removed(out_value)
            }
        }
    }
}

// Iterator

enum IterItem<'a, A: 'a> {
    Consider(&'a Node<A>),
    Yield(&'a A),
}

pub struct Iter<'a, A: 'a> {
    fwd_last: Option<&'a A>,
    fwd_stack: Vec<IterItem<'a, A>>,
    back_last: Option<&'a A>,
    back_stack: Vec<IterItem<'a, A>>,
    remaining: usize,
}

impl<'a, A: 'a + Clone> Iter<'a, A> {
    pub fn new(root: &'a Node<A>, total: usize) -> Self {
        Iter {
            fwd_last: None,
            fwd_stack: vec![IterItem::Consider(root)],
            back_last: None,
            back_stack: vec![IterItem::Consider(root)],
            remaining: total,
        }
    }

    fn push_node(stack: &mut Vec<IterItem<'a, A>>, maybe_node: &'a Option<Ref<Node<A>>>) {
        if let Some(ref node) = *maybe_node {
            stack.push(IterItem::Consider(&node))
        }
    }

    fn push(stack: &mut Vec<IterItem<'a, A>>, node: &'a Node<A>) {
        for n in 0..node.keys.len() {
            let i = node.keys.len() - n;
            Iter::push_node(stack, &node.children[i]);
            stack.push(IterItem::Yield(&node.keys[i - 1]));
        }
        Iter::push_node(stack, &node.children[0]);
    }

    fn push_fwd(&mut self, node: &'a Node<A>) {
        Iter::push(&mut self.fwd_stack, node)
    }

    fn push_node_back(&mut self, maybe_node: &'a Option<Ref<Node<A>>>) {
        if let Some(ref node) = *maybe_node {
            self.back_stack.push(IterItem::Consider(&node))
        }
    }

    fn push_back(&mut self, node: &'a Node<A>) {
        for i in 0..node.keys.len() {
            self.push_node_back(&node.children[i]);
            self.back_stack.push(IterItem::Yield(&node.keys[i]));
        }
        self.push_node_back(&node.children[node.keys.len()]);
    }
}

impl<'a, A> Iterator for Iter<'a, A>
where
    A: 'a + BTreeValue,
{
    type Item = &'a A;

    fn next(&mut self) -> Option<Self::Item> {
        loop {
            match self.fwd_stack.pop() {
                None => {
                    self.remaining = 0;
                    return None;
                }
                Some(IterItem::Consider(node)) => self.push_fwd(&node),
                Some(IterItem::Yield(value)) => {
                    if let Some(ref last) = self.back_last {
                        if value.cmp_values(last) != Ordering::Less {
                            self.fwd_stack.clear();
                            self.back_stack.clear();
                            self.remaining = 0;
                            return None;
                        }
                    }
                    self.remaining -= 1;
                    self.fwd_last = Some(value);
                    return Some(value);
                }
            }
        }
    }

    fn size_hint(&self) -> (usize, Option<usize>) {
        (self.remaining, Some(self.remaining))
    }
}

impl<'a, A> DoubleEndedIterator for Iter<'a, A>
where
    A: 'a + BTreeValue,
{
    fn next_back(&mut self) -> Option<Self::Item> {
        loop {
            match self.back_stack.pop() {
                None => {
                    self.remaining = 0;
                    return None;
                }
                Some(IterItem::Consider(node)) => self.push_back(&node),
                Some(IterItem::Yield(value)) => {
                    if let Some(ref last) = self.fwd_last {
                        if value.cmp_values(last) != Ordering::Greater {
                            self.fwd_stack.clear();
                            self.back_stack.clear();
                            self.remaining = 0;
                            return None;
                        }
                    }
                    self.remaining -= 1;
                    self.back_last = Some(value);
                    return Some(value);
                }
            }
        }
    }
}

impl<'a, A: 'a + BTreeValue> ExactSizeIterator for Iter<'a, A> {}

// Consuming iterator

enum ConsumingIterItem<A> {
    Consider(Node<A>),
    Yield(A),
}

pub struct ConsumingIter<A> {
    fwd_last: Option<A>,
    fwd_stack: Vec<ConsumingIterItem<A>>,
    back_last: Option<A>,
    back_stack: Vec<ConsumingIterItem<A>>,
    remaining: usize,
}

impl<A: Clone> ConsumingIter<A> {
    pub fn new(root: &Node<A>, total: usize) -> Self {
        ConsumingIter {
            fwd_last: None,
            fwd_stack: vec![ConsumingIterItem::Consider(root.clone())],
            back_last: None,
            back_stack: vec![ConsumingIterItem::Consider(root.clone())],
            remaining: total,
        }
    }

    fn push_node(stack: &mut Vec<ConsumingIterItem<A>>, maybe_node: Option<Ref<Node<A>>>) {
        if let Some(node) = maybe_node {
            stack.push(ConsumingIterItem::Consider(clone_ref(node)))
        }
    }

    fn push(stack: &mut Vec<ConsumingIterItem<A>>, mut node: Node<A>) {
        for _n in 0..node.keys.len() {
            ConsumingIter::push_node(stack, node.children.pop_back());
            stack.push(ConsumingIterItem::Yield(node.keys.pop_back()));
        }
        ConsumingIter::push_node(stack, node.children.pop_back());
    }

    fn push_fwd(&mut self, node: Node<A>) {
        ConsumingIter::push(&mut self.fwd_stack, node)
    }

    fn push_node_back(&mut self, maybe_node: Option<Ref<Node<A>>>) {
        if let Some(node) = maybe_node {
            self.back_stack
                .push(ConsumingIterItem::Consider(clone_ref(node)))
        }
    }

    fn push_back(&mut self, mut node: Node<A>) {
        for _i in 0..node.keys.len() {
            self.push_node_back(node.children.pop_front());
            self.back_stack
                .push(ConsumingIterItem::Yield(node.keys.pop_front()));
        }
        self.push_node_back(node.children.pop_back());
    }
}

impl<A> Iterator for ConsumingIter<A>
where
    A: BTreeValue,
{
    type Item = A;

    fn next(&mut self) -> Option<Self::Item> {
        loop {
            match self.fwd_stack.pop() {
                None => {
                    self.remaining = 0;
                    return None;
                }
                Some(ConsumingIterItem::Consider(node)) => self.push_fwd(node),
                Some(ConsumingIterItem::Yield(value)) => {
                    if let Some(ref last) = self.back_last {
                        if value.cmp_values(last) != Ordering::Less {
                            self.fwd_stack.clear();
                            self.back_stack.clear();
                            self.remaining = 0;
                            return None;
                        }
                    }
                    self.remaining -= 1;
                    self.fwd_last = Some(value.clone());
                    return Some(value);
                }
            }
        }
    }

    fn size_hint(&self) -> (usize, Option<usize>) {
        (self.remaining, Some(self.remaining))
    }
}

impl<A> DoubleEndedIterator for ConsumingIter<A>
where
    A: BTreeValue,
{
    fn next_back(&mut self) -> Option<Self::Item> {
        loop {
            match self.back_stack.pop() {
                None => {
                    self.remaining = 0;
                    return None;
                }
                Some(ConsumingIterItem::Consider(node)) => self.push_back(node),
                Some(ConsumingIterItem::Yield(value)) => {
                    if let Some(ref last) = self.fwd_last {
                        if value.cmp_values(last) != Ordering::Greater {
                            self.fwd_stack.clear();
                            self.back_stack.clear();
                            self.remaining = 0;
                            return None;
                        }
                    }
                    self.remaining -= 1;
                    self.back_last = Some(value.clone());
                    return Some(value);
                }
            }
        }
    }
}

impl<A: BTreeValue> ExactSizeIterator for ConsumingIter<A> {}

// DiffIter

pub struct DiffIter<'a, A: 'a> {
    old_stack: Vec<IterItem<'a, A>>,
    new_stack: Vec<IterItem<'a, A>>,
}

#[derive(PartialEq, Eq)]
pub enum DiffItem<'a, A: 'a> {
    Add(&'a A),
    Update { old: &'a A, new: &'a A },
    Remove(&'a A),
}

impl<'a, A: 'a> DiffIter<'a, A> {
    pub fn new(old: &'a Node<A>, new: &'a Node<A>) -> Self {
        DiffIter {
            old_stack: if old.keys.is_empty() {
                Vec::new()
            } else {
                vec![IterItem::Consider(old)]
            },
            new_stack: if new.keys.is_empty() {
                Vec::new()
            } else {
                vec![IterItem::Consider(new)]
            },
        }
    }
}

impl<'a, A> Iterator for DiffIter<'a, A>
where
    A: 'a + BTreeValue + PartialEq,
{
    type Item = DiffItem<'a, A>;

    fn next(&mut self) -> Option<Self::Item> {
        loop {
            match (self.old_stack.pop(), self.new_stack.pop()) {
                (None, None) => return None,
                (None, Some(new)) => match new {
                    IterItem::Consider(new) => Iter::push(&mut self.new_stack, &new),
                    IterItem::Yield(new) => return Some(DiffItem::Add(new)),
                },
                (Some(old), None) => match old {
                    IterItem::Consider(old) => Iter::push(&mut self.old_stack, &old),
                    IterItem::Yield(old) => return Some(DiffItem::Remove(old)),
                },
                (Some(old), Some(new)) => match (old, new) {
                    (IterItem::Consider(old), IterItem::Consider(new)) => {
                        match old.keys[0].cmp_values(&new.keys[0]) {
                            Ordering::Less => {
                                Iter::push(&mut self.old_stack, &old);
                                self.new_stack.push(IterItem::Consider(new));
                            }
                            Ordering::Greater => {
                                self.old_stack.push(IterItem::Consider(old));
                                Iter::push(&mut self.new_stack, &new);
                            }
                            Ordering::Equal => {
                                Iter::push(&mut self.old_stack, &old);
                                Iter::push(&mut self.new_stack, &new);
                            }
                        }
                    }
                    (IterItem::Consider(old), IterItem::Yield(new)) => {
                        Iter::push(&mut self.old_stack, &old);
                        self.new_stack.push(IterItem::Yield(new));
                    }
                    (IterItem::Yield(old), IterItem::Consider(new)) => {
                        self.old_stack.push(IterItem::Yield(old));
                        Iter::push(&mut self.new_stack, &new);
                    }
                    (IterItem::Yield(old), IterItem::Yield(new)) => match old.cmp_values(&new) {
                        Ordering::Less => {
                            self.new_stack.push(IterItem::Yield(new));
                            return Some(DiffItem::Remove(old));
                        }
                        Ordering::Equal => if old != new {
                            return Some(DiffItem::Update { old, new });
                        },
                        Ordering::Greater => {
                            self.old_stack.push(IterItem::Yield(old));
                            return Some(DiffItem::Add(new));
                        }
                    },
                },
            }
        }
    }
}