sum_tree.rs

   1mod cursor;
   2mod tree_map;
   3
   4use arrayvec::ArrayVec;
   5pub use cursor::{Cursor, FilterCursor, Iter};
   6use rayon::prelude::*;
   7use std::marker::PhantomData;
   8use std::mem;
   9use std::{cmp::Ordering, fmt, iter::FromIterator, sync::Arc};
  10pub use tree_map::{MapSeekTarget, TreeMap, TreeSet};
  11
  12#[cfg(test)]
  13pub const TREE_BASE: usize = 2;
  14#[cfg(not(test))]
  15pub const TREE_BASE: usize = 6;
  16
  17/// An item that can be stored in a [`SumTree`]
  18///
  19/// Must be summarized by a type that implements [`Summary`]
  20pub trait Item: Clone {
  21    type Summary: Summary;
  22
  23    fn summary(&self) -> Self::Summary;
  24}
  25
  26/// An [`Item`] whose summary has a specific key that can be used to identify it
  27pub trait KeyedItem: Item {
  28    type Key: for<'a> Dimension<'a, Self::Summary> + Ord;
  29
  30    fn key(&self) -> Self::Key;
  31}
  32
  33/// A type that describes the Sum of all [`Item`]s in a subtree of the [`SumTree`]
  34///
  35/// Each Summary type can have multiple [`Dimensions`] that it measures,
  36/// which can be used to navigate the tree
  37pub trait Summary: Clone + fmt::Debug {
  38    type Context;
  39
  40    fn zero(cx: &Self::Context) -> Self;
  41
  42    fn add_summary(&mut self, summary: &Self, cx: &Self::Context);
  43}
  44
  45/// Each [`Summary`] type can have more than one [`Dimension`] type that it measures.
  46///
  47/// You can use dimensions to seek to a specific location in the [`SumTree`]
  48///
  49/// # Example:
  50/// Zed's rope has a `TextSummary` type that summarizes lines, characters, and bytes.
  51/// Each of these are different dimensions we may want to seek to
  52pub trait Dimension<'a, S: Summary>: Clone + fmt::Debug {
  53    fn zero(cx: &S::Context) -> Self;
  54
  55    fn add_summary(&mut self, summary: &'a S, cx: &S::Context);
  56
  57    fn from_summary(summary: &'a S, cx: &S::Context) -> Self {
  58        let mut dimension = Self::zero(cx);
  59        dimension.add_summary(summary, cx);
  60        dimension
  61    }
  62}
  63
  64impl<'a, T: Summary> Dimension<'a, T> for T {
  65    fn zero(cx: &T::Context) -> Self {
  66        Summary::zero(cx)
  67    }
  68
  69    fn add_summary(&mut self, summary: &'a T, cx: &T::Context) {
  70        Summary::add_summary(self, summary, cx);
  71    }
  72}
  73
  74pub trait SeekTarget<'a, S: Summary, D: Dimension<'a, S>>: fmt::Debug {
  75    fn cmp(&self, cursor_location: &D, cx: &S::Context) -> Ordering;
  76}
  77
  78impl<'a, S: Summary, D: Dimension<'a, S> + Ord> SeekTarget<'a, S, D> for D {
  79    fn cmp(&self, cursor_location: &Self, _: &S::Context) -> Ordering {
  80        Ord::cmp(self, cursor_location)
  81    }
  82}
  83
  84impl<'a, T: Summary> Dimension<'a, T> for () {
  85    fn zero(_: &T::Context) -> Self {
  86        ()
  87    }
  88
  89    fn add_summary(&mut self, _: &'a T, _: &T::Context) {}
  90}
  91
  92impl<'a, T: Summary, D1: Dimension<'a, T>, D2: Dimension<'a, T>> Dimension<'a, T> for (D1, D2) {
  93    fn zero(cx: &T::Context) -> Self {
  94        (D1::zero(cx), D2::zero(cx))
  95    }
  96
  97    fn add_summary(&mut self, summary: &'a T, cx: &T::Context) {
  98        self.0.add_summary(summary, cx);
  99        self.1.add_summary(summary, cx);
 100    }
 101}
 102
 103impl<'a, S: Summary, D1: SeekTarget<'a, S, D1> + Dimension<'a, S>, D2: Dimension<'a, S>>
 104    SeekTarget<'a, S, (D1, D2)> for D1
 105{
 106    fn cmp(&self, cursor_location: &(D1, D2), cx: &S::Context) -> Ordering {
 107        self.cmp(&cursor_location.0, cx)
 108    }
 109}
 110
 111struct End<D>(PhantomData<D>);
 112
 113impl<D> End<D> {
 114    fn new() -> Self {
 115        Self(PhantomData)
 116    }
 117}
 118
 119impl<'a, S: Summary, D: Dimension<'a, S>> SeekTarget<'a, S, D> for End<D> {
 120    fn cmp(&self, _: &D, _: &S::Context) -> Ordering {
 121        Ordering::Greater
 122    }
 123}
 124
 125impl<D> fmt::Debug for End<D> {
 126    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
 127        f.debug_tuple("End").finish()
 128    }
 129}
 130
 131/// Bias is used to settle ambiguities when determining positions in an ordered sequence.
 132///
 133/// The primary use case is for text, where Bias influences
 134/// which character an offset or anchor is associated with.
 135///
 136/// # Examples
 137/// Given the buffer `AˇBCD`:
 138/// - The offset of the cursor is 1
 139/// - [Bias::Left] would attach the cursor to the character `A`
 140/// - [Bias::Right] would attach the cursor to the character `B`
 141///
 142/// Given the buffer `A«BCˇ»D`:
 143/// - The offset of the cursor is 3, and the selection is from 1 to 3
 144/// - The left anchor of the selection has [Bias::Right], attaching it to the character `B`
 145/// - The right anchor of the selection has [Bias::Left], attaching it to the character `C`
 146///
 147/// Given the buffer `{ˇ<...>`, where `<...>` is a folded region:
 148/// - The display offset of the cursor is 1, but the offset in the buffer is determined by the bias
 149/// - [Bias::Left] would attach the cursor to the character `{`, with a buffer offset of 1
 150/// - [Bias::Right] would attach the cursor to the first character of the folded region,
 151///   and the buffer offset would be the offset of the first character of the folded region
 152#[derive(Copy, Clone, Eq, PartialEq, PartialOrd, Ord, Debug, Hash, Default)]
 153pub enum Bias {
 154    /// Attach to the character on the left
 155    #[default]
 156    Left,
 157    /// Attach to the character on the right
 158    Right,
 159}
 160
 161impl Bias {
 162    pub fn invert(self) -> Self {
 163        match self {
 164            Self::Left => Self::Right,
 165            Self::Right => Self::Left,
 166        }
 167    }
 168}
 169
 170/// A B+ tree in which each leaf node contains `Item`s of type `T` and a `Summary`s for each `Item`.
 171/// Each internal node contains a `Summary` of the items in its subtree.
 172///
 173/// The maximum number of items per node is `TREE_BASE * 2`.
 174///
 175/// Any [`Dimension`] supported by the [`Summary`] type can be used to seek to a specific location in the tree.
 176#[derive(Debug, Clone)]
 177pub struct SumTree<T: Item>(Arc<Node<T>>);
 178
 179impl<T: Item> SumTree<T> {
 180    pub fn new(cx: &<T::Summary as Summary>::Context) -> Self {
 181        SumTree(Arc::new(Node::Leaf {
 182            summary: <T::Summary as Summary>::zero(cx),
 183            items: ArrayVec::new(),
 184            item_summaries: ArrayVec::new(),
 185        }))
 186    }
 187
 188    pub fn from_item(item: T, cx: &<T::Summary as Summary>::Context) -> Self {
 189        let mut tree = Self::new(cx);
 190        tree.push(item, cx);
 191        tree
 192    }
 193
 194    pub fn from_iter<I: IntoIterator<Item = T>>(
 195        iter: I,
 196        cx: &<T::Summary as Summary>::Context,
 197    ) -> Self {
 198        let mut nodes = Vec::new();
 199
 200        let mut iter = iter.into_iter().fuse().peekable();
 201        while iter.peek().is_some() {
 202            let items: ArrayVec<T, { 2 * TREE_BASE }> = iter.by_ref().take(2 * TREE_BASE).collect();
 203            let item_summaries: ArrayVec<T::Summary, { 2 * TREE_BASE }> =
 204                items.iter().map(|item| item.summary()).collect();
 205
 206            let mut summary = item_summaries[0].clone();
 207            for item_summary in &item_summaries[1..] {
 208                <T::Summary as Summary>::add_summary(&mut summary, item_summary, cx);
 209            }
 210
 211            nodes.push(Node::Leaf {
 212                summary,
 213                items,
 214                item_summaries,
 215            });
 216        }
 217
 218        let mut parent_nodes = Vec::new();
 219        let mut height = 0;
 220        while nodes.len() > 1 {
 221            height += 1;
 222            let mut current_parent_node = None;
 223            for child_node in nodes.drain(..) {
 224                let parent_node = current_parent_node.get_or_insert_with(|| Node::Internal {
 225                    summary: <T::Summary as Summary>::zero(cx),
 226                    height,
 227                    child_summaries: ArrayVec::new(),
 228                    child_trees: ArrayVec::new(),
 229                });
 230                let Node::Internal {
 231                    summary,
 232                    child_summaries,
 233                    child_trees,
 234                    ..
 235                } = parent_node
 236                else {
 237                    unreachable!()
 238                };
 239                let child_summary = child_node.summary();
 240                <T::Summary as Summary>::add_summary(summary, child_summary, cx);
 241                child_summaries.push(child_summary.clone());
 242                child_trees.push(Self(Arc::new(child_node)));
 243
 244                if child_trees.len() == 2 * TREE_BASE {
 245                    parent_nodes.extend(current_parent_node.take());
 246                }
 247            }
 248            parent_nodes.extend(current_parent_node.take());
 249            mem::swap(&mut nodes, &mut parent_nodes);
 250        }
 251
 252        if nodes.is_empty() {
 253            Self::new(cx)
 254        } else {
 255            debug_assert_eq!(nodes.len(), 1);
 256            Self(Arc::new(nodes.pop().unwrap()))
 257        }
 258    }
 259
 260    pub fn from_par_iter<I, Iter>(iter: I, cx: &<T::Summary as Summary>::Context) -> Self
 261    where
 262        I: IntoParallelIterator<Iter = Iter>,
 263        Iter: IndexedParallelIterator<Item = T>,
 264        T: Send + Sync,
 265        T::Summary: Send + Sync,
 266        <T::Summary as Summary>::Context: Sync,
 267    {
 268        let mut nodes = iter
 269            .into_par_iter()
 270            .chunks(2 * TREE_BASE)
 271            .map(|items| {
 272                let items: ArrayVec<T, { 2 * TREE_BASE }> = items.into_iter().collect();
 273                let item_summaries: ArrayVec<T::Summary, { 2 * TREE_BASE }> =
 274                    items.iter().map(|item| item.summary()).collect();
 275                let mut summary = item_summaries[0].clone();
 276                for item_summary in &item_summaries[1..] {
 277                    <T::Summary as Summary>::add_summary(&mut summary, item_summary, cx);
 278                }
 279                SumTree(Arc::new(Node::Leaf {
 280                    summary,
 281                    items,
 282                    item_summaries,
 283                }))
 284            })
 285            .collect::<Vec<_>>();
 286
 287        let mut height = 0;
 288        while nodes.len() > 1 {
 289            height += 1;
 290            nodes = nodes
 291                .into_par_iter()
 292                .chunks(2 * TREE_BASE)
 293                .map(|child_nodes| {
 294                    let child_trees: ArrayVec<SumTree<T>, { 2 * TREE_BASE }> =
 295                        child_nodes.into_iter().collect();
 296                    let child_summaries: ArrayVec<T::Summary, { 2 * TREE_BASE }> = child_trees
 297                        .iter()
 298                        .map(|child_tree| child_tree.summary().clone())
 299                        .collect();
 300                    let mut summary = child_summaries[0].clone();
 301                    for child_summary in &child_summaries[1..] {
 302                        <T::Summary as Summary>::add_summary(&mut summary, child_summary, cx);
 303                    }
 304                    SumTree(Arc::new(Node::Internal {
 305                        height,
 306                        summary,
 307                        child_summaries,
 308                        child_trees,
 309                    }))
 310                })
 311                .collect::<Vec<_>>();
 312        }
 313
 314        if nodes.is_empty() {
 315            Self::new(cx)
 316        } else {
 317            debug_assert_eq!(nodes.len(), 1);
 318            nodes.pop().unwrap()
 319        }
 320    }
 321
 322    #[allow(unused)]
 323    pub fn items(&self, cx: &<T::Summary as Summary>::Context) -> Vec<T> {
 324        let mut items = Vec::new();
 325        let mut cursor = self.cursor::<()>(cx);
 326        cursor.next(cx);
 327        while let Some(item) = cursor.item() {
 328            items.push(item.clone());
 329            cursor.next(cx);
 330        }
 331        items
 332    }
 333
 334    pub fn iter(&self) -> Iter<T> {
 335        Iter::new(self)
 336    }
 337
 338    pub fn cursor<'a, S>(&'a self, cx: &<T::Summary as Summary>::Context) -> Cursor<T, S>
 339    where
 340        S: Dimension<'a, T::Summary>,
 341    {
 342        Cursor::new(self, cx)
 343    }
 344
 345    /// Note: If the summary type requires a non `()` context, then the filter cursor
 346    /// that is returned cannot be used with Rust's iterators.
 347    pub fn filter<'a, F, U>(
 348        &'a self,
 349        cx: &<T::Summary as Summary>::Context,
 350        filter_node: F,
 351    ) -> FilterCursor<F, T, U>
 352    where
 353        F: FnMut(&T::Summary) -> bool,
 354        U: Dimension<'a, T::Summary>,
 355    {
 356        FilterCursor::new(self, cx, filter_node)
 357    }
 358
 359    #[allow(dead_code)]
 360    pub fn first(&self) -> Option<&T> {
 361        self.leftmost_leaf().0.items().first()
 362    }
 363
 364    pub fn last(&self) -> Option<&T> {
 365        self.rightmost_leaf().0.items().last()
 366    }
 367
 368    pub fn update_last(&mut self, f: impl FnOnce(&mut T), cx: &<T::Summary as Summary>::Context) {
 369        self.update_last_recursive(f, cx);
 370    }
 371
 372    fn update_last_recursive(
 373        &mut self,
 374        f: impl FnOnce(&mut T),
 375        cx: &<T::Summary as Summary>::Context,
 376    ) -> Option<T::Summary> {
 377        match Arc::make_mut(&mut self.0) {
 378            Node::Internal {
 379                summary,
 380                child_summaries,
 381                child_trees,
 382                ..
 383            } => {
 384                let last_summary = child_summaries.last_mut().unwrap();
 385                let last_child = child_trees.last_mut().unwrap();
 386                *last_summary = last_child.update_last_recursive(f, cx).unwrap();
 387                *summary = sum(child_summaries.iter(), cx);
 388                Some(summary.clone())
 389            }
 390            Node::Leaf {
 391                summary,
 392                items,
 393                item_summaries,
 394            } => {
 395                if let Some((item, item_summary)) = items.last_mut().zip(item_summaries.last_mut())
 396                {
 397                    (f)(item);
 398                    *item_summary = item.summary();
 399                    *summary = sum(item_summaries.iter(), cx);
 400                    Some(summary.clone())
 401                } else {
 402                    None
 403                }
 404            }
 405        }
 406    }
 407
 408    pub fn extent<'a, D: Dimension<'a, T::Summary>>(
 409        &'a self,
 410        cx: &<T::Summary as Summary>::Context,
 411    ) -> D {
 412        let mut extent = D::zero(cx);
 413        match self.0.as_ref() {
 414            Node::Internal { summary, .. } | Node::Leaf { summary, .. } => {
 415                extent.add_summary(summary, cx);
 416            }
 417        }
 418        extent
 419    }
 420
 421    pub fn summary(&self) -> &T::Summary {
 422        match self.0.as_ref() {
 423            Node::Internal { summary, .. } => summary,
 424            Node::Leaf { summary, .. } => summary,
 425        }
 426    }
 427
 428    pub fn is_empty(&self) -> bool {
 429        match self.0.as_ref() {
 430            Node::Internal { .. } => false,
 431            Node::Leaf { items, .. } => items.is_empty(),
 432        }
 433    }
 434
 435    pub fn extend<I>(&mut self, iter: I, cx: &<T::Summary as Summary>::Context)
 436    where
 437        I: IntoIterator<Item = T>,
 438    {
 439        self.append(Self::from_iter(iter, cx), cx);
 440    }
 441
 442    pub fn par_extend<I, Iter>(&mut self, iter: I, cx: &<T::Summary as Summary>::Context)
 443    where
 444        I: IntoParallelIterator<Iter = Iter>,
 445        Iter: IndexedParallelIterator<Item = T>,
 446        T: Send + Sync,
 447        T::Summary: Send + Sync,
 448        <T::Summary as Summary>::Context: Sync,
 449    {
 450        self.append(Self::from_par_iter(iter, cx), cx);
 451    }
 452
 453    pub fn push(&mut self, item: T, cx: &<T::Summary as Summary>::Context) {
 454        let summary = item.summary();
 455        self.append(
 456            SumTree(Arc::new(Node::Leaf {
 457                summary: summary.clone(),
 458                items: ArrayVec::from_iter(Some(item)),
 459                item_summaries: ArrayVec::from_iter(Some(summary)),
 460            })),
 461            cx,
 462        );
 463    }
 464
 465    pub fn append(&mut self, other: Self, cx: &<T::Summary as Summary>::Context) {
 466        if self.is_empty() {
 467            *self = other;
 468        } else if !other.0.is_leaf() || !other.0.items().is_empty() {
 469            if self.0.height() < other.0.height() {
 470                for tree in other.0.child_trees() {
 471                    self.append(tree.clone(), cx);
 472                }
 473            } else if let Some(split_tree) = self.push_tree_recursive(other, cx) {
 474                *self = Self::from_child_trees(self.clone(), split_tree, cx);
 475            }
 476        }
 477    }
 478
 479    fn push_tree_recursive(
 480        &mut self,
 481        other: SumTree<T>,
 482        cx: &<T::Summary as Summary>::Context,
 483    ) -> Option<SumTree<T>> {
 484        match Arc::make_mut(&mut self.0) {
 485            Node::Internal {
 486                height,
 487                summary,
 488                child_summaries,
 489                child_trees,
 490                ..
 491            } => {
 492                let other_node = other.0.clone();
 493                <T::Summary as Summary>::add_summary(summary, other_node.summary(), cx);
 494
 495                let height_delta = *height - other_node.height();
 496                let mut summaries_to_append = ArrayVec::<T::Summary, { 2 * TREE_BASE }>::new();
 497                let mut trees_to_append = ArrayVec::<SumTree<T>, { 2 * TREE_BASE }>::new();
 498                if height_delta == 0 {
 499                    summaries_to_append.extend(other_node.child_summaries().iter().cloned());
 500                    trees_to_append.extend(other_node.child_trees().iter().cloned());
 501                } else if height_delta == 1 && !other_node.is_underflowing() {
 502                    summaries_to_append.push(other_node.summary().clone());
 503                    trees_to_append.push(other)
 504                } else {
 505                    let tree_to_append = child_trees
 506                        .last_mut()
 507                        .unwrap()
 508                        .push_tree_recursive(other, cx);
 509                    *child_summaries.last_mut().unwrap() =
 510                        child_trees.last().unwrap().0.summary().clone();
 511
 512                    if let Some(split_tree) = tree_to_append {
 513                        summaries_to_append.push(split_tree.0.summary().clone());
 514                        trees_to_append.push(split_tree);
 515                    }
 516                }
 517
 518                let child_count = child_trees.len() + trees_to_append.len();
 519                if child_count > 2 * TREE_BASE {
 520                    let left_summaries: ArrayVec<_, { 2 * TREE_BASE }>;
 521                    let right_summaries: ArrayVec<_, { 2 * TREE_BASE }>;
 522                    let left_trees;
 523                    let right_trees;
 524
 525                    let midpoint = (child_count + child_count % 2) / 2;
 526                    {
 527                        let mut all_summaries = child_summaries
 528                            .iter()
 529                            .chain(summaries_to_append.iter())
 530                            .cloned();
 531                        left_summaries = all_summaries.by_ref().take(midpoint).collect();
 532                        right_summaries = all_summaries.collect();
 533                        let mut all_trees =
 534                            child_trees.iter().chain(trees_to_append.iter()).cloned();
 535                        left_trees = all_trees.by_ref().take(midpoint).collect();
 536                        right_trees = all_trees.collect();
 537                    }
 538                    *summary = sum(left_summaries.iter(), cx);
 539                    *child_summaries = left_summaries;
 540                    *child_trees = left_trees;
 541
 542                    Some(SumTree(Arc::new(Node::Internal {
 543                        height: *height,
 544                        summary: sum(right_summaries.iter(), cx),
 545                        child_summaries: right_summaries,
 546                        child_trees: right_trees,
 547                    })))
 548                } else {
 549                    child_summaries.extend(summaries_to_append);
 550                    child_trees.extend(trees_to_append);
 551                    None
 552                }
 553            }
 554            Node::Leaf {
 555                summary,
 556                items,
 557                item_summaries,
 558            } => {
 559                let other_node = other.0;
 560
 561                let child_count = items.len() + other_node.items().len();
 562                if child_count > 2 * TREE_BASE {
 563                    let left_items;
 564                    let right_items;
 565                    let left_summaries;
 566                    let right_summaries: ArrayVec<T::Summary, { 2 * TREE_BASE }>;
 567
 568                    let midpoint = (child_count + child_count % 2) / 2;
 569                    {
 570                        let mut all_items = items.iter().chain(other_node.items().iter()).cloned();
 571                        left_items = all_items.by_ref().take(midpoint).collect();
 572                        right_items = all_items.collect();
 573
 574                        let mut all_summaries = item_summaries
 575                            .iter()
 576                            .chain(other_node.child_summaries())
 577                            .cloned();
 578                        left_summaries = all_summaries.by_ref().take(midpoint).collect();
 579                        right_summaries = all_summaries.collect();
 580                    }
 581                    *items = left_items;
 582                    *item_summaries = left_summaries;
 583                    *summary = sum(item_summaries.iter(), cx);
 584                    Some(SumTree(Arc::new(Node::Leaf {
 585                        items: right_items,
 586                        summary: sum(right_summaries.iter(), cx),
 587                        item_summaries: right_summaries,
 588                    })))
 589                } else {
 590                    <T::Summary as Summary>::add_summary(summary, other_node.summary(), cx);
 591                    items.extend(other_node.items().iter().cloned());
 592                    item_summaries.extend(other_node.child_summaries().iter().cloned());
 593                    None
 594                }
 595            }
 596        }
 597    }
 598
 599    fn from_child_trees(
 600        left: SumTree<T>,
 601        right: SumTree<T>,
 602        cx: &<T::Summary as Summary>::Context,
 603    ) -> Self {
 604        let height = left.0.height() + 1;
 605        let mut child_summaries = ArrayVec::new();
 606        child_summaries.push(left.0.summary().clone());
 607        child_summaries.push(right.0.summary().clone());
 608        let mut child_trees = ArrayVec::new();
 609        child_trees.push(left);
 610        child_trees.push(right);
 611        SumTree(Arc::new(Node::Internal {
 612            height,
 613            summary: sum(child_summaries.iter(), cx),
 614            child_summaries,
 615            child_trees,
 616        }))
 617    }
 618
 619    fn leftmost_leaf(&self) -> &Self {
 620        match *self.0 {
 621            Node::Leaf { .. } => self,
 622            Node::Internal {
 623                ref child_trees, ..
 624            } => child_trees.first().unwrap().leftmost_leaf(),
 625        }
 626    }
 627
 628    fn rightmost_leaf(&self) -> &Self {
 629        match *self.0 {
 630            Node::Leaf { .. } => self,
 631            Node::Internal {
 632                ref child_trees, ..
 633            } => child_trees.last().unwrap().rightmost_leaf(),
 634        }
 635    }
 636
 637    #[cfg(debug_assertions)]
 638    pub fn _debug_entries(&self) -> Vec<&T> {
 639        self.iter().collect::<Vec<_>>()
 640    }
 641}
 642
 643impl<T: Item + PartialEq> PartialEq for SumTree<T> {
 644    fn eq(&self, other: &Self) -> bool {
 645        self.iter().eq(other.iter())
 646    }
 647}
 648
 649impl<T: Item + Eq> Eq for SumTree<T> {}
 650
 651impl<T: KeyedItem> SumTree<T> {
 652    pub fn insert_or_replace(
 653        &mut self,
 654        item: T,
 655        cx: &<T::Summary as Summary>::Context,
 656    ) -> Option<T> {
 657        let mut replaced = None;
 658        *self = {
 659            let mut cursor = self.cursor::<T::Key>(cx);
 660            let mut new_tree = cursor.slice(&item.key(), Bias::Left, cx);
 661            if let Some(cursor_item) = cursor.item() {
 662                if cursor_item.key() == item.key() {
 663                    replaced = Some(cursor_item.clone());
 664                    cursor.next(cx);
 665                }
 666            }
 667            new_tree.push(item, cx);
 668            new_tree.append(cursor.suffix(cx), cx);
 669            new_tree
 670        };
 671        replaced
 672    }
 673
 674    pub fn remove(&mut self, key: &T::Key, cx: &<T::Summary as Summary>::Context) -> Option<T> {
 675        let mut removed = None;
 676        *self = {
 677            let mut cursor = self.cursor::<T::Key>(cx);
 678            let mut new_tree = cursor.slice(key, Bias::Left, cx);
 679            if let Some(item) = cursor.item() {
 680                if item.key() == *key {
 681                    removed = Some(item.clone());
 682                    cursor.next(cx);
 683                }
 684            }
 685            new_tree.append(cursor.suffix(cx), cx);
 686            new_tree
 687        };
 688        removed
 689    }
 690
 691    pub fn edit(
 692        &mut self,
 693        mut edits: Vec<Edit<T>>,
 694        cx: &<T::Summary as Summary>::Context,
 695    ) -> Vec<T> {
 696        if edits.is_empty() {
 697            return Vec::new();
 698        }
 699
 700        let mut removed = Vec::new();
 701        edits.sort_unstable_by_key(|item| item.key());
 702
 703        *self = {
 704            let mut cursor = self.cursor::<T::Key>(cx);
 705            let mut new_tree = SumTree::new(cx);
 706            let mut buffered_items = Vec::new();
 707
 708            cursor.seek(&T::Key::zero(cx), Bias::Left, cx);
 709            for edit in edits {
 710                let new_key = edit.key();
 711                let mut old_item = cursor.item();
 712
 713                if old_item
 714                    .as_ref()
 715                    .map_or(false, |old_item| old_item.key() < new_key)
 716                {
 717                    new_tree.extend(buffered_items.drain(..), cx);
 718                    let slice = cursor.slice(&new_key, Bias::Left, cx);
 719                    new_tree.append(slice, cx);
 720                    old_item = cursor.item();
 721                }
 722
 723                if let Some(old_item) = old_item {
 724                    if old_item.key() == new_key {
 725                        removed.push(old_item.clone());
 726                        cursor.next(cx);
 727                    }
 728                }
 729
 730                match edit {
 731                    Edit::Insert(item) => {
 732                        buffered_items.push(item);
 733                    }
 734                    Edit::Remove(_) => {}
 735                }
 736            }
 737
 738            new_tree.extend(buffered_items, cx);
 739            new_tree.append(cursor.suffix(cx), cx);
 740            new_tree
 741        };
 742
 743        removed
 744    }
 745
 746    pub fn get(&self, key: &T::Key, cx: &<T::Summary as Summary>::Context) -> Option<&T> {
 747        let mut cursor = self.cursor::<T::Key>(cx);
 748        if cursor.seek(key, Bias::Left, cx) {
 749            cursor.item()
 750        } else {
 751            None
 752        }
 753    }
 754}
 755
 756impl<T, S> Default for SumTree<T>
 757where
 758    T: Item<Summary = S>,
 759    S: Summary<Context = ()>,
 760{
 761    fn default() -> Self {
 762        Self::new(&())
 763    }
 764}
 765
 766#[derive(Clone, Debug)]
 767pub enum Node<T: Item> {
 768    Internal {
 769        height: u8,
 770        summary: T::Summary,
 771        child_summaries: ArrayVec<T::Summary, { 2 * TREE_BASE }>,
 772        child_trees: ArrayVec<SumTree<T>, { 2 * TREE_BASE }>,
 773    },
 774    Leaf {
 775        summary: T::Summary,
 776        items: ArrayVec<T, { 2 * TREE_BASE }>,
 777        item_summaries: ArrayVec<T::Summary, { 2 * TREE_BASE }>,
 778    },
 779}
 780
 781impl<T: Item> Node<T> {
 782    fn is_leaf(&self) -> bool {
 783        matches!(self, Node::Leaf { .. })
 784    }
 785
 786    fn height(&self) -> u8 {
 787        match self {
 788            Node::Internal { height, .. } => *height,
 789            Node::Leaf { .. } => 0,
 790        }
 791    }
 792
 793    fn summary(&self) -> &T::Summary {
 794        match self {
 795            Node::Internal { summary, .. } => summary,
 796            Node::Leaf { summary, .. } => summary,
 797        }
 798    }
 799
 800    fn child_summaries(&self) -> &[T::Summary] {
 801        match self {
 802            Node::Internal {
 803                child_summaries, ..
 804            } => child_summaries.as_slice(),
 805            Node::Leaf { item_summaries, .. } => item_summaries.as_slice(),
 806        }
 807    }
 808
 809    fn child_trees(&self) -> &ArrayVec<SumTree<T>, { 2 * TREE_BASE }> {
 810        match self {
 811            Node::Internal { child_trees, .. } => child_trees,
 812            Node::Leaf { .. } => panic!("Leaf nodes have no child trees"),
 813        }
 814    }
 815
 816    fn items(&self) -> &ArrayVec<T, { 2 * TREE_BASE }> {
 817        match self {
 818            Node::Leaf { items, .. } => items,
 819            Node::Internal { .. } => panic!("Internal nodes have no items"),
 820        }
 821    }
 822
 823    fn is_underflowing(&self) -> bool {
 824        match self {
 825            Node::Internal { child_trees, .. } => child_trees.len() < TREE_BASE,
 826            Node::Leaf { items, .. } => items.len() < TREE_BASE,
 827        }
 828    }
 829}
 830
 831#[derive(Debug)]
 832pub enum Edit<T: KeyedItem> {
 833    Insert(T),
 834    Remove(T::Key),
 835}
 836
 837impl<T: KeyedItem> Edit<T> {
 838    fn key(&self) -> T::Key {
 839        match self {
 840            Edit::Insert(item) => item.key(),
 841            Edit::Remove(key) => key.clone(),
 842        }
 843    }
 844}
 845
 846fn sum<'a, T, I>(iter: I, cx: &T::Context) -> T
 847where
 848    T: 'a + Summary,
 849    I: Iterator<Item = &'a T>,
 850{
 851    let mut sum = T::zero(cx);
 852    for value in iter {
 853        sum.add_summary(value, cx);
 854    }
 855    sum
 856}
 857
 858#[cfg(test)]
 859mod tests {
 860    use super::*;
 861    use rand::{distributions, prelude::*};
 862    use std::cmp;
 863
 864    #[ctor::ctor]
 865    fn init_logger() {
 866        if std::env::var("RUST_LOG").is_ok() {
 867            env_logger::init();
 868        }
 869    }
 870
 871    #[test]
 872    fn test_extend_and_push_tree() {
 873        let mut tree1 = SumTree::default();
 874        tree1.extend(0..20, &());
 875
 876        let mut tree2 = SumTree::default();
 877        tree2.extend(50..100, &());
 878
 879        tree1.append(tree2, &());
 880        assert_eq!(
 881            tree1.items(&()),
 882            (0..20).chain(50..100).collect::<Vec<u8>>()
 883        );
 884    }
 885
 886    #[test]
 887    fn test_random() {
 888        let mut starting_seed = 0;
 889        if let Ok(value) = std::env::var("SEED") {
 890            starting_seed = value.parse().expect("invalid SEED variable");
 891        }
 892        let mut num_iterations = 100;
 893        if let Ok(value) = std::env::var("ITERATIONS") {
 894            num_iterations = value.parse().expect("invalid ITERATIONS variable");
 895        }
 896        let num_operations = std::env::var("OPERATIONS")
 897            .map_or(5, |o| o.parse().expect("invalid OPERATIONS variable"));
 898
 899        for seed in starting_seed..(starting_seed + num_iterations) {
 900            eprintln!("seed = {}", seed);
 901            let mut rng = StdRng::seed_from_u64(seed);
 902
 903            let rng = &mut rng;
 904            let mut tree = SumTree::<u8>::default();
 905            let count = rng.gen_range(0..10);
 906            if rng.gen() {
 907                tree.extend(rng.sample_iter(distributions::Standard).take(count), &());
 908            } else {
 909                let items = rng
 910                    .sample_iter(distributions::Standard)
 911                    .take(count)
 912                    .collect::<Vec<_>>();
 913                tree.par_extend(items, &());
 914            }
 915
 916            for _ in 0..num_operations {
 917                let splice_end = rng.gen_range(0..tree.extent::<Count>(&()).0 + 1);
 918                let splice_start = rng.gen_range(0..splice_end + 1);
 919                let count = rng.gen_range(0..10);
 920                let tree_end = tree.extent::<Count>(&());
 921                let new_items = rng
 922                    .sample_iter(distributions::Standard)
 923                    .take(count)
 924                    .collect::<Vec<u8>>();
 925
 926                let mut reference_items = tree.items(&());
 927                reference_items.splice(splice_start..splice_end, new_items.clone());
 928
 929                tree = {
 930                    let mut cursor = tree.cursor::<Count>(&());
 931                    let mut new_tree = cursor.slice(&Count(splice_start), Bias::Right, &());
 932                    if rng.gen() {
 933                        new_tree.extend(new_items, &());
 934                    } else {
 935                        new_tree.par_extend(new_items, &());
 936                    }
 937                    cursor.seek(&Count(splice_end), Bias::Right, &());
 938                    new_tree.append(cursor.slice(&tree_end, Bias::Right, &()), &());
 939                    new_tree
 940                };
 941
 942                assert_eq!(tree.items(&()), reference_items);
 943                assert_eq!(
 944                    tree.iter().collect::<Vec<_>>(),
 945                    tree.cursor::<()>(&()).collect::<Vec<_>>()
 946                );
 947
 948                log::info!("tree items: {:?}", tree.items(&()));
 949
 950                let mut filter_cursor =
 951                    tree.filter::<_, Count>(&(), |summary| summary.contains_even);
 952                let expected_filtered_items = tree
 953                    .items(&())
 954                    .into_iter()
 955                    .enumerate()
 956                    .filter(|(_, item)| (item & 1) == 0)
 957                    .collect::<Vec<_>>();
 958
 959                let mut item_ix = if rng.gen() {
 960                    filter_cursor.next(&());
 961                    0
 962                } else {
 963                    filter_cursor.prev(&());
 964                    expected_filtered_items.len().saturating_sub(1)
 965                };
 966                while item_ix < expected_filtered_items.len() {
 967                    log::info!("filter_cursor, item_ix: {}", item_ix);
 968                    let actual_item = filter_cursor.item().unwrap();
 969                    let (reference_index, reference_item) = expected_filtered_items[item_ix];
 970                    assert_eq!(actual_item, &reference_item);
 971                    assert_eq!(filter_cursor.start().0, reference_index);
 972                    log::info!("next");
 973                    filter_cursor.next(&());
 974                    item_ix += 1;
 975
 976                    while item_ix > 0 && rng.gen_bool(0.2) {
 977                        log::info!("prev");
 978                        filter_cursor.prev(&());
 979                        item_ix -= 1;
 980
 981                        if item_ix == 0 && rng.gen_bool(0.2) {
 982                            filter_cursor.prev(&());
 983                            assert_eq!(filter_cursor.item(), None);
 984                            assert_eq!(filter_cursor.start().0, 0);
 985                            filter_cursor.next(&());
 986                        }
 987                    }
 988                }
 989                assert_eq!(filter_cursor.item(), None);
 990
 991                let mut before_start = false;
 992                let mut cursor = tree.cursor::<Count>(&());
 993                let start_pos = rng.gen_range(0..=reference_items.len());
 994                cursor.seek(&Count(start_pos), Bias::Right, &());
 995                let mut pos = rng.gen_range(start_pos..=reference_items.len());
 996                cursor.seek_forward(&Count(pos), Bias::Right, &());
 997
 998                for i in 0..10 {
 999                    assert_eq!(cursor.start().0, pos);
1000
1001                    if pos > 0 {
1002                        assert_eq!(cursor.prev_item().unwrap(), &reference_items[pos - 1]);
1003                    } else {
1004                        assert_eq!(cursor.prev_item(), None);
1005                    }
1006
1007                    if pos < reference_items.len() && !before_start {
1008                        assert_eq!(cursor.item().unwrap(), &reference_items[pos]);
1009                    } else {
1010                        assert_eq!(cursor.item(), None);
1011                    }
1012
1013                    if before_start {
1014                        assert_eq!(cursor.next_item(), reference_items.first());
1015                    } else if pos + 1 < reference_items.len() {
1016                        assert_eq!(cursor.next_item().unwrap(), &reference_items[pos + 1]);
1017                    } else {
1018                        assert_eq!(cursor.next_item(), None);
1019                    }
1020
1021                    if i < 5 {
1022                        cursor.next(&());
1023                        if pos < reference_items.len() {
1024                            pos += 1;
1025                            before_start = false;
1026                        }
1027                    } else {
1028                        cursor.prev(&());
1029                        if pos == 0 {
1030                            before_start = true;
1031                        }
1032                        pos = pos.saturating_sub(1);
1033                    }
1034                }
1035            }
1036
1037            for _ in 0..10 {
1038                let end = rng.gen_range(0..tree.extent::<Count>(&()).0 + 1);
1039                let start = rng.gen_range(0..end + 1);
1040                let start_bias = if rng.gen() { Bias::Left } else { Bias::Right };
1041                let end_bias = if rng.gen() { Bias::Left } else { Bias::Right };
1042
1043                let mut cursor = tree.cursor::<Count>(&());
1044                cursor.seek(&Count(start), start_bias, &());
1045                let slice = cursor.slice(&Count(end), end_bias, &());
1046
1047                cursor.seek(&Count(start), start_bias, &());
1048                let summary = cursor.summary::<_, Sum>(&Count(end), end_bias, &());
1049
1050                assert_eq!(summary.0, slice.summary().sum);
1051            }
1052        }
1053    }
1054
1055    #[test]
1056    fn test_cursor() {
1057        // Empty tree
1058        let tree = SumTree::<u8>::default();
1059        let mut cursor = tree.cursor::<IntegersSummary>(&());
1060        assert_eq!(
1061            cursor.slice(&Count(0), Bias::Right, &()).items(&()),
1062            Vec::<u8>::new()
1063        );
1064        assert_eq!(cursor.item(), None);
1065        assert_eq!(cursor.prev_item(), None);
1066        assert_eq!(cursor.next_item(), None);
1067        assert_eq!(cursor.start().sum, 0);
1068        cursor.prev(&());
1069        assert_eq!(cursor.item(), None);
1070        assert_eq!(cursor.prev_item(), None);
1071        assert_eq!(cursor.next_item(), None);
1072        assert_eq!(cursor.start().sum, 0);
1073        cursor.next(&());
1074        assert_eq!(cursor.item(), None);
1075        assert_eq!(cursor.prev_item(), None);
1076        assert_eq!(cursor.next_item(), None);
1077        assert_eq!(cursor.start().sum, 0);
1078
1079        // Single-element tree
1080        let mut tree = SumTree::<u8>::default();
1081        tree.extend(vec![1], &());
1082        let mut cursor = tree.cursor::<IntegersSummary>(&());
1083        assert_eq!(
1084            cursor.slice(&Count(0), Bias::Right, &()).items(&()),
1085            Vec::<u8>::new()
1086        );
1087        assert_eq!(cursor.item(), Some(&1));
1088        assert_eq!(cursor.prev_item(), None);
1089        assert_eq!(cursor.next_item(), None);
1090        assert_eq!(cursor.start().sum, 0);
1091
1092        cursor.next(&());
1093        assert_eq!(cursor.item(), None);
1094        assert_eq!(cursor.prev_item(), Some(&1));
1095        assert_eq!(cursor.next_item(), None);
1096        assert_eq!(cursor.start().sum, 1);
1097
1098        cursor.prev(&());
1099        assert_eq!(cursor.item(), Some(&1));
1100        assert_eq!(cursor.prev_item(), None);
1101        assert_eq!(cursor.next_item(), None);
1102        assert_eq!(cursor.start().sum, 0);
1103
1104        let mut cursor = tree.cursor::<IntegersSummary>(&());
1105        assert_eq!(cursor.slice(&Count(1), Bias::Right, &()).items(&()), [1]);
1106        assert_eq!(cursor.item(), None);
1107        assert_eq!(cursor.prev_item(), Some(&1));
1108        assert_eq!(cursor.next_item(), None);
1109        assert_eq!(cursor.start().sum, 1);
1110
1111        cursor.seek(&Count(0), Bias::Right, &());
1112        assert_eq!(
1113            cursor
1114                .slice(&tree.extent::<Count>(&()), Bias::Right, &())
1115                .items(&()),
1116            [1]
1117        );
1118        assert_eq!(cursor.item(), None);
1119        assert_eq!(cursor.prev_item(), Some(&1));
1120        assert_eq!(cursor.next_item(), None);
1121        assert_eq!(cursor.start().sum, 1);
1122
1123        // Multiple-element tree
1124        let mut tree = SumTree::default();
1125        tree.extend(vec![1, 2, 3, 4, 5, 6], &());
1126        let mut cursor = tree.cursor::<IntegersSummary>(&());
1127
1128        assert_eq!(cursor.slice(&Count(2), Bias::Right, &()).items(&()), [1, 2]);
1129        assert_eq!(cursor.item(), Some(&3));
1130        assert_eq!(cursor.prev_item(), Some(&2));
1131        assert_eq!(cursor.next_item(), Some(&4));
1132        assert_eq!(cursor.start().sum, 3);
1133
1134        cursor.next(&());
1135        assert_eq!(cursor.item(), Some(&4));
1136        assert_eq!(cursor.prev_item(), Some(&3));
1137        assert_eq!(cursor.next_item(), Some(&5));
1138        assert_eq!(cursor.start().sum, 6);
1139
1140        cursor.next(&());
1141        assert_eq!(cursor.item(), Some(&5));
1142        assert_eq!(cursor.prev_item(), Some(&4));
1143        assert_eq!(cursor.next_item(), Some(&6));
1144        assert_eq!(cursor.start().sum, 10);
1145
1146        cursor.next(&());
1147        assert_eq!(cursor.item(), Some(&6));
1148        assert_eq!(cursor.prev_item(), Some(&5));
1149        assert_eq!(cursor.next_item(), None);
1150        assert_eq!(cursor.start().sum, 15);
1151
1152        cursor.next(&());
1153        cursor.next(&());
1154        assert_eq!(cursor.item(), None);
1155        assert_eq!(cursor.prev_item(), Some(&6));
1156        assert_eq!(cursor.next_item(), None);
1157        assert_eq!(cursor.start().sum, 21);
1158
1159        cursor.prev(&());
1160        assert_eq!(cursor.item(), Some(&6));
1161        assert_eq!(cursor.prev_item(), Some(&5));
1162        assert_eq!(cursor.next_item(), None);
1163        assert_eq!(cursor.start().sum, 15);
1164
1165        cursor.prev(&());
1166        assert_eq!(cursor.item(), Some(&5));
1167        assert_eq!(cursor.prev_item(), Some(&4));
1168        assert_eq!(cursor.next_item(), Some(&6));
1169        assert_eq!(cursor.start().sum, 10);
1170
1171        cursor.prev(&());
1172        assert_eq!(cursor.item(), Some(&4));
1173        assert_eq!(cursor.prev_item(), Some(&3));
1174        assert_eq!(cursor.next_item(), Some(&5));
1175        assert_eq!(cursor.start().sum, 6);
1176
1177        cursor.prev(&());
1178        assert_eq!(cursor.item(), Some(&3));
1179        assert_eq!(cursor.prev_item(), Some(&2));
1180        assert_eq!(cursor.next_item(), Some(&4));
1181        assert_eq!(cursor.start().sum, 3);
1182
1183        cursor.prev(&());
1184        assert_eq!(cursor.item(), Some(&2));
1185        assert_eq!(cursor.prev_item(), Some(&1));
1186        assert_eq!(cursor.next_item(), Some(&3));
1187        assert_eq!(cursor.start().sum, 1);
1188
1189        cursor.prev(&());
1190        assert_eq!(cursor.item(), Some(&1));
1191        assert_eq!(cursor.prev_item(), None);
1192        assert_eq!(cursor.next_item(), Some(&2));
1193        assert_eq!(cursor.start().sum, 0);
1194
1195        cursor.prev(&());
1196        assert_eq!(cursor.item(), None);
1197        assert_eq!(cursor.prev_item(), None);
1198        assert_eq!(cursor.next_item(), Some(&1));
1199        assert_eq!(cursor.start().sum, 0);
1200
1201        cursor.next(&());
1202        assert_eq!(cursor.item(), Some(&1));
1203        assert_eq!(cursor.prev_item(), None);
1204        assert_eq!(cursor.next_item(), Some(&2));
1205        assert_eq!(cursor.start().sum, 0);
1206
1207        let mut cursor = tree.cursor::<IntegersSummary>(&());
1208        assert_eq!(
1209            cursor
1210                .slice(&tree.extent::<Count>(&()), Bias::Right, &())
1211                .items(&()),
1212            tree.items(&())
1213        );
1214        assert_eq!(cursor.item(), None);
1215        assert_eq!(cursor.prev_item(), Some(&6));
1216        assert_eq!(cursor.next_item(), None);
1217        assert_eq!(cursor.start().sum, 21);
1218
1219        cursor.seek(&Count(3), Bias::Right, &());
1220        assert_eq!(
1221            cursor
1222                .slice(&tree.extent::<Count>(&()), Bias::Right, &())
1223                .items(&()),
1224            [4, 5, 6]
1225        );
1226        assert_eq!(cursor.item(), None);
1227        assert_eq!(cursor.prev_item(), Some(&6));
1228        assert_eq!(cursor.next_item(), None);
1229        assert_eq!(cursor.start().sum, 21);
1230
1231        // Seeking can bias left or right
1232        cursor.seek(&Count(1), Bias::Left, &());
1233        assert_eq!(cursor.item(), Some(&1));
1234        cursor.seek(&Count(1), Bias::Right, &());
1235        assert_eq!(cursor.item(), Some(&2));
1236
1237        // Slicing without resetting starts from where the cursor is parked at.
1238        cursor.seek(&Count(1), Bias::Right, &());
1239        assert_eq!(
1240            cursor.slice(&Count(3), Bias::Right, &()).items(&()),
1241            vec![2, 3]
1242        );
1243        assert_eq!(
1244            cursor.slice(&Count(6), Bias::Left, &()).items(&()),
1245            vec![4, 5]
1246        );
1247        assert_eq!(
1248            cursor.slice(&Count(6), Bias::Right, &()).items(&()),
1249            vec![6]
1250        );
1251    }
1252
1253    #[test]
1254    fn test_edit() {
1255        let mut tree = SumTree::<u8>::default();
1256
1257        let removed = tree.edit(vec![Edit::Insert(1), Edit::Insert(2), Edit::Insert(0)], &());
1258        assert_eq!(tree.items(&()), vec![0, 1, 2]);
1259        assert_eq!(removed, Vec::<u8>::new());
1260        assert_eq!(tree.get(&0, &()), Some(&0));
1261        assert_eq!(tree.get(&1, &()), Some(&1));
1262        assert_eq!(tree.get(&2, &()), Some(&2));
1263        assert_eq!(tree.get(&4, &()), None);
1264
1265        let removed = tree.edit(vec![Edit::Insert(2), Edit::Insert(4), Edit::Remove(0)], &());
1266        assert_eq!(tree.items(&()), vec![1, 2, 4]);
1267        assert_eq!(removed, vec![0, 2]);
1268        assert_eq!(tree.get(&0, &()), None);
1269        assert_eq!(tree.get(&1, &()), Some(&1));
1270        assert_eq!(tree.get(&2, &()), Some(&2));
1271        assert_eq!(tree.get(&4, &()), Some(&4));
1272    }
1273
1274    #[test]
1275    fn test_from_iter() {
1276        assert_eq!(
1277            SumTree::from_iter(0..100, &()).items(&()),
1278            (0..100).collect::<Vec<_>>()
1279        );
1280
1281        // Ensure `from_iter` works correctly when the given iterator restarts
1282        // after calling `next` if `None` was already returned.
1283        let mut ix = 0;
1284        let iterator = std::iter::from_fn(|| {
1285            ix = (ix + 1) % 2;
1286            if ix == 1 {
1287                Some(1)
1288            } else {
1289                None
1290            }
1291        });
1292        assert_eq!(SumTree::from_iter(iterator, &()).items(&()), vec![1]);
1293    }
1294
1295    #[derive(Clone, Default, Debug)]
1296    pub struct IntegersSummary {
1297        count: usize,
1298        sum: usize,
1299        contains_even: bool,
1300        max: u8,
1301    }
1302
1303    #[derive(Ord, PartialOrd, Default, Eq, PartialEq, Clone, Debug)]
1304    struct Count(usize);
1305
1306    #[derive(Ord, PartialOrd, Default, Eq, PartialEq, Clone, Debug)]
1307    struct Sum(usize);
1308
1309    impl Item for u8 {
1310        type Summary = IntegersSummary;
1311
1312        fn summary(&self) -> Self::Summary {
1313            IntegersSummary {
1314                count: 1,
1315                sum: *self as usize,
1316                contains_even: (*self & 1) == 0,
1317                max: *self,
1318            }
1319        }
1320    }
1321
1322    impl KeyedItem for u8 {
1323        type Key = u8;
1324
1325        fn key(&self) -> Self::Key {
1326            *self
1327        }
1328    }
1329
1330    impl Summary for IntegersSummary {
1331        type Context = ();
1332
1333        fn zero(_cx: &()) -> Self {
1334            Default::default()
1335        }
1336
1337        fn add_summary(&mut self, other: &Self, _: &()) {
1338            self.count += other.count;
1339            self.sum += other.sum;
1340            self.contains_even |= other.contains_even;
1341            self.max = cmp::max(self.max, other.max);
1342        }
1343    }
1344
1345    impl<'a> Dimension<'a, IntegersSummary> for u8 {
1346        fn zero(_cx: &()) -> Self {
1347            Default::default()
1348        }
1349
1350        fn add_summary(&mut self, summary: &IntegersSummary, _: &()) {
1351            *self = summary.max;
1352        }
1353    }
1354
1355    impl<'a> Dimension<'a, IntegersSummary> for Count {
1356        fn zero(_cx: &()) -> Self {
1357            Default::default()
1358        }
1359
1360        fn add_summary(&mut self, summary: &IntegersSummary, _: &()) {
1361            self.0 += summary.count;
1362        }
1363    }
1364
1365    impl<'a> SeekTarget<'a, IntegersSummary, IntegersSummary> for Count {
1366        fn cmp(&self, cursor_location: &IntegersSummary, _: &()) -> Ordering {
1367            self.0.cmp(&cursor_location.count)
1368        }
1369    }
1370
1371    impl<'a> Dimension<'a, IntegersSummary> for Sum {
1372        fn zero(_cx: &()) -> Self {
1373            Default::default()
1374        }
1375
1376        fn add_summary(&mut self, summary: &IntegersSummary, _: &()) {
1377            self.0 += summary.sum;
1378        }
1379    }
1380}