sum_tree.rs

  1mod cursor;
  2
  3use arrayvec::ArrayVec;
  4pub use cursor::Cursor;
  5pub use cursor::FilterCursor;
  6use std::{cmp::Ordering, fmt, iter::FromIterator, 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 {
 14    type Summary: Summary;
 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 Summary: Default + Clone + fmt::Debug {
 26    type Context;
 27
 28    fn add_summary(&mut self, summary: &Self, cx: &Self::Context);
 29}
 30
 31pub trait Dimension<'a, S: Summary>: Clone + fmt::Debug + Default {
 32    fn add_summary(&mut self, _summary: &'a S, _: &S::Context);
 33}
 34
 35impl<'a, T: Summary> Dimension<'a, T> for () {
 36    fn add_summary(&mut self, _: &'a T, _: &T::Context) {}
 37}
 38
 39pub trait SeekDimension<'a, T: Summary>: Dimension<'a, T> {
 40    fn cmp(&self, other: &Self, cx: &T::Context) -> Ordering;
 41}
 42
 43impl<'a, S: Summary, T: Dimension<'a, S> + Ord> SeekDimension<'a, S> for T {
 44    fn cmp(&self, other: &Self, _ctx: &S::Context) -> Ordering {
 45        Ord::cmp(self, other)
 46    }
 47}
 48
 49#[derive(Copy, Clone, Eq, PartialEq, Debug, Hash)]
 50pub enum Bias {
 51    Left,
 52    Right,
 53}
 54
 55impl PartialOrd for Bias {
 56    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
 57        Some(self.cmp(other))
 58    }
 59}
 60
 61impl Ord for Bias {
 62    fn cmp(&self, other: &Self) -> Ordering {
 63        match (self, other) {
 64            (Self::Left, Self::Left) => Ordering::Equal,
 65            (Self::Left, Self::Right) => Ordering::Less,
 66            (Self::Right, Self::Right) => Ordering::Equal,
 67            (Self::Right, Self::Left) => Ordering::Greater,
 68        }
 69    }
 70}
 71
 72#[derive(Debug, Clone)]
 73pub struct SumTree<T: Item>(Arc<Node<T>>);
 74
 75impl<T: Item> SumTree<T> {
 76    pub fn new() -> Self {
 77        SumTree(Arc::new(Node::Leaf {
 78            summary: T::Summary::default(),
 79            items: ArrayVec::new(),
 80            item_summaries: ArrayVec::new(),
 81        }))
 82    }
 83
 84    pub fn from_item(item: T, cx: &<T::Summary as Summary>::Context) -> Self {
 85        let mut tree = Self::new();
 86        tree.push(item, cx);
 87        tree
 88    }
 89
 90    pub fn from_iter<I: IntoIterator<Item = T>>(
 91        iter: I,
 92        cx: &<T::Summary as Summary>::Context,
 93    ) -> Self {
 94        let mut tree = Self::new();
 95        tree.extend(iter, cx);
 96        tree
 97    }
 98
 99    #[allow(unused)]
100    pub fn items(&self, cx: &<T::Summary as Summary>::Context) -> Vec<T> {
101        let mut items = Vec::new();
102        let mut cursor = self.cursor::<(), ()>();
103        cursor.next(cx);
104        while let Some(item) = cursor.item() {
105            items.push(item.clone());
106            cursor.next(cx);
107        }
108        items
109    }
110
111    pub fn cursor<'a, S, U>(&'a self) -> Cursor<T, S, U>
112    where
113        S: Dimension<'a, T::Summary>,
114        U: Dimension<'a, T::Summary>,
115    {
116        Cursor::new(self)
117    }
118
119    pub fn filter<'a, F, U>(
120        &'a self,
121        filter_node: F,
122        cx: &<T::Summary as Summary>::Context,
123    ) -> FilterCursor<F, T, U>
124    where
125        F: Fn(&T::Summary) -> bool,
126        U: Dimension<'a, T::Summary>,
127    {
128        FilterCursor::new(self, filter_node, cx)
129    }
130
131    #[allow(dead_code)]
132    pub fn first(&self) -> Option<&T> {
133        self.leftmost_leaf().0.items().first()
134    }
135
136    pub fn last(&self) -> Option<&T> {
137        self.rightmost_leaf().0.items().last()
138    }
139
140    pub fn update_last(&mut self, f: impl FnOnce(&mut T), cx: &<T::Summary as Summary>::Context) {
141        self.update_last_recursive(f, cx);
142    }
143
144    fn update_last_recursive(
145        &mut self,
146        f: impl FnOnce(&mut T),
147        cx: &<T::Summary as Summary>::Context,
148    ) -> Option<T::Summary> {
149        match Arc::make_mut(&mut self.0) {
150            Node::Internal {
151                summary,
152                child_summaries,
153                child_trees,
154                ..
155            } => {
156                let last_summary = child_summaries.last_mut().unwrap();
157                let last_child = child_trees.last_mut().unwrap();
158                *last_summary = last_child.update_last_recursive(f, cx).unwrap();
159                *summary = sum(child_summaries.iter(), cx);
160                Some(summary.clone())
161            }
162            Node::Leaf {
163                summary,
164                items,
165                item_summaries,
166            } => {
167                if let Some((item, item_summary)) = items.last_mut().zip(item_summaries.last_mut())
168                {
169                    (f)(item);
170                    *item_summary = item.summary();
171                    *summary = sum(item_summaries.iter(), cx);
172                    Some(summary.clone())
173                } else {
174                    None
175                }
176            }
177        }
178    }
179
180    pub fn extent<'a, D: Dimension<'a, T::Summary>>(
181        &'a self,
182        cx: &<T::Summary as Summary>::Context,
183    ) -> D {
184        let mut extent = D::default();
185        match self.0.as_ref() {
186            Node::Internal { summary, .. } | Node::Leaf { summary, .. } => {
187                extent.add_summary(summary, cx);
188            }
189        }
190        extent
191    }
192
193    pub fn summary(&self) -> T::Summary {
194        match self.0.as_ref() {
195            Node::Internal { summary, .. } => summary.clone(),
196            Node::Leaf { summary, .. } => summary.clone(),
197        }
198    }
199
200    pub fn is_empty(&self) -> bool {
201        match self.0.as_ref() {
202            Node::Internal { .. } => false,
203            Node::Leaf { items, .. } => items.is_empty(),
204        }
205    }
206
207    pub fn extend<I>(&mut self, iter: I, cx: &<T::Summary as Summary>::Context)
208    where
209        I: IntoIterator<Item = T>,
210    {
211        let mut leaf: Option<Node<T>> = None;
212
213        for item in iter {
214            if leaf.is_some() && leaf.as_ref().unwrap().items().len() == 2 * TREE_BASE {
215                self.push_tree(SumTree(Arc::new(leaf.take().unwrap())), cx);
216            }
217
218            if leaf.is_none() {
219                leaf = Some(Node::Leaf::<T> {
220                    summary: T::Summary::default(),
221                    items: ArrayVec::new(),
222                    item_summaries: ArrayVec::new(),
223                });
224            }
225
226            if let Some(Node::Leaf {
227                summary,
228                items,
229                item_summaries,
230            }) = leaf.as_mut()
231            {
232                let item_summary = item.summary();
233                summary.add_summary(&item_summary, cx);
234                items.push(item);
235                item_summaries.push(item_summary);
236            } else {
237                unreachable!()
238            }
239        }
240
241        if leaf.is_some() {
242            self.push_tree(SumTree(Arc::new(leaf.take().unwrap())), cx);
243        }
244    }
245
246    pub fn push(&mut self, item: T, cx: &<T::Summary as Summary>::Context) {
247        let summary = item.summary();
248        self.push_tree(
249            SumTree(Arc::new(Node::Leaf {
250                summary: summary.clone(),
251                items: ArrayVec::from_iter(Some(item)),
252                item_summaries: ArrayVec::from_iter(Some(summary)),
253            })),
254            cx,
255        );
256    }
257
258    pub fn push_tree(&mut self, other: Self, cx: &<T::Summary as Summary>::Context) {
259        if !other.0.is_leaf() || other.0.items().len() > 0 {
260            if self.0.height() < other.0.height() {
261                for tree in other.0.child_trees() {
262                    self.push_tree(tree.clone(), cx);
263                }
264            } else if let Some(split_tree) = self.push_tree_recursive(other, cx) {
265                *self = Self::from_child_trees(self.clone(), split_tree, cx);
266            }
267        }
268    }
269
270    fn push_tree_recursive(
271        &mut self,
272        other: SumTree<T>,
273        cx: &<T::Summary as Summary>::Context,
274    ) -> Option<SumTree<T>> {
275        match Arc::make_mut(&mut self.0) {
276            Node::Internal {
277                height,
278                summary,
279                child_summaries,
280                child_trees,
281                ..
282            } => {
283                let other_node = other.0.clone();
284                summary.add_summary(other_node.summary(), cx);
285
286                let height_delta = *height - other_node.height();
287                let mut summaries_to_append = ArrayVec::<T::Summary, { 2 * TREE_BASE }>::new();
288                let mut trees_to_append = ArrayVec::<SumTree<T>, { 2 * TREE_BASE }>::new();
289                if height_delta == 0 {
290                    summaries_to_append.extend(other_node.child_summaries().iter().cloned());
291                    trees_to_append.extend(other_node.child_trees().iter().cloned());
292                } else if height_delta == 1 && !other_node.is_underflowing() {
293                    summaries_to_append.push(other_node.summary().clone());
294                    trees_to_append.push(other)
295                } else {
296                    let tree_to_append = child_trees
297                        .last_mut()
298                        .unwrap()
299                        .push_tree_recursive(other, cx);
300                    *child_summaries.last_mut().unwrap() =
301                        child_trees.last().unwrap().0.summary().clone();
302
303                    if let Some(split_tree) = tree_to_append {
304                        summaries_to_append.push(split_tree.0.summary().clone());
305                        trees_to_append.push(split_tree);
306                    }
307                }
308
309                let child_count = child_trees.len() + trees_to_append.len();
310                if child_count > 2 * TREE_BASE {
311                    let left_summaries: ArrayVec<_, { 2 * TREE_BASE }>;
312                    let right_summaries: ArrayVec<_, { 2 * TREE_BASE }>;
313                    let left_trees;
314                    let right_trees;
315
316                    let midpoint = (child_count + child_count % 2) / 2;
317                    {
318                        let mut all_summaries = child_summaries
319                            .iter()
320                            .chain(summaries_to_append.iter())
321                            .cloned();
322                        left_summaries = all_summaries.by_ref().take(midpoint).collect();
323                        right_summaries = all_summaries.collect();
324                        let mut all_trees =
325                            child_trees.iter().chain(trees_to_append.iter()).cloned();
326                        left_trees = all_trees.by_ref().take(midpoint).collect();
327                        right_trees = all_trees.collect();
328                    }
329                    *summary = sum(left_summaries.iter(), cx);
330                    *child_summaries = left_summaries;
331                    *child_trees = left_trees;
332
333                    Some(SumTree(Arc::new(Node::Internal {
334                        height: *height,
335                        summary: sum(right_summaries.iter(), cx),
336                        child_summaries: right_summaries,
337                        child_trees: right_trees,
338                    })))
339                } else {
340                    child_summaries.extend(summaries_to_append);
341                    child_trees.extend(trees_to_append);
342                    None
343                }
344            }
345            Node::Leaf {
346                summary,
347                items,
348                item_summaries,
349            } => {
350                let other_node = other.0;
351
352                let child_count = items.len() + other_node.items().len();
353                if child_count > 2 * TREE_BASE {
354                    let left_items;
355                    let right_items;
356                    let left_summaries;
357                    let right_summaries: ArrayVec<T::Summary, { 2 * TREE_BASE }>;
358
359                    let midpoint = (child_count + child_count % 2) / 2;
360                    {
361                        let mut all_items = items.iter().chain(other_node.items().iter()).cloned();
362                        left_items = all_items.by_ref().take(midpoint).collect();
363                        right_items = all_items.collect();
364
365                        let mut all_summaries = item_summaries
366                            .iter()
367                            .chain(other_node.child_summaries())
368                            .cloned();
369                        left_summaries = all_summaries.by_ref().take(midpoint).collect();
370                        right_summaries = all_summaries.collect();
371                    }
372                    *items = left_items;
373                    *item_summaries = left_summaries;
374                    *summary = sum(item_summaries.iter(), cx);
375                    Some(SumTree(Arc::new(Node::Leaf {
376                        items: right_items,
377                        summary: sum(right_summaries.iter(), cx),
378                        item_summaries: right_summaries,
379                    })))
380                } else {
381                    summary.add_summary(other_node.summary(), cx);
382                    items.extend(other_node.items().iter().cloned());
383                    item_summaries.extend(other_node.child_summaries().iter().cloned());
384                    None
385                }
386            }
387        }
388    }
389
390    fn from_child_trees(
391        left: SumTree<T>,
392        right: SumTree<T>,
393        cx: &<T::Summary as Summary>::Context,
394    ) -> Self {
395        let height = left.0.height() + 1;
396        let mut child_summaries = ArrayVec::new();
397        child_summaries.push(left.0.summary().clone());
398        child_summaries.push(right.0.summary().clone());
399        let mut child_trees = ArrayVec::new();
400        child_trees.push(left);
401        child_trees.push(right);
402        SumTree(Arc::new(Node::Internal {
403            height,
404            summary: sum(child_summaries.iter(), cx),
405            child_summaries,
406            child_trees,
407        }))
408    }
409
410    fn leftmost_leaf(&self) -> &Self {
411        match *self.0 {
412            Node::Leaf { .. } => self,
413            Node::Internal {
414                ref child_trees, ..
415            } => child_trees.first().unwrap().leftmost_leaf(),
416        }
417    }
418
419    fn rightmost_leaf(&self) -> &Self {
420        match *self.0 {
421            Node::Leaf { .. } => self,
422            Node::Internal {
423                ref child_trees, ..
424            } => child_trees.last().unwrap().rightmost_leaf(),
425        }
426    }
427}
428
429impl<T: KeyedItem> SumTree<T> {
430    pub fn insert_or_replace(&mut self, item: T, cx: &<T::Summary as Summary>::Context) -> bool {
431        let mut replaced = false;
432        *self = {
433            let mut cursor = self.cursor::<T::Key, ()>();
434            let mut new_tree = cursor.slice(&item.key(), Bias::Left, cx);
435            if cursor
436                .item()
437                .map_or(false, |cursor_item| cursor_item.key() == item.key())
438            {
439                cursor.next(cx);
440                replaced = true;
441            }
442            new_tree.push(item, cx);
443            new_tree.push_tree(cursor.suffix(cx), cx);
444            new_tree
445        };
446        replaced
447    }
448
449    pub fn edit(
450        &mut self,
451        mut edits: Vec<Edit<T>>,
452        cx: &<T::Summary as Summary>::Context,
453    ) -> Vec<T> {
454        if edits.is_empty() {
455            return Vec::new();
456        }
457
458        let mut removed = Vec::new();
459        edits.sort_unstable_by_key(|item| item.key());
460
461        *self = {
462            let mut cursor = self.cursor::<T::Key, ()>();
463            let mut new_tree = SumTree::new();
464            let mut buffered_items = Vec::new();
465
466            cursor.seek(&T::Key::default(), Bias::Left, cx);
467            for edit in edits {
468                let new_key = edit.key();
469                let mut old_item = cursor.item();
470
471                if old_item
472                    .as_ref()
473                    .map_or(false, |old_item| old_item.key() < new_key)
474                {
475                    new_tree.extend(buffered_items.drain(..), cx);
476                    let slice = cursor.slice(&new_key, Bias::Left, cx);
477                    new_tree.push_tree(slice, cx);
478                    old_item = cursor.item();
479                }
480
481                if let Some(old_item) = old_item {
482                    if old_item.key() == new_key {
483                        removed.push(old_item.clone());
484                        cursor.next(cx);
485                    }
486                }
487
488                match edit {
489                    Edit::Insert(item) => {
490                        buffered_items.push(item);
491                    }
492                    Edit::Remove(_) => {}
493                }
494            }
495
496            new_tree.extend(buffered_items, cx);
497            new_tree.push_tree(cursor.suffix(cx), cx);
498            new_tree
499        };
500
501        removed
502    }
503
504    pub fn get(&self, key: &T::Key, cx: &<T::Summary as Summary>::Context) -> Option<&T> {
505        let mut cursor = self.cursor::<T::Key, ()>();
506        if cursor.seek(key, Bias::Left, cx) {
507            cursor.item()
508        } else {
509            None
510        }
511    }
512}
513
514impl<T: Item> Default for SumTree<T> {
515    fn default() -> Self {
516        Self::new()
517    }
518}
519
520#[derive(Clone, Debug)]
521pub enum Node<T: Item> {
522    Internal {
523        height: u8,
524        summary: T::Summary,
525        child_summaries: ArrayVec<T::Summary, { 2 * TREE_BASE }>,
526        child_trees: ArrayVec<SumTree<T>, { 2 * TREE_BASE }>,
527    },
528    Leaf {
529        summary: T::Summary,
530        items: ArrayVec<T, { 2 * TREE_BASE }>,
531        item_summaries: ArrayVec<T::Summary, { 2 * TREE_BASE }>,
532    },
533}
534
535impl<T: Item> Node<T> {
536    fn is_leaf(&self) -> bool {
537        match self {
538            Node::Leaf { .. } => true,
539            _ => false,
540        }
541    }
542
543    fn height(&self) -> u8 {
544        match self {
545            Node::Internal { height, .. } => *height,
546            Node::Leaf { .. } => 0,
547        }
548    }
549
550    fn summary(&self) -> &T::Summary {
551        match self {
552            Node::Internal { summary, .. } => summary,
553            Node::Leaf { summary, .. } => summary,
554        }
555    }
556
557    fn child_summaries(&self) -> &[T::Summary] {
558        match self {
559            Node::Internal {
560                child_summaries, ..
561            } => child_summaries.as_slice(),
562            Node::Leaf { item_summaries, .. } => item_summaries.as_slice(),
563        }
564    }
565
566    fn child_trees(&self) -> &ArrayVec<SumTree<T>, { 2 * TREE_BASE }> {
567        match self {
568            Node::Internal { child_trees, .. } => child_trees,
569            Node::Leaf { .. } => panic!("Leaf nodes have no child trees"),
570        }
571    }
572
573    fn items(&self) -> &ArrayVec<T, { 2 * TREE_BASE }> {
574        match self {
575            Node::Leaf { items, .. } => items,
576            Node::Internal { .. } => panic!("Internal nodes have no items"),
577        }
578    }
579
580    fn is_underflowing(&self) -> bool {
581        match self {
582            Node::Internal { child_trees, .. } => child_trees.len() < TREE_BASE,
583            Node::Leaf { items, .. } => items.len() < TREE_BASE,
584        }
585    }
586}
587
588#[derive(Debug)]
589pub enum Edit<T: KeyedItem> {
590    Insert(T),
591    Remove(T::Key),
592}
593
594impl<T: KeyedItem> Edit<T> {
595    fn key(&self) -> T::Key {
596        match self {
597            Edit::Insert(item) => item.key(),
598            Edit::Remove(key) => key.clone(),
599        }
600    }
601}
602
603fn sum<'a, T, I>(iter: I, cx: &T::Context) -> T
604where
605    T: 'a + Summary,
606    I: Iterator<Item = &'a T>,
607{
608    let mut sum = T::default();
609    for value in iter {
610        sum.add_summary(value, cx);
611    }
612    sum
613}
614
615#[cfg(test)]
616mod tests {
617    use super::*;
618    use rand::{distributions, prelude::*};
619    use std::cmp;
620    use std::ops::Add;
621
622    #[test]
623    fn test_extend_and_push_tree() {
624        let mut tree1 = SumTree::new();
625        tree1.extend(0..20, &());
626
627        let mut tree2 = SumTree::new();
628        tree2.extend(50..100, &());
629
630        tree1.push_tree(tree2, &());
631        assert_eq!(
632            tree1.items(&()),
633            (0..20).chain(50..100).collect::<Vec<u8>>()
634        );
635    }
636
637    #[crate::test(self, iterations = 100)]
638    fn test_random(mut rng: StdRng) {
639        let rng = &mut rng;
640        let mut tree = SumTree::<u8>::new();
641        let count = rng.gen_range(0..10);
642        tree.extend(rng.sample_iter(distributions::Standard).take(count), &());
643
644        for _ in 0..5 {
645            let splice_end = rng.gen_range(0..tree.extent::<Count>(&()).0 + 1);
646            let splice_start = rng.gen_range(0..splice_end + 1);
647            let count = rng.gen_range(0..3);
648            let tree_end = tree.extent::<Count>(&());
649            let new_items = rng
650                .sample_iter(distributions::Standard)
651                .take(count)
652                .collect::<Vec<u8>>();
653
654            let mut reference_items = tree.items(&());
655            reference_items.splice(splice_start..splice_end, new_items.clone());
656
657            tree = {
658                let mut cursor = tree.cursor::<Count, ()>();
659                let mut new_tree = cursor.slice(&Count(splice_start), Bias::Right, &());
660                new_tree.extend(new_items, &());
661                cursor.seek(&Count(splice_end), Bias::Right, &());
662                new_tree.push_tree(cursor.slice(&tree_end, Bias::Right, &()), &());
663                new_tree
664            };
665
666            assert_eq!(tree.items(&()), reference_items);
667
668            let mut filter_cursor = tree.filter::<_, Count>(|summary| summary.contains_even, &());
669            let mut reference_filter = tree
670                .items(&())
671                .into_iter()
672                .enumerate()
673                .filter(|(_, item)| (item & 1) == 0);
674            while let Some(actual_item) = filter_cursor.item() {
675                let (reference_index, reference_item) = reference_filter.next().unwrap();
676                assert_eq!(actual_item, &reference_item);
677                assert_eq!(filter_cursor.start().0, reference_index);
678                filter_cursor.next(&());
679            }
680            assert!(reference_filter.next().is_none());
681
682            let mut pos = rng.gen_range(0..tree.extent::<Count>(&()).0 + 1);
683            let mut before_start = false;
684            let mut cursor = tree.cursor::<Count, Count>();
685            cursor.seek(&Count(pos), Bias::Right, &());
686
687            for i in 0..10 {
688                assert_eq!(cursor.sum_start().0, pos);
689
690                if pos > 0 {
691                    assert_eq!(cursor.prev_item().unwrap(), &reference_items[pos - 1]);
692                } else {
693                    assert_eq!(cursor.prev_item(), None);
694                }
695
696                if pos < reference_items.len() && !before_start {
697                    assert_eq!(cursor.item().unwrap(), &reference_items[pos]);
698                } else {
699                    assert_eq!(cursor.item(), None);
700                }
701
702                if i < 5 {
703                    cursor.next(&());
704                    if pos < reference_items.len() {
705                        pos += 1;
706                        before_start = false;
707                    }
708                } else {
709                    cursor.prev(&());
710                    if pos == 0 {
711                        before_start = true;
712                    }
713                    pos = pos.saturating_sub(1);
714                }
715            }
716        }
717
718        for _ in 0..10 {
719            let end = rng.gen_range(0..tree.extent::<Count>(&()).0 + 1);
720            let start = rng.gen_range(0..end + 1);
721            let start_bias = if rng.gen() { Bias::Left } else { Bias::Right };
722            let end_bias = if rng.gen() { Bias::Left } else { Bias::Right };
723
724            let mut cursor = tree.cursor::<Count, ()>();
725            cursor.seek(&Count(start), start_bias, &());
726            let slice = cursor.slice(&Count(end), end_bias, &());
727
728            cursor.seek(&Count(start), start_bias, &());
729            let summary = cursor.summary::<Sum>(&Count(end), end_bias, &());
730
731            assert_eq!(summary, slice.summary().sum);
732        }
733    }
734
735    #[test]
736    fn test_cursor() {
737        // Empty tree
738        let tree = SumTree::<u8>::new();
739        let mut cursor = tree.cursor::<Count, Sum>();
740        assert_eq!(
741            cursor.slice(&Count(0), Bias::Right, &()).items(&()),
742            Vec::<u8>::new()
743        );
744        assert_eq!(cursor.item(), None);
745        assert_eq!(cursor.prev_item(), None);
746        assert_eq!(cursor.sum_start(), &Sum(0));
747
748        // Single-element tree
749        let mut tree = SumTree::<u8>::new();
750        tree.extend(vec![1], &());
751        let mut cursor = tree.cursor::<Count, Sum>();
752        assert_eq!(
753            cursor.slice(&Count(0), Bias::Right, &()).items(&()),
754            Vec::<u8>::new()
755        );
756        assert_eq!(cursor.item(), Some(&1));
757        assert_eq!(cursor.prev_item(), None);
758        assert_eq!(cursor.sum_start(), &Sum(0));
759
760        cursor.next(&());
761        assert_eq!(cursor.item(), None);
762        assert_eq!(cursor.prev_item(), Some(&1));
763        assert_eq!(cursor.sum_start(), &Sum(1));
764
765        cursor.prev(&());
766        assert_eq!(cursor.item(), Some(&1));
767        assert_eq!(cursor.prev_item(), None);
768        assert_eq!(cursor.sum_start(), &Sum(0));
769
770        let mut cursor = tree.cursor::<Count, Sum>();
771        assert_eq!(cursor.slice(&Count(1), Bias::Right, &()).items(&()), [1]);
772        assert_eq!(cursor.item(), None);
773        assert_eq!(cursor.prev_item(), Some(&1));
774        assert_eq!(cursor.sum_start(), &Sum(1));
775
776        cursor.seek(&Count(0), Bias::Right, &());
777        assert_eq!(
778            cursor
779                .slice(&tree.extent::<Count>(&()), Bias::Right, &())
780                .items(&()),
781            [1]
782        );
783        assert_eq!(cursor.item(), None);
784        assert_eq!(cursor.prev_item(), Some(&1));
785        assert_eq!(cursor.sum_start(), &Sum(1));
786
787        // Multiple-element tree
788        let mut tree = SumTree::new();
789        tree.extend(vec![1, 2, 3, 4, 5, 6], &());
790        let mut cursor = tree.cursor::<Count, Sum>();
791
792        assert_eq!(cursor.slice(&Count(2), Bias::Right, &()).items(&()), [1, 2]);
793        assert_eq!(cursor.item(), Some(&3));
794        assert_eq!(cursor.prev_item(), Some(&2));
795        assert_eq!(cursor.sum_start(), &Sum(3));
796
797        cursor.next(&());
798        assert_eq!(cursor.item(), Some(&4));
799        assert_eq!(cursor.prev_item(), Some(&3));
800        assert_eq!(cursor.sum_start(), &Sum(6));
801
802        cursor.next(&());
803        assert_eq!(cursor.item(), Some(&5));
804        assert_eq!(cursor.prev_item(), Some(&4));
805        assert_eq!(cursor.sum_start(), &Sum(10));
806
807        cursor.next(&());
808        assert_eq!(cursor.item(), Some(&6));
809        assert_eq!(cursor.prev_item(), Some(&5));
810        assert_eq!(cursor.sum_start(), &Sum(15));
811
812        cursor.next(&());
813        cursor.next(&());
814        assert_eq!(cursor.item(), None);
815        assert_eq!(cursor.prev_item(), Some(&6));
816        assert_eq!(cursor.sum_start(), &Sum(21));
817
818        cursor.prev(&());
819        assert_eq!(cursor.item(), Some(&6));
820        assert_eq!(cursor.prev_item(), Some(&5));
821        assert_eq!(cursor.sum_start(), &Sum(15));
822
823        cursor.prev(&());
824        assert_eq!(cursor.item(), Some(&5));
825        assert_eq!(cursor.prev_item(), Some(&4));
826        assert_eq!(cursor.sum_start(), &Sum(10));
827
828        cursor.prev(&());
829        assert_eq!(cursor.item(), Some(&4));
830        assert_eq!(cursor.prev_item(), Some(&3));
831        assert_eq!(cursor.sum_start(), &Sum(6));
832
833        cursor.prev(&());
834        assert_eq!(cursor.item(), Some(&3));
835        assert_eq!(cursor.prev_item(), Some(&2));
836        assert_eq!(cursor.sum_start(), &Sum(3));
837
838        cursor.prev(&());
839        assert_eq!(cursor.item(), Some(&2));
840        assert_eq!(cursor.prev_item(), Some(&1));
841        assert_eq!(cursor.sum_start(), &Sum(1));
842
843        cursor.prev(&());
844        assert_eq!(cursor.item(), Some(&1));
845        assert_eq!(cursor.prev_item(), None);
846        assert_eq!(cursor.sum_start(), &Sum(0));
847
848        cursor.prev(&());
849        assert_eq!(cursor.item(), None);
850        assert_eq!(cursor.prev_item(), None);
851        assert_eq!(cursor.sum_start(), &Sum(0));
852
853        cursor.next(&());
854        assert_eq!(cursor.item(), Some(&1));
855        assert_eq!(cursor.prev_item(), None);
856        assert_eq!(cursor.sum_start(), &Sum(0));
857
858        let mut cursor = tree.cursor::<Count, Sum>();
859        assert_eq!(
860            cursor
861                .slice(&tree.extent::<Count>(&()), Bias::Right, &())
862                .items(&()),
863            tree.items(&())
864        );
865        assert_eq!(cursor.item(), None);
866        assert_eq!(cursor.prev_item(), Some(&6));
867        assert_eq!(cursor.sum_start(), &Sum(21));
868
869        cursor.seek(&Count(3), Bias::Right, &());
870        assert_eq!(
871            cursor
872                .slice(&tree.extent::<Count>(&()), Bias::Right, &())
873                .items(&()),
874            [4, 5, 6]
875        );
876        assert_eq!(cursor.item(), None);
877        assert_eq!(cursor.prev_item(), Some(&6));
878        assert_eq!(cursor.sum_start(), &Sum(21));
879
880        // Seeking can bias left or right
881        cursor.seek(&Count(1), Bias::Left, &());
882        assert_eq!(cursor.item(), Some(&1));
883        cursor.seek(&Count(1), Bias::Right, &());
884        assert_eq!(cursor.item(), Some(&2));
885
886        // Slicing without resetting starts from where the cursor is parked at.
887        cursor.seek(&Count(1), Bias::Right, &());
888        assert_eq!(
889            cursor.slice(&Count(3), Bias::Right, &()).items(&()),
890            vec![2, 3]
891        );
892        assert_eq!(
893            cursor.slice(&Count(6), Bias::Left, &()).items(&()),
894            vec![4, 5]
895        );
896        assert_eq!(
897            cursor.slice(&Count(6), Bias::Right, &()).items(&()),
898            vec![6]
899        );
900    }
901
902    #[test]
903    fn test_edit() {
904        let mut tree = SumTree::<u8>::new();
905
906        let removed = tree.edit(vec![Edit::Insert(1), Edit::Insert(2), Edit::Insert(0)], &());
907        assert_eq!(tree.items(&()), vec![0, 1, 2]);
908        assert_eq!(removed, Vec::<u8>::new());
909        assert_eq!(tree.get(&0, &()), Some(&0));
910        assert_eq!(tree.get(&1, &()), Some(&1));
911        assert_eq!(tree.get(&2, &()), Some(&2));
912        assert_eq!(tree.get(&4, &()), None);
913
914        let removed = tree.edit(vec![Edit::Insert(2), Edit::Insert(4), Edit::Remove(0)], &());
915        assert_eq!(tree.items(&()), vec![1, 2, 4]);
916        assert_eq!(removed, vec![0, 2]);
917        assert_eq!(tree.get(&0, &()), None);
918        assert_eq!(tree.get(&1, &()), Some(&1));
919        assert_eq!(tree.get(&2, &()), Some(&2));
920        assert_eq!(tree.get(&4, &()), Some(&4));
921    }
922
923    #[derive(Clone, Default, Debug)]
924    pub struct IntegersSummary {
925        count: Count,
926        sum: Sum,
927        contains_even: bool,
928        max: u8,
929    }
930
931    #[derive(Ord, PartialOrd, Default, Eq, PartialEq, Clone, Debug)]
932    struct Count(usize);
933
934    #[derive(Ord, PartialOrd, Default, Eq, PartialEq, Clone, Debug)]
935    struct Sum(usize);
936
937    impl Item for u8 {
938        type Summary = IntegersSummary;
939
940        fn summary(&self) -> Self::Summary {
941            IntegersSummary {
942                count: Count(1),
943                sum: Sum(*self as usize),
944                contains_even: (*self & 1) == 0,
945                max: *self,
946            }
947        }
948    }
949
950    impl KeyedItem for u8 {
951        type Key = u8;
952
953        fn key(&self) -> Self::Key {
954            *self
955        }
956    }
957
958    impl Summary for IntegersSummary {
959        type Context = ();
960
961        fn add_summary(&mut self, other: &Self, _: &()) {
962            self.count.0 += &other.count.0;
963            self.sum.0 += &other.sum.0;
964            self.contains_even |= other.contains_even;
965            self.max = cmp::max(self.max, other.max);
966        }
967    }
968
969    impl<'a> Dimension<'a, IntegersSummary> for u8 {
970        fn add_summary(&mut self, summary: &IntegersSummary, _: &()) {
971            *self = summary.max;
972        }
973    }
974
975    impl<'a> Dimension<'a, IntegersSummary> for Count {
976        fn add_summary(&mut self, summary: &IntegersSummary, _: &()) {
977            self.0 += summary.count.0;
978        }
979    }
980
981    impl<'a> Dimension<'a, IntegersSummary> for Sum {
982        fn add_summary(&mut self, summary: &IntegersSummary, _: &()) {
983            self.0 += summary.sum.0;
984        }
985    }
986
987    impl<'a> Add<&'a Self> for Sum {
988        type Output = Self;
989
990        fn add(mut self, other: &Self) -> Self {
991            self.0 += other.0;
992            self
993        }
994    }
995}