rbtree-ts/src/b+tree.ts

A sorted list of key-value pairs in a fast, typed in-memory B+ tree with a powerful API.

// B+ tree by David Piepgrass. License: MIT
export {
  ISet,
  ISetF,
  ISetSink,
  ISetSource,
  ISortedMap,
  ISortedMapF,
  ISortedMapSource,
  ISortedSet,
  ISortedSetF,
  ISortedSetSource
} from "../types/interfaces";

export type EditRangeResult<V, R = number> = {
  value?: V;
  break?: R;
  delete?: boolean;
};

type index = number;

// Informative microbenchmarks & stuff:
// http://www.jayconrod.com/posts/52/a-tour-of-v8-object-representation (very educational)
// https://blog.mozilla.org/luke/2012/10/02/optimizing-javascript-variable-access/ (local vars are faster than properties)
// http://benediktmeurer.de/2017/12/13/an-introduction-to-speculative-optimization-in-v8/ (other stuff)
// https://jsperf.com/js-in-operator-vs-alternatives (avoid 'in' operator; `.p!==undefined` faster than `hasOwnProperty('p')` in all browsers)
// https://jsperf.com/instanceof-vs-typeof-vs-constructor-vs-member (speed of type tests varies wildly across browsers)
// https://jsperf.com/detecting-arrays-new (a.constructor===Array is best across browsers, assuming a is an object)
// https://jsperf.com/shallow-cloning-methods (a constructor is faster than Object.create; hand-written clone faster than Object.assign)
// https://jsperf.com/ways-to-fill-an-array (slice-and-replace is fastest)
// https://jsperf.com/math-min-max-vs-ternary-vs-if (Math.min/max is slow on Edge)
// https://jsperf.com/array-vs-property-access-speed (v.x/v.y is faster than a[0]/a[1] in major browsers IF hidden class is constant)
// https://jsperf.com/detect-not-null-or-undefined (`x==null` slightly slower than `x===null||x===undefined` on all browsers)
// Overall, microbenchmarks suggest Firefox is the fastest browser for JavaScript and Edge is the slowest.
// Lessons from https://v8project.blogspot.com/2017/09/elements-kinds-in-v8.html:
//   - Avoid holes in arrays. Avoid `new Array(N)`, it will be "holey" permanently.
//   - Don't read outside bounds of an array (it scans prototype chain).
//   - Small integer arrays are stored differently from doubles
//   - Adding non-numbers to an array deoptimizes it permanently into a general array
//   - Objects can be used like arrays (e.g. have length property) but are slower
//   - V8 source (NewElementsCapacity in src/objects.h): arrays grow by 50% + 16 elements

/** Compares two numbers, strings, arrays of numbers/strings, Dates,
 *  or objects that have a valueOf() method returning a number or string.
 *  Optimized for numbers. Returns 1 if a>b, -1 if a<b, and 0 if a===b.
 */
export function defaultComparator(a: any, b: any) {
  var c = a - b;
  if (c === c) return c; // a & b are number
  // General case (c is NaN): string / arrays / Date / incomparable things
  if (a) a = a.valueOf();
  if (b) b = b.valueOf();
  return a < b ? -1 : a > b ? 1 : a == b ? 0 : c;
}

/**
 * A reasonably fast collection of key-value pairs with a powerful API.
 * Largely compatible with the standard Map. BTree is a B+ tree data structure,
 * so the collection is sorted by key.
 *
 * B+ trees tend to use memory more efficiently than hashtables such as the
 * standard Map, especially when the collection contains a large number of
 * items. However, maintaining the sort order makes them modestly slower:
 * O(log size) rather than O(1). This B+ tree implementation supports O(1)
 * fast cloning. It also supports freeze(), which can be used to ensure that
 * a BTree is not changed accidentally.
 *
 * Confusingly, the ES6 Map.forEach(c) method calls c(value,key) instead of
 * c(key,value), in contrast to other methods such as set() and entries()
 * which put the key first. I can only assume that the order was reversed on
 * the theory that users would usually want to examine values and ignore keys.
 * BTree's forEach() therefore works the same way, but a second method
 * `.forEachPair((key,value)=>{...})` is provided which sends you the key
 * first and the value second; this method is slightly faster because it is
 * the "native" for-each method for this class.
 *
 * Out of the box, BTree supports keys that are numbers, strings, arrays of
 * numbers/strings, Date, and objects that have a valueOf() method returning a
 * number or string. Other data types, such as arrays of Date or custom
 * objects, require a custom comparator, which you must pass as the second
 * argument to the constructor (the first argument is an optional list of
 * initial items). Symbols cannot be used as keys because they are unordered
 * (one Symbol is never "greater" or "less" than another).
 *
 * @example
 * Given a {name: string, age: number} object, you can create a tree sorted by
 * name and then by age like this:
 *
 *     var tree = new BTree(undefined, (a, b) => {
 *       if (a.name > b.name)
 *         return 1; // Return a number >0 when a > b
 *       else if (a.name < b.name)
 *         return -1; // Return a number <0 when a < b
 *       else // names are equal (or incomparable)
 *         return a.age - b.age; // Return >0 when a.age > b.age
 *     });
 *
 *     tree.set({name:"Bill", age:17}, "happy");
 *     tree.set({name:"Fran", age:40}, "busy & stressed");
 *     tree.set({name:"Bill", age:55}, "recently laid off");
 *     tree.forEachPair((k, v) => {
 *       console.log(`Name: ${k.name} Age: ${k.age} Status: ${v}`);
 *     });
 *
 * @description
 * The "range" methods (`forEach, forRange, editRange`) will return the number
 * of elements that were scanned. In addition, the callback can return {break:R}
 * to stop early and return R from the outer function.
 *
 * - TODO: Test performance of preallocating values array at max size
 * - TODO: Add fast initialization when a sorted array is provided to constructor
 *
 * For more documentation see https://github.com/qwertie/btree-typescript
 *
 * Are you a C# developer? You might like the similar data structures I made for C#:
 * BDictionary, BList, etc. See http://core.loyc.net/collections/
 *
 * @author David Piepgrass
 */
export default class BTree<K = any, V = any> {
  private _root: BNode<K, V> = EmptyLeaf as BNode<K, V>;
  _size: number = 0;
  _maxNodeSize: number;
  _compare: (a: K, b: K) => number;

  /**
   * Initializes an empty B+ tree.
   * @param compare Custom function to compare pairs of elements in the tree.
   *   This is not required for numbers, strings and arrays of numbers/strings.
   * @param entries A set of key-value pairs to initialize the tree
   * @param maxNodeSize Branching factor (maximum items or children per node)
   *   Must be in range 4..256. If undefined or <4 then default is used; if >256 then 256.
   */
  public constructor(
    compare?: (a: K, b: K) => number,
    maxNodeSize?: number,
    entries?: [K, V][]
  ) {
    this._maxNodeSize = maxNodeSize! >= 4 ? Math.min(maxNodeSize!, 256) : 32;
    this._compare = compare || defaultComparator;
    if (entries) this.setPairs(entries);
  }

  // ES6 Map<K,V> methods ///////////////////////////////////////////////////

  /** Gets the number of key-value pairs in the tree. */
  get size() {
    return this._size;
  }
  /** Gets the number of key-value pairs in the tree. */
  get length() {
    return this._size;
  }
  /** Returns true iff the tree contains no key-value pairs. */
  get isEmpty() {
    return this._size === 0;
  }

  /** Releases the tree so that its size is 0. */
  clear() {
    this._root = EmptyLeaf as BNode<K, V>;
    this._size = 0;
  }

  forEach(
    callback: (v: V, k: K, tree: BTree<K, V>) => void,
    thisArg?: any
  ): number;

  /** Runs a function for each key-value pair, in order from smallest to
   *  largest key. For compatibility with ES6 Map, the argument order to
   *  the callback is backwards: value first, then key. Call forEachPair
   *  instead to receive the key as the first argument.
   * @param thisArg If provided, this parameter is assigned as the `this`
   *        value for each callback.
   * @returns the number of values that were sent to the callback,
   *        or the R value if the callback returned {break:R}. */
  forEach<R = number>(
    callback: (v: V, k: K, tree: BTree<K, V>) => { break?: R } | void,
    thisArg?: any
  ): R | number {
    if (thisArg !== undefined) callback = callback.bind(thisArg);
    return this.forEachPair((k, v) => callback(v, k, this));
  }

  /** Runs a function for each key-value pair, in order from smallest to
   *  largest key. The callback can return {break:R} (where R is any value
   *  except undefined) to stop immediately and return R from forEachPair.
   * @param onFound A function that is called for each key-value pair. This
   *        function can return {break:R} to stop early with result R.
   *        The reason that you must return {break:R} instead of simply R
   *        itself is for consistency with editRange(), which allows
   *        multiple actions, not just breaking.
   * @param initialCounter This is the value of the third argument of
   *        `onFound` the first time it is called. The counter increases
   *        by one each time `onFound` is called. Default value: 0
   * @returns the number of pairs sent to the callback (plus initialCounter,
   *        if you provided one). If the callback returned {break:R} then
   *        the R value is returned instead. */
  forEachPair<R = number>(
    callback: (k: K, v: V, counter: number) => { break?: R } | void,
    initialCounter?: number
  ): R | number {
    var low = this.minKey(),
      high = this.maxKey();
    return this.forRange(low!, high!, true, callback, initialCounter);
  }

  /**
   * Finds a pair in the tree and returns the associated value.
   * @param defaultValue a value to return if the key was not found.
   * @returns the value, or defaultValue if the key was not found.
   * @description Computational complexity: O(log size)
   */
  get(key: K, defaultValue?: V): V | undefined {
    return this._root.get(key, defaultValue, this);
  }

  /**
   * Adds or overwrites a key-value pair in the B+ tree.
   * @param key the key is used to determine the sort order of
   *        data in the tree.
   * @param value data to associate with the key (optional)
   * @param overwrite Whether to overwrite an existing key-value pair
   *        (default: true). If this is false and there is an existing
   *        key-value pair then this method has no effect.
   * @returns true if a new key-value pair was added.
   * @description Computational complexity: O(log size)
   * Note: when overwriting a previous entry, the key is updated
   * as well as the value. This has no effect unless the new key
   * has data that does not affect its sort order.
   */
  set(key: K, value: V, overwrite?: boolean): boolean {
    if (this._root.isShared) this._root = this._root.clone();
    var result = this._root.set(key, value, overwrite, this);
    if (result === true || result === false) return result;
    // Root node has split, so create a new root node.
    this._root = new BNodeInternal<K, V>([this._root, result]);
    return true;
  }

  /**
   * Returns true if the key exists in the B+ tree, false if not.
   * Use get() for best performance; use has() if you need to
   * distinguish between "undefined value" and "key not present".
   * @param key Key to detect
   * @description Computational complexity: O(log size)
   */
  has(key: K): boolean {
    return this.forRange(key, key, true, undefined) !== 0;
  }

  /**
   * Removes a single key-value pair from the B+ tree.
   * @param key Key to find
   * @returns true if a pair was found and removed, false otherwise.
   * @description Computational complexity: O(log size)
   */
  delete(key: K): boolean {
    return this.editRange(key, key, true, DeleteRange) !== 0;
  }

  // Clone-mutators /////////////////////////////////////////////////////////

  /** Returns a copy of the tree with the specified key set (the value is undefined). */
  with(key: K): BTree<K, V | undefined>;
  /** Returns a copy of the tree with the specified key-value pair set. */
  with<V2>(key: K, value: V2, overwrite?: boolean): BTree<K, V | V2>;
  with<V2>(
    key: K,
    value?: V2,
    overwrite?: boolean
  ): BTree<K, V | V2 | undefined> {
    let nu = this.clone() as BTree<K, V | V2 | undefined>;
    return nu.set(key, value, overwrite) || overwrite ? nu : this;
  }

  /** Returns a copy of the tree with the specified key-value pairs set. */
  withPairs<V2>(pairs: [K, V | V2][], overwrite: boolean): BTree<K, V | V2> {
    let nu = this.clone() as BTree<K, V | V2>;
    return nu.setPairs(pairs, overwrite) !== 0 || overwrite ? nu : this;
  }

  withKeys(
    keys: K[],
    returnThisIfUnchanged?: boolean
  ): BTree<K, V | undefined> {
    let nu = this.clone() as BTree<K, V | undefined>,
      changed = false;
    for (var i = 0; i < keys.length; i++)
      changed = nu.set(keys[i], undefined, false) || changed;
    return returnThisIfUnchanged && !changed ? this : nu;
  }

  /** Returns a copy of the tree with the specified key removed.
   * @param returnThisIfUnchanged if true, returns this if the key didn't exist.
   *  Performance note: due to the architecture of this class, node(s) leading
   *  to where the key would have been stored are cloned even when the key
   *  turns out not to exist and the collection is unchanged.
   */
  without(key: K, returnThisIfUnchanged?: boolean): BTree<K, V> {
    return this.withoutRange(key, key, true, returnThisIfUnchanged);
  }

  /** Returns a copy of the tree with the specified keys removed.
   * @param returnThisIfUnchanged if true, returns this if none of the keys
   *  existed. Performance note: due to the architecture of this class,
   *  node(s) leading to where the key would have been stored are cloned
   *  even when the key turns out not to exist.
   */
  withoutKeys(keys: K[], returnThisIfUnchanged?: boolean): BTree<K, V> {
    let nu = this.clone();
    return nu.deleteKeys(keys) || !returnThisIfUnchanged ? nu : this;
  }

  /** Returns a copy of the tree with the specified range of keys removed. */
  withoutRange(
    low: K,
    high: K,
    includeHigh: boolean,
    returnThisIfUnchanged?: boolean
  ): BTree<K, V> {
    let nu = this.clone();
    if (nu.deleteRange(low, high, includeHigh) === 0 && returnThisIfUnchanged)
      return this;
    return nu;
  }

  /** Returns a copy of the tree with pairs removed whenever the callback
   *  function returns false. `where()` is a synonym for this method. */
  filter(
    callback: (k: K, v: V, counter: number) => boolean,
    returnThisIfUnchanged?: boolean
  ): BTree<K, V> {
    var nu = this.greedyClone();
    var del: any;
    nu.editAll((k, v, i) => {
      if (!callback(k, v, i)) return (del = Delete);
    });
    if (!del && returnThisIfUnchanged) return this;
    return nu;
  }

  /** Returns a copy of the tree with all values altered by a callback function. */
  mapValues<R>(callback: (v: V, k: K, counter: number) => R): BTree<K, R> {
    var tmp = {} as { value: R };
    var nu = this.greedyClone();
    nu.editAll((k, v, i) => {
      return (tmp.value = callback(v, k, i)), tmp as any;
    });
    return (nu as any) as BTree<K, R>;
  }

  /** Performs a reduce operation like the `reduce` method of `Array`.
   *  It is used to combine all pairs into a single value, or perform
   *  conversions. `reduce` is best understood by example. For example,
   *  `tree.reduce((P, pair) => P * pair[0], 1)` multiplies all keys
   *  together. It means "start with P=1, and for each pair multiply
   *  it by the key in pair[0]". Another example would be converting
   *  the tree to a Map (in this example, note that M.set returns M):
   *
   *  var M = tree.reduce((M, pair) => M.set(pair[0],pair[1]), new Map())
   *
   *  **Note**: the same array is sent to the callback on every iteration.
   */
  reduce<R>(
    callback: (
      previous: R,
      currentPair: [K, V],
      counter: number,
      tree: BTree<K, V>
    ) => R,
    initialValue: R
  ): R;
  reduce<R>(
    callback: (
      previous: R | undefined,
      currentPair: [K, V],
      counter: number,
      tree: BTree<K, V>
    ) => R
  ): R | undefined;
  reduce<R>(
    callback: (
      previous: R | undefined,
      currentPair: [K, V],
      counter: number,
      tree: BTree<K, V>
    ) => R,
    initialValue?: R
  ): R | undefined {
    let i = 0,
      p = initialValue;
    var it = this.entries(this.minKey(), ReusedArray),
      next;
    while (!(next = it.next()).done) p = callback(p, next.value, i++, this);
    return p;
  }

  // Iterator methods ///////////////////////////////////////////////////////

  /** Returns an iterator that provides items in order (ascending order if
   *  the collection's comparator uses ascending order, as is the default.)
   *  @param lowestKey First key to be iterated, or undefined to start at
   *         minKey(). If the specified key doesn't exist then iteration
   *         starts at the next higher key (according to the comparator).
   *  @param reusedArray Optional array used repeatedly to store key-value
   *         pairs, to avoid creating a new array on every iteration.
   */
  entries(lowestKey?: K, reusedArray?: (K | V)[]): IterableIterator<[K, V]> {
    var info = this.findPath(lowestKey);
    if (info === undefined) return iterator<[K, V]>();
    var { nodequeue, nodeindex, leaf } = info;
    var state = reusedArray !== undefined ? 1 : 0;
    var i =
      lowestKey === undefined
        ? -1
        : leaf.indexOf(lowestKey, 0, this._compare) - 1;

    return iterator<[K, V]>(() => {
      jump: for (;;) {
        switch (state) {
          case 0:
            if (++i < leaf.keys.length)
              return { done: false, value: [leaf.keys[i], leaf.values[i]] };
            state = 2;
            continue;
          case 1:
            if (++i < leaf.keys.length) {
              (reusedArray![0] = leaf.keys[i]),
                (reusedArray![1] = leaf.values[i]);
              return { done: false, value: reusedArray as [K, V] };
            }
            state = 2;
          case 2:
            // Advance to the next leaf node
            for (var level = -1; ; ) {
              if (++level >= nodequeue.length) {
                state = 3;
                continue jump;
              }
              if (++nodeindex[level] < nodequeue[level].length) break;
            }
            for (; level > 0; level--) {
              nodequeue[level - 1] = (nodequeue[level][
                nodeindex[level]
              ] as BNodeInternal<K, V>).children;
              nodeindex[level - 1] = 0;
            }
            leaf = nodequeue[0][nodeindex[0]];
            i = -1;
            state = reusedArray !== undefined ? 1 : 0;
            continue;
          case 3:
            return { done: true, value: undefined };
        }
      }
    });
  }

  /** Returns an iterator that provides items in reversed order.
   *  @param highestKey Key at which to start iterating, or undefined to
   *         start at minKey(). If the specified key doesn't exist then iteration
   *         starts at the next lower key (according to the comparator).
   *  @param reusedArray Optional array used repeatedly to store key-value
   *         pairs, to avoid creating a new array on every iteration.
   *  @param skipHighest Iff this flag is true and the highestKey exists in the
   *         collection, the pair matching highestKey is skipped, not iterated.
   */
  entriesReversed(
    highestKey?: K,
    reusedArray?: (K | V)[],
    skipHighest?: boolean
  ): IterableIterator<[K, V]> {
    if ((highestKey = highestKey || this.maxKey()) === undefined)
      return iterator<[K, V]>(); // collection is empty
    var { nodequeue, nodeindex, leaf } =
      this.findPath(highestKey) || this.findPath(this.maxKey())!;
    check(!nodequeue[0] || leaf === nodequeue[0][nodeindex[0]], "wat!");
    var i = leaf.indexOf(highestKey, 0, this._compare);
    if (!(skipHighest || this._compare(leaf.keys[i], highestKey) > 0)) i++;
    var state = reusedArray !== undefined ? 1 : 0;

    return iterator<[K, V]>(() => {
      jump: for (;;) {
        switch (state) {
          case 0:
            if (--i >= 0)
              return { done: false, value: [leaf.keys[i], leaf.values[i]] };
            state = 2;
            continue;
          case 1:
            if (--i >= 0) {
              (reusedArray![0] = leaf.keys[i]),
                (reusedArray![1] = leaf.values[i]);
              return { done: false, value: reusedArray as [K, V] };
            }
            state = 2;
          case 2:
            // Advance to the next leaf node
            for (var level = -1; ; ) {
              if (++level >= nodequeue.length) {
                state = 3;
                continue jump;
              }
              if (--nodeindex[level] >= 0) break;
            }
            for (; level > 0; level--) {
              nodequeue[level - 1] = (nodequeue[level][
                nodeindex[level]
              ] as BNodeInternal<K, V>).children;
              nodeindex[level - 1] = nodequeue[level - 1].length - 1;
            }
            leaf = nodequeue[0][nodeindex[0]];
            i = leaf.keys.length;
            state = reusedArray !== undefined ? 1 : 0;
            continue;
          case 3:
            return { done: true, value: undefined };
        }
      }
    });
  }

  /* Used by entries() and entriesReversed() to prepare to start iterating.
   * It develops a "node queue" for each non-leaf level of the tree.
   * Levels are numbered "bottom-up" so that level 0 is a list of leaf
   * nodes from a low-level non-leaf node. The queue at a given level L
   * consists of nodequeue[L] which is the children of a BNodeInternal,
   * and nodeindex[L], the current index within that child list, such
   * such that nodequeue[L-1] === nodequeue[L][nodeindex[L]].children.
   * (However inside this function the order is reversed.)
   */
  private findPath(
    key?: K
  ):
    | { nodequeue: BNode<K, V>[][]; nodeindex: number[]; leaf: BNode<K, V> }
    | undefined {
    var nextnode = this._root;
    var nodequeue: BNode<K, V>[][], nodeindex: number[];

    if (nextnode.isLeaf) {
      (nodequeue = EmptyArray), (nodeindex = EmptyArray); // avoid allocations
    } else {
      (nodequeue = []), (nodeindex = []);
      for (var d = 0; !nextnode.isLeaf; d++) {
        nodequeue[d] = (nextnode as BNodeInternal<K, V>).children;
        nodeindex[d] =
          key === undefined ? 0 : nextnode.indexOf(key, 0, this._compare);
        if (nodeindex[d] >= nodequeue[d].length) return; // first key > maxKey()
        nextnode = nodequeue[d][nodeindex[d]];
      }
      nodequeue.reverse();
      nodeindex.reverse();
    }
    return { nodequeue, nodeindex, leaf: nextnode };
  }

  // Additional methods /////////////////////////////////////////////////////

  /** Returns the maximum number of children/values before nodes will split. */
  get maxNodeSize() {
    return this._maxNodeSize;
  }

  /** Gets the lowest key in the tree. Complexity: O(log size) */
  minKey(): K | undefined {
    return this._root.minKey();
  }

  /** Gets the highest key in the tree. Complexity: O(1) */
  maxKey(): K | undefined {
    return this._root.maxKey();
  }

  /** Quickly clones the tree by marking the root node as shared.
   *  Both copies remain editable. When you modify either copy, any
   *  nodes that are shared (or potentially shared) between the two
   *  copies are cloned so that the changes do not affect other copies.
   *  This is known as copy-on-write behavior, or "lazy copying". */
  clone(): BTree<K, V> {
    this._root.isShared = true;
    var result = new BTree<K, V>(this._compare, this._maxNodeSize, undefined);
    result._root = this._root;
    result._size = this._size;
    return result;
  }

  /** Performs a greedy clone, immediately duplicating any nodes that are
   *  not currently marked as shared, in order to avoid marking any nodes
   *  as shared.
   *  @param force Clone all nodes, even shared ones.
   */
  greedyClone(force?: boolean): BTree<K, V> {
    var result = new BTree<K, V>(this._compare, this._maxNodeSize, undefined);
    result._root = this._root.greedyClone(force);
    result._size = this._size;
    return result;
  }

  /** Gets an array filled with the contents of the tree, sorted by key */
  toArray(maxLength: number = 0x7fffffff): { key: K, data: V}[] {
    let min = this.minKey(),
      max = this.maxKey();
    if (min !== undefined) return this.getRange(min, max!, true, maxLength).map(array  => ({ key: array[0], data: array[1] }));
    return [];
  }

  /** Gets an array of all keys, sorted */
  keysArray() {
    var results: K[] = [];
    this._root.forRange(
      this.minKey()!,
      this.maxKey()!,
      true,
      false,
      this,
      0,
      (k, v) => {
        results.push(k);
      }
    );
    return results;
  }

  /** Gets an array of all values, sorted by key */
  valuesArray() {
    var results: V[] = [];
    this._root.forRange(
      this.minKey()!,
      this.maxKey()!,
      true,
      false,
      this,
      0,
      (k, v) => {
        results.push(v);
      }
    );
    return results;
  }

  /** Gets a string representing the tree's data based on toArray(). */
  toString() {
    return this.toArray().toString();
  }

  /** Stores a key-value pair only if the key doesn't already exist in the tree.
   * @returns true if a new key was added
   */
  setIfNotPresent(key: K, value: V): boolean {
    return this.set(key, value, false);
  }

  /** Returns the next pair whose key is larger than the specified key (or undefined if there is none) */
  nextHigherPair(key: K): [K, V] | undefined {
    var it = this.entries(key, ReusedArray);
    var r = it.next();
    if (!r.done && this._compare(r.value[0], key) <= 0) r = it.next();
    return r.value;
  }

  /** Returns the next key larger than the specified key (or undefined if there is none) */
  nextHigherKey(key: K): K | undefined {
    var p = this.nextHigherPair(key);
    return p ? p[0] : p;
  }

  /** Returns the next pair whose key is smaller than the specified key (or undefined if there is none) */
  nextLowerPair(key: K): [K, V] | undefined {
    var it = this.entriesReversed(key, ReusedArray, true);
    return it.next().value;
  }

  /** Returns the next key smaller than the specified key (or undefined if there is none) */
  nextLowerKey(key: K): K | undefined {
    var p = this.nextLowerPair(key);
    return p ? p[0] : p;
  }

  /** Edits the value associated with a key in the tree, if it already exists.
   * @returns true if the key existed, false if not.
   */
  changeIfPresent(key: K, value: V): boolean {
    return this.editRange(key, key, true, (k, v) => ({ value })) !== 0;
  }

  /**
   * Builds an array of pairs from the specified range of keys, sorted by key.
   * Each returned pair is also an array: pair[0] is the key, pair[1] is the value.
   * @param low The first key in the array will be greater than or equal to `low`.
   * @param high This method returns when a key larger than this is reached.
   * @param includeHigh If the `high` key is present, its pair will be included
   *        in the output if and only if this parameter is true. Note: if the
   *        `low` key is present, it is always included in the output.
   * @param maxLength Length limit. getRange will stop scanning the tree when
   *                  the array reaches this size.
   * @description Computational complexity: O(result.length + log size)
   */
  getRange(
    low: K,
    high: K,
    includeHigh?: boolean,
    maxLength: number = 0x3ffffff
  ): [K, V][] {
    var results: [K, V][] = [];
    this._root.forRange(low, high, includeHigh, false, this, 0, (k, v) => {
      results.push([k, v]);
      return results.length > maxLength ? Break : undefined;
    });
    return results;
  }

  /** Adds all pairs from a list of key-value pairs.
   * @param pairs Pairs to add to this tree. If there are duplicate keys,
   *        later pairs currently overwrite earlier ones (e.g. [[0,1],[0,7]]
   *        associates 0 with 7.)
   * @param overwrite Whether to overwrite pairs that already exist (if false,
   *        pairs[i] is ignored when the key pairs[i][0] already exists.)
   * @returns The number of pairs added to the collection.
   * @description Computational complexity: O(pairs.length * log(size + pairs.length))
   */
  setPairs(pairs: [K, V][], overwrite?: boolean): number {
    var added = 0;
    for (var i = 0; i < pairs.length; i++)
      if (this.set(pairs[i][0], pairs[i][1], overwrite)) added++;
    return added;
  }

  forRange(
    low: K,
    high: K,
    includeHigh: boolean,
    onFound?: (k: K, v: V, counter: number) => void,
    initialCounter?: number
  ): number;

  /**
   * Scans the specified range of keys, in ascending order by key.
   * Note: the callback `onFound` must not insert or remove items in the
   * collection. Doing so may cause incorrect data to be sent to the
   * callback afterward.
   * @param low The first key scanned will be greater than or equal to `low`.
   * @param high Scanning stops when a key larger than this is reached.
   * @param includeHigh If the `high` key is present, `onFound` is called for
   *        that final pair if and only if this parameter is true.
   * @param onFound A function that is called for each key-value pair. This
   *        function can return {break:R} to stop early with result R.
   * @param initialCounter Initial third argument of onFound. This value
   *        increases by one each time `onFound` is called. Default: 0
   * @returns The number of values found, or R if the callback returned
   *        `{break:R}` to stop early.
   * @description Computational complexity: O(number of items scanned + log size)
   */
  forRange<R = number>(
    low: K,
    high: K,
    includeHigh: boolean,
    onFound?: (k: K, v: V, counter: number) => { break?: R } | void,
    initialCounter?: number
  ): R | number {
    var r = this._root.forRange(
      low,
      high,
      includeHigh,
      false,
      this,
      initialCounter || 0,
      onFound
    );
    return typeof r === "number" ? r : r.break!;
  }

  /**
   * Scans and potentially modifies values for a subsequence of keys.
   * Note: the callback `onFound` should ideally be a pure function.
   *   Specfically, it must not insert items, call clone(), or change
   *   the collection except via return value; out-of-band editing may
   *   cause an exception or may cause incorrect data to be sent to
   *   the callback (duplicate or missed items). It must not cause a
   *   clone() of the collection, otherwise the clone could be modified
   *   by changes requested by the callback.
   * @param low The first key scanned will be greater than or equal to `low`.
   * @param high Scanning stops when a key larger than this is reached.
   * @param includeHigh If the `high` key is present, `onFound` is called for
   *        that final pair if and only if this parameter is true.
   * @param onFound A function that is called for each key-value pair. This
   *        function can return `{value:v}` to change the value associated
   *        with the current key, `{delete:true}` to delete the current pair,
   *        `{break:R}` to stop early with result R, or it can return nothing
   *        (undefined or {}) to cause no effect and continue iterating.
   *        `{break:R}` can be combined with one of the other two commands.
   *        The third argument `counter` is the number of items iterated
   *        previously; it equals 0 when `onFound` is called the first time.
   * @returns The number of values scanned, or R if the callback returned
   *        `{break:R}` to stop early.
   * @description
   *   Computational complexity: O(number of items scanned + log size)
   *   Note: if the tree has been cloned with clone(), any shared
   *   nodes are copied before `onFound` is called. This takes O(n) time
   *   where n is proportional to the amount of shared data scanned.
   */
  editRange<R = V>(
    low: K,
    high: K,
    includeHigh: boolean,
    onFound: (k: K, v: V, counter: number) => EditRangeResult<V, R> | void,
    initialCounter?: number
  ): R | number {
    var root = this._root;
    if (root.isShared) this._root = root = root.clone();
    try {
      var r = root.forRange(
        low,
        high,
        includeHigh,
        true,
        this,
        initialCounter || 0,
        onFound
      );
      return typeof r === "number" ? r : r.break!;
    } finally {
      while (root.keys.length <= 1 && !root.isLeaf)
        this._root = root =
          root.keys.length === 0
            ? EmptyLeaf
            : ((root as any) as BNodeInternal<K, V>).children[0];
    }
  }

  /** Same as `editRange` except that the callback is called for all pairs. */
  editAll<R = V>(
    onFound: (k: K, v: V, counter: number) => EditRangeResult<V, R> | void,
    initialCounter?: number
  ): R | number {
    return this.editRange(
      this.minKey()!,
      this.maxKey()!,
      true,
      onFound,
      initialCounter
    );
  }

  /**
   * Removes a range of key-value pairs from the B+ tree.
   * @param low The first key scanned will be greater than or equal to `low`.
   * @param high Scanning stops when a key larger than this is reached.
   * @param includeHigh Specifies whether the `high` key, if present, is deleted.
   * @returns The number of key-value pairs that were deleted.
   * @description Computational complexity: O(log size + number of items deleted)
   */
  deleteRange(low: K, high: K, includeHigh: boolean): number {
    return this.editRange(low, high, includeHigh, DeleteRange);
  }

  /** Deletes a series of keys from the collection. */
  deleteKeys(keys: K[]): number {
    for (var i = 0, r = 0; i < keys.length; i++) if (this.delete(keys[i])) r++;
    return r;
  }

  /** Gets the height of the tree: the number of internal nodes between the
   *  BTree object and its leaf nodes (zero if there are no internal nodes). */
  get height(): number {
    for (var node = this._root, h = -1; node != null; h++)
      node = (node as any).children;
    return h;
  }

  /** Makes the object read-only to ensure it is not accidentally modified.
   *  Freezing does not have to be permanent; unfreeze() reverses the effect.
   *  This is accomplished by replacing mutator functions with a function
   *  that throws an Error. Compared to using a property (e.g. this.isFrozen)
   *  this implementation gives better performance in non-frozen BTrees.
   */

  /** Scans the tree for signs of serious bugs (e.g. this.size doesn't match
   *  number of elements, internal nodes not caching max element properly...)
   *  Computational complexity: O(number of nodes), i.e. O(size). This method
   *  skips the most expensive test - whether all keys are sorted - but it
   *  does check that maxKey() of the children of internal nodes are sorted. */
  checkValid() {
    var size = this._root.checkValid(0, this);
    check(
      size === this.size,
      "size mismatch: counted ",
      size,
      "but stored",
      this.size
    );
  }
}

declare const Symbol: any;
if (Symbol && Symbol.iterator)
  // iterator is equivalent to entries()
  (BTree as any).prototype[Symbol.iterator] = BTree.prototype.entries;
(BTree as any).prototype.where = BTree.prototype.filter;
(BTree as any).prototype.setRange = BTree.prototype.setPairs;
(BTree as any).prototype.add = BTree.prototype.set;

function iterator<T>(
  next: () => { done: boolean; value?: T } = () => ({
    done: true,
    value: undefined,
  })
): IterableIterator<T> {
  var result: any = { next };
  if (Symbol && Symbol.iterator)
    result[Symbol.iterator] = function () {
      return this;
    };
  return result;
}

/** Leaf node / base class. **************************************************/
class BNode<K, V> {
  // If this is an internal node, _keys[i] is the highest key in children[i].
  keys: K[];
  values: V[];
  isShared: true | undefined;
  get isLeaf() {
    return (this as any).children === undefined;
  }

  constructor(keys: K[] = [], values?: V[]) {
    this.keys = keys;
    this.values = values || (undefVals as any[]);
    this.isShared = undefined;
  }

  // Shared methods /////////////////////////////////////////////////////////

  maxKey() {
    return this.keys[this.keys.length - 1];
  }

  // If key not found, returns i^failXor where i is the insertion index.
  // Callers that don't care whether there was a match will set failXor=0.
  indexOf(key: K, failXor: number, cmp: (a: K, b: K) => number): index {
    // TODO: benchmark multiple search strategies
    const keys = this.keys;
    var lo = 0,
      hi = keys.length,
      mid = hi >> 1;
    while (lo < hi) {
      var c = cmp(keys[mid], key);
      if (c < 0) lo = mid + 1;
      else if (c > 0)
        // key < keys[mid]
        hi = mid;
      else if (c === 0) return mid;
      else {
        // c is NaN or otherwise invalid
        if (key === key)
          // at least the search key is not NaN
          return keys.length;
        else throw new Error("BTree: NaN was used as a key");
      }
      mid = (lo + hi) >> 1;
    }
    return mid ^ failXor;

    // Unrolled version: benchmarks show same speed, not worth using
    /*var i = 1, c: number = 0, sum = 0;
    if (keys.length >= 4) {
      i = 3;
      if (keys.length >= 8) {
        i = 7;
        if (keys.length >= 16) {
          i = 15;
          if (keys.length >= 32) {
            i = 31;
            if (keys.length >= 64) {
              i = 127;
              i += (c = i < keys.length ? cmp(keys[i], key) : 1) < 0 ? 64 : -64;
              sum += c;
              i += (c = i < keys.length ? cmp(keys[i], key) : 1) < 0 ? 32 : -32;
              sum += c;
            }
            i += (c = i < keys.length ? cmp(keys[i], key) : 1) < 0 ? 16 : -16;
            sum += c;
          }
          i += (c = i < keys.length ? cmp(keys[i], key) : 1) < 0 ? 8 : -8;
          sum += c;
        }
        i += (c = i < keys.length ? cmp(keys[i], key) : 1) < 0 ? 4 : -4;
        sum += c;
      }
      i += (c = i < keys.length ? cmp(keys[i], key) : 1) < 0 ? 2 : -2;
      sum += c;
    }
    i += (c = i < keys.length ? cmp(keys[i], key) : 1) < 0 ? 1 : -1;
    c = i < keys.length ? cmp(keys[i], key) : 1;
    sum += c;
    if (c < 0) {
      ++i;
      c = i < keys.length ? cmp(keys[i], key) : 1;
      sum += c;
    }
    if (sum !== sum) {
      if (key === key) // at least the search key is not NaN
        return keys.length ^ failXor;
      else
        throw new Error("BTree: NaN was used as a key");
    }
    return c === 0 ? i : i ^ failXor;*/
  }

  // Leaf Node: misc //////////////////////////////////////////////////////////

  minKey() {
    return this.keys[0];
  }

  clone(): BNode<K, V> {
    var v = this.values;
    return new BNode<K, V>(
      this.keys.slice(0),
      v === undefVals ? v : v.slice(0)
    );
  }

  greedyClone(force?: boolean): BNode<K, V> {
    return this.isShared && !force ? this : this.clone();
  }

  get(key: K, defaultValue: V | undefined, tree: BTree<K, V>): V | undefined {
    var i = this.indexOf(key, -1, tree._compare);
    return i < 0 ? defaultValue : this.values[i];
  }

  checkValid(depth: number, tree: BTree<K, V>): number {
    var kL = this.keys.length,
      vL = this.values.length;
    check(
      this.values === undefVals ? kL <= vL : kL === vL,
      "keys/values length mismatch: depth",
      depth,
      "with lengths",
      kL,
      vL
    );
    // Note: we don't check for "node too small" because sometimes a node
    // can legitimately have size 1. This occurs if there is a batch
    // deletion, leaving a node of size 1, and the siblings are full so
    // it can't be merged with adjacent nodes. However, the parent will
    // verify that the average node size is at least half of the maximum.
    check(depth == 0 || kL > 0, "empty leaf at depth", depth);
    return kL;
  }

  // Leaf Node: set & node splitting //////////////////////////////////////////

  set(
    key: K,
    value: V,
    overwrite: boolean | undefined,
    tree: BTree<K, V>
  ): boolean | BNode<K, V> {
    var i = this.indexOf(key, -1, tree._compare);
    if (i < 0) {
      // key does not exist yet
      i = ~i;
      tree._size++;

      if (this.keys.length < tree._maxNodeSize) {
        return this.insertInLeaf(i, key, value, tree);
      } else {
        // This leaf node is full and must split
        var newRightSibling = this.splitOffRightSide(),
          target: BNode<K, V> = this;
        if (i > this.keys.length) {
          i -= this.keys.length;
          target = newRightSibling;
        }
        target.insertInLeaf(i, key, value, tree);
        return newRightSibling;
      }
    } else {
      // Key already exists
      if (overwrite !== false) {
        if (value !== undefined) this.reifyValues();
        // usually this is a no-op, but some users may wish to edit the key
        this.keys[i] = key;
        this.values[i] = value;
      }
      return false;
    }
  }

  reifyValues() {
    if (this.values === undefVals)
      return (this.values = this.values.slice(0, this.keys.length));
    return this.values;
  }

  insertInLeaf(i: index, key: K, value: V, tree: BTree<K, V>) {
    this.keys.splice(i, 0, key);
    if (this.values === undefVals) {
      while (undefVals.length < tree._maxNodeSize) undefVals.push(undefined);
      if (value === undefined) {
        return true;
      } else {
        this.values = undefVals.slice(0, this.keys.length - 1);
      }
    }
    this.values.splice(i, 0, value);
    return true;
  }

  takeFromRight(rhs: BNode<K, V>) {
    // Reminder: parent node must update its copy of key for this node
    // assert: neither node is shared
    // assert rhs.keys.length > (maxNodeSize/2 && this.keys.length<maxNodeSize)
    var v = this.values;
    if (rhs.values === undefVals) {
      if (v !== undefVals) v.push(undefined as any);
    } else {
      v = this.reifyValues();
      v.push(rhs.values.shift()!);
    }
    this.keys.push(rhs.keys.shift()!);
  }

  takeFromLeft(lhs: BNode<K, V>) {
    // Reminder: parent node must update its copy of key for this node
    // assert: neither node is shared
    // assert rhs.keys.length > (maxNodeSize/2 && this.keys.length<maxNodeSize)
    var v = this.values;
    if (lhs.values === undefVals) {
      if (v !== undefVals) v.unshift(undefined as any);
    } else {
      v = this.reifyValues();
      v.unshift(lhs.values.pop()!);
    }
    this.keys.unshift(lhs.keys.pop()!);
  }

  splitOffRightSide(): BNode<K, V> {
    // Reminder: parent node must update its copy of key for this node
    var half = this.keys.length >> 1,
      keys = this.keys.splice(half);
    var values =
      this.values === undefVals ? undefVals : this.values.splice(half);
    return new BNode<K, V>(keys, values);
  }

  // Leaf Node: scanning & deletions //////////////////////////////////////////

  forRange<R>(
    low: K,
    high: K,
    includeHigh: boolean | undefined,
    editMode: boolean,
    tree: BTree<K, V>,
    count: number,
    onFound?: (k: K, v: V, counter: number) => EditRangeResult<V, R> | void
  ): EditRangeResult<V, R> | number {
    var cmp = tree._compare;
    var iLow, iHigh;
    if (high === low) {
      if (!includeHigh) return count;
      iHigh = (iLow = this.indexOf(low, -1, cmp)) + 1;
      if (iLow < 0) return count;
    } else {
      iLow = this.indexOf(low, 0, cmp);
      iHigh = this.indexOf(high, -1, cmp);
      if (iHigh < 0) iHigh = ~iHigh;
      else if (includeHigh === true) iHigh++;
    }
    var keys = this.keys,
      values = this.values;
    if (onFound !== undefined) {
      for (var i = iLow; i < iHigh; i++) {
        var key = keys[i];
        var result = onFound(key, values[i], count++);
        if (result !== undefined) {
          if (editMode === true) {
            if (key !== keys[i] || this.isShared === true)
              throw new Error("BTree illegally changed or cloned in editRange");
            if (result.delete) {
              this.keys.splice(i, 1);
              if (this.values !== undefVals) this.values.splice(i, 1);
              tree._size--;
              i--;
              iHigh--;
            } else if (result.hasOwnProperty("value")) {
              values![i] = result.value!;
            }
          }
          if (result.break !== undefined) return result;
        }
      }
    } else count += iHigh - iLow;
    return count;
  }

  /** Adds entire contents of right-hand sibling (rhs is left unchanged) */
  mergeSibling(rhs: BNode<K, V>, _: number) {
    this.keys.push.apply(this.keys, rhs.keys);
    if (this.values === undefVals) {
      if (rhs.values === undefVals) return;
      this.values = this.values.slice(0, this.keys.length);
    }
    this.values.push.apply(this.values, rhs.reifyValues());
  }
}

/** Internal node (non-leaf node) ********************************************/
class BNodeInternal<K, V> extends BNode<K, V> {
  // Note: conventionally B+ trees have one fewer key than the number of
  // children, but I find it easier to keep the array lengths equal: each
  // keys[i] caches the value of children[i].maxKey().
  children: BNode<K, V>[];

  constructor(children: BNode<K, V>[], keys?: K[]) {
    if (!keys) {
      keys = [];
      for (var i = 0; i < children.length; i++) keys[i] = children[i].maxKey();
    }
    super(keys);
    this.children = children;
  }

  clone(): BNode<K, V> {
    var children = this.children.slice(0);
    for (var i = 0; i < children.length; i++) children[i].isShared = true;
    return new BNodeInternal<K, V>(children, this.keys.slice(0));
  }

  greedyClone(force?: boolean): BNode<K, V> {
    if (this.isShared && !force) return this;
    var nu = new BNodeInternal<K, V>(
      this.children.slice(0),
      this.keys.slice(0)
    );
    for (var i = 0; i < nu.children.length; i++)
      nu.children[i] = nu.children[i].greedyClone();
    return nu;
  }

  minKey() {
    return this.children[0].minKey();
  }

  get(key: K, defaultValue: V | undefined, tree: BTree<K, V>): V | undefined {
    var i = this.indexOf(key, 0, tree._compare),
      children = this.children;
    return i < children.length
      ? children[i].get(key, defaultValue, tree)
      : undefined;
  }

  checkValid(depth: number, tree: BTree<K, V>): number {
    var kL = this.keys.length,
      cL = this.children.length;
    check(
      kL === cL,
      "keys/children length mismatch: depth",
      depth,
      "lengths",
      kL,
      cL
    );
    check(kL > 1, "internal node has length", kL, "at depth", depth);
    var size = 0,
      c = this.children,
      k = this.keys,
      childSize = 0;
    for (var i = 0; i < cL; i++) {
      size += c[i].checkValid(depth + 1, tree);
      childSize += c[i].keys.length;
      check(size >= childSize, "wtf"); // no way this will ever fail
      check(
        i === 0 || c[i - 1].constructor === c[i].constructor,
        "type mismatch"
      );
      if (c[i].maxKey() != k[i])
        check(
          false,
          "keys[",
          i,
          "] =",
          k[i],
          "is wrong, should be ",
          c[i].maxKey(),
          "at depth",
          depth
        );
      if (!(i === 0 || tree._compare(k[i - 1], k[i]) < 0))
        check(
          false,
          "sort violation at depth",
          depth,
          "index",
          i,
          "keys",
          k[i - 1],
          k[i]
        );
    }
    var toofew = childSize < (tree.maxNodeSize >> 1) * cL;
    if (toofew || childSize > tree.maxNodeSize * cL)
      check(
        false,
        toofew ? "too few" : "too many",
        "children (",
        childSize,
        size,
        ") at depth",
        depth,
        ", maxNodeSize:",
        tree.maxNodeSize,
        "children.length:",
        cL
      );
    return size;
  }

  // Internal Node: set & node splitting //////////////////////////////////////

  set(
    key: K,
    value: V,
    overwrite: boolean | undefined,
    tree: BTree<K, V>
  ): boolean | BNodeInternal<K, V> {
    var c = this.children,
      max = tree._maxNodeSize,
      cmp = tree._compare;
    var i = Math.min(this.indexOf(key, 0, cmp), c.length - 1),
      child = c[i];

    if (child.isShared) c[i] = child = child.clone();
    if (child.keys.length >= max) {
      // child is full; inserting anything else will cause a split.
      // Shifting an item to the left or right sibling may avoid a split.
      // We can do a shift if the adjacent node is not full and if the
      // current key can still be placed in the same node after the shift.
      var other: BNode<K, V>;
      if (
        i > 0 &&
        (other = c[i - 1]).keys.length < max &&
        cmp(child.keys[0], key) < 0
      ) {
        if (other.isShared) c[i - 1] = other = other.clone();
        other.takeFromRight(child);
        this.keys[i - 1] = other.maxKey();
      } else if (
        (other = c[i + 1]) !== undefined &&
        other.keys.length < max &&
        cmp(child.maxKey(), key) < 0
      ) {
        if (other.isShared) c[i + 1] = other = other.clone();
        other.takeFromLeft(child);
        this.keys[i] = c[i].maxKey();
      }
    }

    var result = child.set(key, value, overwrite, tree);
    if (result === false) return false;
    this.keys[i] = child.maxKey();
    if (result === true) return true;

    // The child has split and `result` is a new right child... does it fit?
    if (this.keys.length < max) {
      // yes
      this.insert(i + 1, result);
      return true;
    } else {
      // no, we must split also
      var newRightSibling = this.splitOffRightSide(),
        target: BNodeInternal<K, V> = this;
      if (cmp(result.maxKey(), this.maxKey()) > 0) {
        target = newRightSibling;
        i -= this.keys.length;
      }
      target.insert(i + 1, result);
      return newRightSibling;
    }
  }

  insert(i: index, child: BNode<K, V>) {