mod.rs

  1mod cursor;
  2
  3use arrayvec::ArrayVec;
  4pub use cursor::Cursor;
  5pub use cursor::FilterCursor;
  6use std::{fmt, iter::FromIterator, ops::AddAssign, sync::Arc};
  7
  8#[cfg(test)]
  9const TREE_BASE: usize = 2;
 10#[cfg(not(test))]
 11const TREE_BASE: usize = 6;
 12
 13pub trait Item: Clone + fmt::Debug {
 14    type Summary: for<'a> AddAssign<&'a Self::Summary> + Default + Clone + fmt::Debug;
 15
 16    fn summary(&self) -> Self::Summary;
 17}
 18
 19pub trait KeyedItem: Item {
 20    type Key: for<'a> Dimension<'a, Self::Summary> + Ord;
 21
 22    fn key(&self) -> Self::Key;
 23}
 24
 25pub trait Dimension<'a, Summary: Default>: 'a + Clone + fmt::Debug + Default {
 26    fn add_summary(&mut self, summary: &'a Summary);
 27}
 28
 29impl<'a, T: Default> Dimension<'a, T> for () {
 30    fn add_summary(&mut self, _: &'a T) {}
 31}
 32
 33#[derive(Copy, Clone, Eq, PartialEq)]
 34pub enum SeekBias {
 35    Left,
 36    Right,
 37}
 38
 39#[derive(Debug, Clone)]
 40pub struct SumTree<T: Item>(Arc<Node<T>>);
 41
 42impl<T: Item> SumTree<T> {
 43    pub fn new() -> Self {
 44        SumTree(Arc::new(Node::Leaf {
 45            summary: T::Summary::default(),
 46            items: ArrayVec::new(),
 47            item_summaries: ArrayVec::new(),
 48        }))
 49    }
 50
 51    pub fn from_item(item: T) -> Self {
 52        let mut tree = Self::new();
 53        tree.push(item);
 54        tree
 55    }
 56
 57    #[allow(unused)]
 58    pub fn items(&self) -> Vec<T> {
 59        let mut cursor = self.cursor::<(), ()>();
 60        cursor.descend_to_first_item(self, |_| true);
 61        cursor.cloned().collect()
 62    }
 63
 64    pub fn cursor<'a, S, U>(&'a self) -> Cursor<T, S, U>
 65    where
 66        S: Dimension<'a, T::Summary>,
 67        U: Dimension<'a, T::Summary>,
 68    {
 69        Cursor::new(self)
 70    }
 71
 72    pub fn filter<'a, F, U>(&'a self, filter_node: F) -> FilterCursor<F, T, U>
 73    where
 74        F: Fn(&T::Summary) -> bool,
 75        U: Dimension<'a, T::Summary>,
 76    {
 77        FilterCursor::new(self, filter_node)
 78    }
 79
 80    #[allow(dead_code)]
 81    pub fn first(&self) -> Option<&T> {
 82        self.leftmost_leaf().0.items().first()
 83    }
 84
 85    pub fn last(&self) -> Option<&T> {
 86        self.rightmost_leaf().0.items().last()
 87    }
 88
 89    pub fn extent<'a, D: Dimension<'a, T::Summary>>(&'a self) -> D {
 90        let mut extent = D::default();
 91        match self.0.as_ref() {
 92            Node::Internal { summary, .. } | Node::Leaf { summary, .. } => {
 93                extent.add_summary(summary)
 94            }
 95        }
 96        extent
 97    }
 98
 99    pub fn summary(&self) -> T::Summary {
100        match self.0.as_ref() {
101            Node::Internal { summary, .. } => summary.clone(),
102            Node::Leaf { summary, .. } => summary.clone(),
103        }
104    }
105
106    pub fn is_empty(&self) -> bool {
107        match self.0.as_ref() {
108            Node::Internal { .. } => false,
109            Node::Leaf { items, .. } => items.is_empty(),
110        }
111    }
112
113    pub fn extend<I>(&mut self, iter: I)
114    where
115        I: IntoIterator<Item = T>,
116    {
117        let mut leaf: Option<Node<T>> = None;
118
119        for item in iter {
120            if leaf.is_some() && leaf.as_ref().unwrap().items().len() == 2 * TREE_BASE {
121                self.push_tree(SumTree(Arc::new(leaf.take().unwrap())));
122            }
123
124            if leaf.is_none() {
125                leaf = Some(Node::Leaf::<T> {
126                    summary: T::Summary::default(),
127                    items: ArrayVec::new(),
128                    item_summaries: ArrayVec::new(),
129                });
130            }
131
132            if let Some(Node::Leaf {
133                summary,
134                items,
135                item_summaries,
136            }) = leaf.as_mut()
137            {
138                let item_summary = item.summary();
139                *summary += &item_summary;
140                items.push(item);
141                item_summaries.push(item_summary);
142            } else {
143                unreachable!()
144            }
145        }
146
147        if leaf.is_some() {
148            self.push_tree(SumTree(Arc::new(leaf.take().unwrap())));
149        }
150    }
151
152    pub fn push(&mut self, item: T) {
153        let summary = item.summary();
154        self.push_tree(SumTree::from_child_trees(vec![SumTree(Arc::new(
155            Node::Leaf {
156                summary: summary.clone(),
157                items: ArrayVec::from_iter(Some(item)),
158                item_summaries: ArrayVec::from_iter(Some(summary)),
159            },
160        ))]))
161    }
162
163    pub fn push_tree(&mut self, other: Self) {
164        let other_node = other.0.clone();
165        if !other_node.is_leaf() || other_node.items().len() > 0 {
166            if self.0.height() < other_node.height() {
167                for tree in other_node.child_trees() {
168                    self.push_tree(tree.clone());
169                }
170            } else if let Some(split_tree) = self.push_tree_recursive(other) {
171                *self = Self::from_child_trees(vec![self.clone(), split_tree]);
172            }
173        }
174    }
175
176    fn push_tree_recursive(&mut self, other: SumTree<T>) -> Option<SumTree<T>> {
177        match Arc::make_mut(&mut self.0) {
178            Node::Internal {
179                height,
180                summary,
181                child_summaries,
182                child_trees,
183                ..
184            } => {
185                let other_node = other.0.clone();
186                *summary += other_node.summary();
187
188                let height_delta = *height - other_node.height();
189                let mut summaries_to_append = ArrayVec::<[T::Summary; 2 * TREE_BASE]>::new();
190                let mut trees_to_append = ArrayVec::<[SumTree<T>; 2 * TREE_BASE]>::new();
191                if height_delta == 0 {
192                    summaries_to_append.extend(other_node.child_summaries().iter().cloned());
193                    trees_to_append.extend(other_node.child_trees().iter().cloned());
194                } else if height_delta == 1 && !other_node.is_underflowing() {
195                    summaries_to_append.push(other_node.summary().clone());
196                    trees_to_append.push(other)
197                } else {
198                    let tree_to_append = child_trees.last_mut().unwrap().push_tree_recursive(other);
199                    *child_summaries.last_mut().unwrap() =
200                        child_trees.last().unwrap().0.summary().clone();
201
202                    if let Some(split_tree) = tree_to_append {
203                        summaries_to_append.push(split_tree.0.summary().clone());
204                        trees_to_append.push(split_tree);
205                    }
206                }
207
208                let child_count = child_trees.len() + trees_to_append.len();
209                if child_count > 2 * TREE_BASE {
210                    let left_summaries: ArrayVec<_>;
211                    let right_summaries: ArrayVec<_>;
212                    let left_trees;
213                    let right_trees;
214
215                    let midpoint = (child_count + child_count % 2) / 2;
216                    {
217                        let mut all_summaries = child_summaries
218                            .iter()
219                            .chain(summaries_to_append.iter())
220                            .cloned();
221                        left_summaries = all_summaries.by_ref().take(midpoint).collect();
222                        right_summaries = all_summaries.collect();
223                        let mut all_trees =
224                            child_trees.iter().chain(trees_to_append.iter()).cloned();
225                        left_trees = all_trees.by_ref().take(midpoint).collect();
226                        right_trees = all_trees.collect();
227                    }
228                    *summary = sum(left_summaries.iter());
229                    *child_summaries = left_summaries;
230                    *child_trees = left_trees;
231
232                    Some(SumTree(Arc::new(Node::Internal {
233                        height: *height,
234                        summary: sum(right_summaries.iter()),
235                        child_summaries: right_summaries,
236                        child_trees: right_trees,
237                    })))
238                } else {
239                    child_summaries.extend(summaries_to_append);
240                    child_trees.extend(trees_to_append);
241                    None
242                }
243            }
244            Node::Leaf {
245                summary,
246                items,
247                item_summaries,
248            } => {
249                let other_node = other.0;
250
251                let child_count = items.len() + other_node.items().len();
252                if child_count > 2 * TREE_BASE {
253                    let left_items;
254                    let right_items;
255                    let left_summaries;
256                    let right_summaries: ArrayVec<[T::Summary; 2 * TREE_BASE]>;
257
258                    let midpoint = (child_count + child_count % 2) / 2;
259                    {
260                        let mut all_items = items.iter().chain(other_node.items().iter()).cloned();
261                        left_items = all_items.by_ref().take(midpoint).collect();
262                        right_items = all_items.collect();
263
264                        let mut all_summaries = item_summaries
265                            .iter()
266                            .chain(other_node.child_summaries())
267                            .cloned();
268                        left_summaries = all_summaries.by_ref().take(midpoint).collect();
269                        right_summaries = all_summaries.collect();
270                    }
271                    *items = left_items;
272                    *item_summaries = left_summaries;
273                    *summary = sum(item_summaries.iter());
274                    Some(SumTree(Arc::new(Node::Leaf {
275                        items: right_items,
276                        summary: sum(right_summaries.iter()),
277                        item_summaries: right_summaries,
278                    })))
279                } else {
280                    *summary += other_node.summary();
281                    items.extend(other_node.items().iter().cloned());
282                    item_summaries.extend(other_node.child_summaries().iter().cloned());
283                    None
284                }
285            }
286        }
287    }
288
289    fn from_child_trees(child_trees: Vec<SumTree<T>>) -> Self {
290        let height = child_trees[0].0.height() + 1;
291        let mut child_summaries = ArrayVec::new();
292        for child in &child_trees {
293            child_summaries.push(child.0.summary().clone());
294        }
295        let summary = sum(child_summaries.iter());
296        SumTree(Arc::new(Node::Internal {
297            height,
298            summary,
299            child_summaries,
300            child_trees: ArrayVec::from_iter(child_trees),
301        }))
302    }
303
304    fn leftmost_leaf(&self) -> &Self {
305        match *self.0 {
306            Node::Leaf { .. } => self,
307            Node::Internal {
308                ref child_trees, ..
309            } => child_trees.first().unwrap().leftmost_leaf(),
310        }
311    }
312
313    fn rightmost_leaf(&self) -> &Self {
314        match *self.0 {
315            Node::Leaf { .. } => self,
316            Node::Internal {
317                ref child_trees, ..
318            } => child_trees.last().unwrap().rightmost_leaf(),
319        }
320    }
321}
322
323impl<T: KeyedItem> SumTree<T> {
324    #[allow(unused)]
325    pub fn insert(&mut self, item: T) {
326        *self = {
327            let mut cursor = self.cursor::<T::Key, ()>();
328            let mut new_tree = cursor.slice(&item.key(), SeekBias::Left);
329            new_tree.push(item);
330            new_tree.push_tree(cursor.suffix());
331            new_tree
332        };
333    }
334
335    pub fn edit(&mut self, edits: &mut [Edit<T>]) {
336        if edits.is_empty() {
337            return;
338        }
339
340        edits.sort_unstable_by_key(|item| item.key());
341
342        *self = {
343            let mut cursor = self.cursor::<T::Key, ()>();
344            let mut new_tree = SumTree::new();
345            let mut buffered_items = Vec::new();
346
347            cursor.seek(&T::Key::default(), SeekBias::Left);
348            for edit in edits {
349                let new_key = edit.key();
350                let mut old_item = cursor.item();
351
352                if old_item
353                    .as_ref()
354                    .map_or(false, |old_item| old_item.key() < new_key)
355                {
356                    new_tree.extend(buffered_items.drain(..));
357                    let slice = cursor.slice(&new_key, SeekBias::Left);
358                    new_tree.push_tree(slice);
359                    old_item = cursor.item();
360                }
361                if old_item.map_or(false, |old_item| old_item.key() == new_key) {
362                    cursor.next();
363                }
364                match edit {
365                    Edit::Insert(item) => {
366                        buffered_items.push(item.clone());
367                    }
368                }
369            }
370
371            new_tree.extend(buffered_items);
372            new_tree.push_tree(cursor.suffix());
373            new_tree
374        };
375    }
376
377    pub fn get(&self, key: &T::Key) -> Option<&T> {
378        let mut cursor = self.cursor::<T::Key, ()>();
379        if cursor.seek(key, SeekBias::Left) {
380            cursor.item()
381        } else {
382            None
383        }
384    }
385}
386
387impl<T: Item> Default for SumTree<T> {
388    fn default() -> Self {
389        Self::new()
390    }
391}
392
393#[derive(Clone, Debug)]
394pub enum Node<T: Item> {
395    Internal {
396        height: u8,
397        summary: T::Summary,
398        child_summaries: ArrayVec<[T::Summary; 2 * TREE_BASE]>,
399        child_trees: ArrayVec<[SumTree<T>; 2 * TREE_BASE]>,
400    },
401    Leaf {
402        summary: T::Summary,
403        items: ArrayVec<[T; 2 * TREE_BASE]>,
404        item_summaries: ArrayVec<[T::Summary; 2 * TREE_BASE]>,
405    },
406}
407
408impl<T: Item> Node<T> {
409    fn is_leaf(&self) -> bool {
410        match self {
411            Node::Leaf { .. } => true,
412            _ => false,
413        }
414    }
415
416    fn height(&self) -> u8 {
417        match self {
418            Node::Internal { height, .. } => *height,
419            Node::Leaf { .. } => 0,
420        }
421    }
422
423    fn summary(&self) -> &T::Summary {
424        match self {
425            Node::Internal { summary, .. } => summary,
426            Node::Leaf { summary, .. } => summary,
427        }
428    }
429
430    fn child_summaries(&self) -> &[T::Summary] {
431        match self {
432            Node::Internal {
433                child_summaries, ..
434            } => child_summaries.as_slice(),
435            Node::Leaf { item_summaries, .. } => item_summaries.as_slice(),
436        }
437    }
438
439    fn child_trees(&self) -> &ArrayVec<[SumTree<T>; 2 * TREE_BASE]> {
440        match self {
441            Node::Internal { child_trees, .. } => child_trees,
442            Node::Leaf { .. } => panic!("Leaf nodes have no child trees"),
443        }
444    }
445
446    fn items(&self) -> &ArrayVec<[T; 2 * TREE_BASE]> {
447        match self {
448            Node::Leaf { items, .. } => items,
449            Node::Internal { .. } => panic!("Internal nodes have no items"),
450        }
451    }
452
453    fn is_underflowing(&self) -> bool {
454        match self {
455            Node::Internal { child_trees, .. } => child_trees.len() < TREE_BASE,
456            Node::Leaf { items, .. } => items.len() < TREE_BASE,
457        }
458    }
459}
460
461#[derive(Debug)]
462pub enum Edit<T: KeyedItem> {
463    Insert(T),
464}
465
466impl<T: KeyedItem> Edit<T> {
467    fn key(&self) -> T::Key {
468        match self {
469            Edit::Insert(item) => item.key(),
470        }
471    }
472}
473
474fn sum<'a, T, I>(iter: I) -> T
475where
476    T: 'a + Default + AddAssign<&'a T>,
477    I: Iterator<Item = &'a T>,
478{
479    let mut sum = T::default();
480    for value in iter {
481        sum += value;
482    }
483    sum
484}
485
486#[cfg(test)]
487mod tests {
488    use super::*;
489    use std::ops::Add;
490
491    #[test]
492    fn test_extend_and_push_tree() {
493        let mut tree1 = SumTree::new();
494        tree1.extend(0..20);
495
496        let mut tree2 = SumTree::new();
497        tree2.extend(50..100);
498
499        tree1.push_tree(tree2);
500        assert_eq!(tree1.items(), (0..20).chain(50..100).collect::<Vec<u8>>());
501    }
502
503    #[test]
504    fn test_random() {
505        for seed in 0..100 {
506            use rand::{distributions, prelude::*};
507
508            let rng = &mut StdRng::seed_from_u64(seed);
509
510            let mut tree = SumTree::<u8>::new();
511            let count = rng.gen_range(0..10);
512            tree.extend(rng.sample_iter(distributions::Standard).take(count));
513
514            for _ in 0..5 {
515                let splice_end = rng.gen_range(0..tree.extent::<Count>().0 + 1);
516                let splice_start = rng.gen_range(0..splice_end + 1);
517                let count = rng.gen_range(0..3);
518                let tree_end = tree.extent::<Count>();
519                let new_items = rng
520                    .sample_iter(distributions::Standard)
521                    .take(count)
522                    .collect::<Vec<u8>>();
523
524                let mut reference_items = tree.items();
525                reference_items.splice(splice_start..splice_end, new_items.clone());
526
527                tree = {
528                    let mut cursor = tree.cursor::<Count, ()>();
529                    let mut new_tree = cursor.slice(&Count(splice_start), SeekBias::Right);
530                    new_tree.extend(new_items);
531                    cursor.seek(&Count(splice_end), SeekBias::Right);
532                    new_tree.push_tree(cursor.slice(&tree_end, SeekBias::Right));
533                    new_tree
534                };
535
536                assert_eq!(tree.items(), reference_items);
537
538                let mut filter_cursor = tree.filter::<_, Count>(|summary| summary.contains_even);
539                let mut reference_filter = tree
540                    .items()
541                    .into_iter()
542                    .enumerate()
543                    .filter(|(_, item)| (item & 1) == 0);
544                while let Some(actual_item) = filter_cursor.item() {
545                    let (reference_index, reference_item) = reference_filter.next().unwrap();
546                    assert_eq!(actual_item, &reference_item);
547                    assert_eq!(filter_cursor.start().0, reference_index);
548                    filter_cursor.next();
549                }
550                assert!(reference_filter.next().is_none());
551
552                let mut pos = rng.gen_range(0..tree.extent::<Count>().0 + 1);
553                let mut before_start = false;
554                let mut cursor = tree.cursor::<Count, Count>();
555                cursor.seek(&Count(pos), SeekBias::Right);
556
557                for i in 0..10 {
558                    assert_eq!(cursor.start().0, pos);
559
560                    if pos > 0 {
561                        assert_eq!(cursor.prev_item().unwrap(), &reference_items[pos - 1]);
562                    } else {
563                        assert_eq!(cursor.prev_item(), None);
564                    }
565
566                    if pos < reference_items.len() && !before_start {
567                        assert_eq!(cursor.item().unwrap(), &reference_items[pos]);
568                    } else {
569                        assert_eq!(cursor.item(), None);
570                    }
571
572                    if i < 5 {
573                        cursor.next();
574                        if pos < reference_items.len() {
575                            pos += 1;
576                            before_start = false;
577                        }
578                    } else {
579                        cursor.prev();
580                        if pos == 0 {
581                            before_start = true;
582                        }
583                        pos = pos.saturating_sub(1);
584                    }
585                }
586            }
587
588            for _ in 0..10 {
589                let end = rng.gen_range(0..tree.extent::<Count>().0 + 1);
590                let start = rng.gen_range(0..end + 1);
591                let start_bias = if rng.gen() {
592                    SeekBias::Left
593                } else {
594                    SeekBias::Right
595                };
596                let end_bias = if rng.gen() {
597                    SeekBias::Left
598                } else {
599                    SeekBias::Right
600                };
601
602                let mut cursor = tree.cursor::<Count, ()>();
603                cursor.seek(&Count(start), start_bias);
604                let slice = cursor.slice(&Count(end), end_bias);
605
606                cursor.seek(&Count(start), start_bias);
607                let summary = cursor.summary::<Sum>(&Count(end), end_bias);
608
609                assert_eq!(summary, slice.summary().sum);
610            }
611        }
612    }
613
614    #[test]
615    fn test_cursor() {
616        // Empty tree
617        let tree = SumTree::<u8>::new();
618        let mut cursor = tree.cursor::<Count, Sum>();
619        assert_eq!(
620            cursor.slice(&Count(0), SeekBias::Right).items(),
621            Vec::<u8>::new()
622        );
623        assert_eq!(cursor.item(), None);
624        assert_eq!(cursor.prev_item(), None);
625        assert_eq!(cursor.start(), &Sum(0));
626
627        // Single-element tree
628        let mut tree = SumTree::<u8>::new();
629        tree.extend(vec![1]);
630        let mut cursor = tree.cursor::<Count, Sum>();
631        assert_eq!(
632            cursor.slice(&Count(0), SeekBias::Right).items(),
633            Vec::<u8>::new()
634        );
635        assert_eq!(cursor.item(), Some(&1));
636        assert_eq!(cursor.prev_item(), None);
637        assert_eq!(cursor.start(), &Sum(0));
638
639        cursor.next();
640        assert_eq!(cursor.item(), None);
641        assert_eq!(cursor.prev_item(), Some(&1));
642        assert_eq!(cursor.start(), &Sum(1));
643
644        cursor.prev();
645        assert_eq!(cursor.item(), Some(&1));
646        assert_eq!(cursor.prev_item(), None);
647        assert_eq!(cursor.start(), &Sum(0));
648
649        let mut cursor = tree.cursor::<Count, Sum>();
650        assert_eq!(cursor.slice(&Count(1), SeekBias::Right).items(), [1]);
651        assert_eq!(cursor.item(), None);
652        assert_eq!(cursor.prev_item(), Some(&1));
653        assert_eq!(cursor.start(), &Sum(1));
654
655        cursor.seek(&Count(0), SeekBias::Right);
656        assert_eq!(
657            cursor
658                .slice(&tree.extent::<Count>(), SeekBias::Right)
659                .items(),
660            [1]
661        );
662        assert_eq!(cursor.item(), None);
663        assert_eq!(cursor.prev_item(), Some(&1));
664        assert_eq!(cursor.start(), &Sum(1));
665
666        // Multiple-element tree
667        let mut tree = SumTree::new();
668        tree.extend(vec![1, 2, 3, 4, 5, 6]);
669        let mut cursor = tree.cursor::<Count, Sum>();
670
671        assert_eq!(cursor.slice(&Count(2), SeekBias::Right).items(), [1, 2]);
672        assert_eq!(cursor.item(), Some(&3));
673        assert_eq!(cursor.prev_item(), Some(&2));
674        assert_eq!(cursor.start(), &Sum(3));
675
676        cursor.next();
677        assert_eq!(cursor.item(), Some(&4));
678        assert_eq!(cursor.prev_item(), Some(&3));
679        assert_eq!(cursor.start(), &Sum(6));
680
681        cursor.next();
682        assert_eq!(cursor.item(), Some(&5));
683        assert_eq!(cursor.prev_item(), Some(&4));
684        assert_eq!(cursor.start(), &Sum(10));
685
686        cursor.next();
687        assert_eq!(cursor.item(), Some(&6));
688        assert_eq!(cursor.prev_item(), Some(&5));
689        assert_eq!(cursor.start(), &Sum(15));
690
691        cursor.next();
692        cursor.next();
693        assert_eq!(cursor.item(), None);
694        assert_eq!(cursor.prev_item(), Some(&6));
695        assert_eq!(cursor.start(), &Sum(21));
696
697        cursor.prev();
698        assert_eq!(cursor.item(), Some(&6));
699        assert_eq!(cursor.prev_item(), Some(&5));
700        assert_eq!(cursor.start(), &Sum(15));
701
702        cursor.prev();
703        assert_eq!(cursor.item(), Some(&5));
704        assert_eq!(cursor.prev_item(), Some(&4));
705        assert_eq!(cursor.start(), &Sum(10));
706
707        cursor.prev();
708        assert_eq!(cursor.item(), Some(&4));
709        assert_eq!(cursor.prev_item(), Some(&3));
710        assert_eq!(cursor.start(), &Sum(6));
711
712        cursor.prev();
713        assert_eq!(cursor.item(), Some(&3));
714        assert_eq!(cursor.prev_item(), Some(&2));
715        assert_eq!(cursor.start(), &Sum(3));
716
717        cursor.prev();
718        assert_eq!(cursor.item(), Some(&2));
719        assert_eq!(cursor.prev_item(), Some(&1));
720        assert_eq!(cursor.start(), &Sum(1));
721
722        cursor.prev();
723        assert_eq!(cursor.item(), Some(&1));
724        assert_eq!(cursor.prev_item(), None);
725        assert_eq!(cursor.start(), &Sum(0));
726
727        cursor.prev();
728        assert_eq!(cursor.item(), None);
729        assert_eq!(cursor.prev_item(), None);
730        assert_eq!(cursor.start(), &Sum(0));
731
732        cursor.next();
733        assert_eq!(cursor.item(), Some(&1));
734        assert_eq!(cursor.prev_item(), None);
735        assert_eq!(cursor.start(), &Sum(0));
736
737        let mut cursor = tree.cursor::<Count, Sum>();
738        assert_eq!(
739            cursor
740                .slice(&tree.extent::<Count>(), SeekBias::Right)
741                .items(),
742            tree.items()
743        );
744        assert_eq!(cursor.item(), None);
745        assert_eq!(cursor.prev_item(), Some(&6));
746        assert_eq!(cursor.start(), &Sum(21));
747
748        cursor.seek(&Count(3), SeekBias::Right);
749        assert_eq!(
750            cursor
751                .slice(&tree.extent::<Count>(), SeekBias::Right)
752                .items(),
753            [4, 5, 6]
754        );
755        assert_eq!(cursor.item(), None);
756        assert_eq!(cursor.prev_item(), Some(&6));
757        assert_eq!(cursor.start(), &Sum(21));
758
759        // Seeking can bias left or right
760        cursor.seek(&Count(1), SeekBias::Left);
761        assert_eq!(cursor.item(), Some(&1));
762        cursor.seek(&Count(1), SeekBias::Right);
763        assert_eq!(cursor.item(), Some(&2));
764
765        // Slicing without resetting starts from where the cursor is parked at.
766        cursor.seek(&Count(1), SeekBias::Right);
767        assert_eq!(cursor.slice(&Count(3), SeekBias::Right).items(), vec![2, 3]);
768        assert_eq!(cursor.slice(&Count(6), SeekBias::Left).items(), vec![4, 5]);
769        assert_eq!(cursor.slice(&Count(6), SeekBias::Right).items(), vec![6]);
770    }
771
772    #[derive(Clone, Default, Debug)]
773    pub struct IntegersSummary {
774        count: Count,
775        sum: Sum,
776        contains_even: bool,
777    }
778
779    #[derive(Ord, PartialOrd, Default, Eq, PartialEq, Clone, Debug)]
780    struct Count(usize);
781
782    #[derive(Ord, PartialOrd, Default, Eq, PartialEq, Clone, Debug)]
783    struct Sum(usize);
784
785    impl Item for u8 {
786        type Summary = IntegersSummary;
787
788        fn summary(&self) -> Self::Summary {
789            IntegersSummary {
790                count: Count(1),
791                sum: Sum(*self as usize),
792                contains_even: (*self & 1) == 0,
793            }
794        }
795    }
796
797    impl<'a> AddAssign<&'a Self> for IntegersSummary {
798        fn add_assign(&mut self, other: &Self) {
799            self.count.0 += &other.count.0;
800            self.sum.0 += &other.sum.0;
801            self.contains_even |= other.contains_even;
802        }
803    }
804
805    impl<'a> Dimension<'a, IntegersSummary> for Count {
806        fn add_summary(&mut self, summary: &IntegersSummary) {
807            self.0 += summary.count.0;
808        }
809    }
810
811    // impl<'a> Add<&'a Self> for Count {
812    //     type Output = Self;
813    //
814    //     fn add(mut self, other: &Self) -> Self {
815    //         self.0 += other.0;
816    //         self
817    //     }
818    // }
819
820    impl<'a> Dimension<'a, IntegersSummary> for Sum {
821        fn add_summary(&mut self, summary: &IntegersSummary) {
822            self.0 += summary.sum.0;
823        }
824    }
825
826    impl<'a> Add<&'a Self> for Sum {
827        type Output = Self;
828
829        fn add(mut self, other: &Self) -> Self {
830            self.0 += other.0;
831            self
832        }
833    }
834}