Class RedBlackTree<K, V, R>

Represents a Red-Black Tree (self-balancing BST) supporting map-like mode and stable O(log n) updates.

Remarks

Time O(1), Space O(1)

Example

// basic Red-Black Tree with simple number keys
 // Create a simple Red-Black Tree with numeric keys
    const tree = new RedBlackTree([5, 2, 8, 1, 9]);

    tree.print();
    //   _2___
    //  /     \
    //  1    _8_
    //      /   \
    //      5   9

    // Verify the tree maintains sorted order
    console.log([...tree.keys()]); // [1, 2, 5, 8, 9];

    // Check size
    console.log(tree.size); // 5;

Example

// Red-Black Tree with key-value pairs for lookups
 interface Employee {
      id: number;
      name: string;
    }

    // Create tree with employee data
    const employees = new RedBlackTree<number, Employee>([
      [1, { id: 1, name: 'Alice' }],
      [3, { id: 3, name: 'Charlie' }],
      [2, { id: 2, name: 'Bob' }]
    ]);

    // Retrieve employee by ID
    const alice = employees.get(1);
    console.log(alice?.name); // 'Alice';

    // Verify sorted order by ID
    console.log([...employees.keys()]); // [1, 2, 3];

Example

// Red-Black Tree range search for filtering
 interface Product {
      name: string;
      price: number;
    }

    const products = new RedBlackTree<number, Product>([
      [10, { name: 'Item A', price: 10 }],
      [25, { name: 'Item B', price: 25 }],
      [40, { name: 'Item C', price: 40 }],
      [50, { name: 'Item D', price: 50 }]
    ]);

    // Find products in price range [20, 45]
    const pricesInRange = products.rangeSearch([20, 45], node => {
      return products.get(node)?.name;
    });

    console.log(pricesInRange); // ['Item B', 'Item C'];

Example

// Red-Black Tree as database index for stock market data
 interface StockPrice {
      symbol: string;
      volume: number;
      timestamp: Date;
    }

    // Simulate real-time stock price index
    const priceIndex = new RedBlackTree<number, StockPrice>([
      [142.5, { symbol: 'AAPL', volume: 1000000, timestamp: new Date() }],
      [335.2, { symbol: 'MSFT', volume: 800000, timestamp: new Date() }],
      [3285.04, { symbol: 'AMZN', volume: 500000, timestamp: new Date() }],
      [267.98, { symbol: 'META', volume: 750000, timestamp: new Date() }],
      [234.57, { symbol: 'GOOGL', volume: 900000, timestamp: new Date() }]
    ]);

    // Find highest-priced stock
    const maxPrice = priceIndex.getRightMost();
    console.log(priceIndex.get(maxPrice)?.symbol); // 'AMZN';

    // Find stocks in price range [200, 400] for portfolio balancing
    const stocksInRange = priceIndex.rangeSearch([200, 400], node => {
      const stock = priceIndex.get(node);
      return {
        symbol: stock?.symbol,
        price: node,
        volume: stock?.volume
      };
    });

    console.log(stocksInRange.length); // 3;
    console.log(stocksInRange.some((s: any) => s.symbol === 'GOOGL')); // true;
    console.log(stocksInRange.some((s: any) => s.symbol === 'META')); // true;
    console.log(stocksInRange.some((s: any) => s.symbol === 'MSFT')); // true;

Type Parameters

K = any
V = any
R = any
1. Efficient self-balancing, but not completely balanced. Compared with AVLTree, the addition and deletion efficiency is high, but the query efficiency is slightly lower.
2. It is BST itself. Compared with Heap which is not completely ordered, RedBlackTree is completely ordered.

Hierarchy (view full)

BST<K, V, R>
- RedBlackTree
  - TreeMultiMap
  - TreeCounter

Implements

IBinaryTree<K, V, R>

Index

Properties

`Protected`_comparator

_comparator: Comparator<K>

The comparator function used to determine the order of keys in the tree.

Remarks

Time O(1) Space O(1)

Accessors

comparator

get comparator(): Comparator<K>
Gets the comparator function used by the tree.

Returns Comparator<K>
The comparator function.

Remarks
Time O(1)
Inherited from BST.comparator
- Defined in data-structures/binary-tree/bst.ts:401

isDuplicate

get isDuplicate(): boolean
Gets whether the tree allows duplicate keys.

Returns boolean
True if duplicates are allowed, false otherwise.

Remarks
Time O(1)
Implementation of IBinaryTree.isDuplicate
Inherited from BST.isDuplicate
- Defined in data-structures/binary-tree/binary-tree.ts:400

isMapMode

get isMapMode(): boolean
Gets whether the tree is in Map mode.

Returns boolean
True if in Map mode, false otherwise.

Remarks
In Map mode (default), values are stored in an external Map, and nodes only hold keys. If false, values are stored directly on the nodes. Time O(1)
Implementation of IBinaryTree.isMapMode
Inherited from BST.isMapMode
- Defined in data-structures/binary-tree/binary-tree.ts:388

NIL

get NIL(): BinaryTreeNode<K, V>
Gets the sentinel NIL node (used in self-balancing trees like Red-Black Tree).

Returns BinaryTreeNode<K, V>
The NIL node.

Remarks
Time O(1)
Implementation of IBinaryTree.NIL
Inherited from BST.NIL
- Defined in data-structures/binary-tree/binary-tree.ts:448

root

get root(): undefined | RedBlackTreeNode<K, V>
Get the current root node.

Returns undefined | RedBlackTreeNode<K, V>
Root node, or undefined.

Remarks
Time O(1), Space O(1)
Implementation of IBinaryTree.root
Overrides BST.root
- Defined in data-structures/binary-tree/red-black-tree.ts:306

size

get size(): number
Gets the number of nodes in the tree.

Returns number
The size of the tree.

Remarks
Time O(1)
Implementation of IBinaryTree.size
Inherited from BST.size
- Defined in data-structures/binary-tree/binary-tree.ts:436

store

get store(): Map<K, undefined | V>
Gets the external value store (used in Map mode).

Returns Map<K, undefined | V>
The map storing key-value pairs.

Remarks
Time O(1)
Implementation of IBinaryTree.store
Inherited from BST.store
- Defined in data-structures/binary-tree/binary-tree.ts:412

toEntryFn

get toEntryFn(): undefined | ToEntryFn<K, V, R>
Gets the function used to convert raw data objects (R) into [key, value] entries.

Returns undefined | ToEntryFn<K, V, R>
The conversion function.

Remarks
Time O(1)
Implementation of IBinaryTree.toEntryFn
Inherited from BST.toEntryFn
- Defined in data-structures/binary-tree/binary-tree.ts:460

Methods

`Protected`_bound

_bound(keyNodeEntryOrPredicate, isLower, iterationType): undefined | BSTNode<K, V>
(Protected) Core bound search implementation supporting all parameter types. Unified logic for both lowerBound and upperBound. Resolves various input types (Key, Node, Entry, Predicate) using parent class utilities.
Parameters
- keyNodeEntryOrPredicate:
      | undefined
      | null
      | K
      | BSTNode<K, V>
      | [undefined | null | K, undefined | V]
      | NodePredicate<BSTNode<K, V>>
  The key, node, entry, or predicate function to search for.
- isLower: boolean
  True for lowerBound (>=), false for upperBound (>).
- iterationType: IterationType
  The iteration type (RECURSIVE or ITERATIVE).
Returns undefined | BSTNode<K, V>
The first matching node, or undefined if no such node exists.
Inherited from BST._bound
- Defined in data-structures/binary-tree/bst.ts:1709

`Protected`_boundByKey

_boundByKey(key, isLower, iterationType): undefined | BSTNode<K, V>
(Protected) Binary search for bound by key with pruning optimization. Performs standard BST binary search, choosing left or right subtree based on comparator result. For lowerBound: finds first node where key >= target. For upperBound: finds first node where key > target.
Parameters
- key: K
  The target key to search for.
- isLower: boolean
  True for lowerBound (>=), false for upperBound (>).
- iterationType: IterationType
  The iteration type (RECURSIVE or ITERATIVE).
Returns undefined | BSTNode<K, V>
The first node matching the bound condition, or undefined if none exists.
Inherited from BST._boundByKey
- Defined in data-structures/binary-tree/bst.ts:1765

`Protected`_boundByPredicate

_boundByPredicate(predicate, iterationType): undefined | BSTNode<K, V>
(Protected) In-order traversal search by predicate. Falls back to linear in-order traversal when predicate-based search is required. Returns the first node that satisfies the predicate function. Note: Predicate-based search cannot leverage BST's binary search optimization. Time Complexity: O(n) since it may visit every node.
Parameters
- predicate: NodePredicate<BSTNode<K, V>>
  The predicate function to test nodes.
- iterationType: IterationType
  The iteration type (RECURSIVE or ITERATIVE).
Returns undefined | BSTNode<K, V>
The first node satisfying predicate, or undefined if none found.
Inherited from BST._boundByPredicate
- Defined in data-structures/binary-tree/bst.ts:1820

`Protected`_clearNodes

_clearNodes(): void
(Protected) Clears all nodes from the tree.

Returns void
Remarks
Time O(1)
Inherited from BST._clearNodes
- Defined in data-structures/binary-tree/binary-tree.ts:2482

`Protected`_clearValues

_clearValues(): void
(Protected) Clears all values from the external store.

Returns void
Remarks
Time O(N)
Inherited from BST._clearValues
- Defined in data-structures/binary-tree/binary-tree.ts:2491

`Protected`_clone

_clone(cloned): void
(Protected) Helper for cloning. Performs a BFS and adds all nodes to the new tree.
Parameters
- cloned: BinaryTree<K, V, R>
  The new, empty tree instance to populate.
Returns void
Remarks
Time O(N * M) (O(N) BFS + O(M) add for each node).
Inherited from BST._clone
- Defined in data-structures/binary-tree/binary-tree.ts:2212

`Protected`_compare

_compare(a, b): number
(Protected) Compares two keys using the tree's comparator and reverse setting.
Parameters
- a: K
  The first key.
- b: K
  The second key.
Returns number
A number (1, -1, or 0) representing the comparison.

Remarks
Time O(1) Space O(1)
Inherited from BST._compare
- Defined in data-structures/binary-tree/bst.ts:1960

`Protected`_createDefaultComparator

_createDefaultComparator(): Comparator<K>
(Protected) Creates the default comparator function for keys that don't have a custom comparator.

Returns Comparator<K>
The default comparator function.

Remarks
Time O(1) Space O(1)
Inherited from BST._createDefaultComparator
- Defined in data-structures/binary-tree/bst.ts:1442

`Protected`_createInstance

_createInstance<TK, TV, TR>(options?): this
(Protected) Creates a new, empty instance of the same BST constructor.
Type Parameters
- TK = K
- TV = V
- TR = R
Parameters
- Optionaloptions: Partial<RedBlackTreeOptions<TK, TV, TR>>
  Options for the new BST.
Returns this
A new, empty BST.

Remarks
Time O(1)
Overrides BST._createInstance
- Defined in data-structures/binary-tree/red-black-tree.ts:477

`Protected`_createLike

_createLike<TK, TV, TR>(iter?, options?): RedBlackTree<TK, TV, TR>
(Protected) Creates a new instance of the same BST constructor, potentially with different generic types.
Type Parameters
- TK = K
- TV = V
- TR = R
Parameters
- iter: Iterable<
      | undefined
      | null
      | TK
      | TR
      | RedBlackTreeNode<TK, TV>
      | [undefined | null | TK, undefined | TV], any, any> = []
  An iterable to populate the new BST.
- Optionaloptions: Partial<RedBlackTreeOptions<TK, TV, TR>>
  Options for the new BST.
Returns RedBlackTree<TK, TV, TR>
A new BST.

Remarks
Time O(N log N) or O(N^2) (from constructor) due to processing the iterable.
Overrides BST._createLike
- Defined in data-structures/binary-tree/red-black-tree.ts:485

`Protected`_DEFAULT_NODE_CALLBACK

_DEFAULT_NODE_CALLBACK(node): undefined | K
(Protected) Default callback function, returns the node's key.
Parameters
- node: undefined | null | BinaryTreeNode<K, V>
  The node.
Returns undefined | K
The node's key or undefined.

Remarks
Time O(1)
Inherited from BST._DEFAULT_NODE_CALLBACK
- Defined in data-structures/binary-tree/binary-tree.ts:2120

`Protected`_deleteByKey

_deleteByKey(key): boolean
(Private) Deletes a node by its key.
Parameters
- key: K
  The key of the node to delete.
Returns boolean
True if the node was found and deleted, false otherwise.

Remarks
Standard BST deletion algorithm. Time O(log N), O(N) worst-case. Space O(1).
Inherited from BST._deleteByKey
- Defined in data-structures/binary-tree/bst.ts:1971

`Protected`_deleteFixup

_deleteFixup(node): void
(Protected) Restore red-black properties after deletion (recolor/rotate).
Parameters
- node: undefined | RedBlackTreeNode<K, V>
  Child that replaced the deleted node (may be undefined).
Returns void
void

Remarks
Time O(log n), Space O(1)
- Defined in data-structures/binary-tree/red-black-tree.ts:639

`Protected`_dfs

_dfs<C>(callback, pattern?, onlyOne?, startNode?, iterationType?, includeNull?, shouldVisitLeft?, shouldVisitRight?, shouldVisitRoot?, shouldProcessRoot?): ReturnType<C>[]
Type Parameters
- C extends NodeCallback<BinaryTreeNode<K, V>>
  Callback type.
Parameters
- callback: C
  Function to call on nodes.
- Optionalpattern: DFSOrderPattern
  Traversal order.
- OptionalonlyOne: boolean
  Stop after first match.
- OptionalstartNode:
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>
  Starting node.
- OptionaliterationType: IterationType
  Traversal method.
- OptionalincludeNull: boolean
  Include nulls.
- OptionalshouldVisitLeft: ((node: undefined | null | BinaryTreeNode<K, V>) => boolean)
  Predicate to traverse left.
  - - (node): boolean
    - Parameters
      node: undefined | null | BinaryTreeNode<K, V>
      Returns boolean
- OptionalshouldVisitRight: ((node: undefined | null | BinaryTreeNode<K, V>) => boolean)
  Predicate to traverse right.
  - - (node): boolean
    - Parameters
      node: undefined | null | BinaryTreeNode<K, V>
      Returns boolean
- OptionalshouldVisitRoot: ((node: undefined | null | BinaryTreeNode<K, V>) => boolean)
  Predicate to visit root.
  - - (node): boolean
    - Parameters
      node: undefined | null | BinaryTreeNode<K, V>
      Returns boolean
- OptionalshouldProcessRoot: ((node: undefined | null | BinaryTreeNode<K, V>) => boolean)
  Predicate to process root.
  - - (node): boolean
    - Parameters
      node: undefined | null | BinaryTreeNode<K, V>
      Returns boolean
Returns ReturnType<C>[]
Array of callback results.
Inherited from BST._dfs
- Defined in data-structures/binary-tree/binary-tree.ts:1929

`Protected`_displayAux

_displayAux(node, options): NodeDisplayLayout
(Protected) Recursive helper for toVisual.
Parameters
- node: undefined | null | BinaryTreeNode<K, V>
  The current node.
- options: BinaryTreePrintOptions
  Print options.
Returns NodeDisplayLayout
Layout information for this subtree.

Remarks
Time O(N), Space O(N*H) or O(N^2)
Inherited from BST._displayAux
- Defined in data-structures/binary-tree/binary-tree.ts:2237

`Protected`_ensurePredicate

_ensurePredicate(keyNodeEntryOrPredicate): NodePredicate<BinaryTreeNode<K, V>>
(Protected) Converts a key, node, entry, or predicate into a standardized predicate function.
Parameters
- keyNodeEntryOrPredicate:
      | undefined
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>
      | NodePredicate<BinaryTreeNode<K, V>>
  The item to convert.
Returns NodePredicate<BinaryTreeNode<K, V>>
A predicate function.

Remarks
Time O(1)
Inherited from BST._ensurePredicate
- Defined in data-structures/binary-tree/binary-tree.ts:2391

`Protected`_extractKey

_extractKey(keyNodeOrEntry): undefined | null | K
(Protected) Extracts the key from a key, node, or entry.
Parameters
- keyNodeOrEntry:
      | undefined
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>
  The item.
Returns undefined | null | K
The extracted key.

Remarks
Time O(1)
Inherited from BST._extractKey
- Defined in data-structures/binary-tree/binary-tree.ts:2451

`Protected`_floorByKey

_floorByKey(key, iterationType): undefined | BSTNode<K, V>
(Protected) Binary search for floor by key with pruning optimization. Performs standard BST binary search, choosing left or right subtree based on comparator result. Finds first node where key <= target.
Parameters
- key: K
  The target key to search for.
- iterationType: IterationType
  The iteration type (RECURSIVE or ITERATIVE).
Returns undefined | BSTNode<K, V>
The first node with key <= target, or undefined if none exists.

Remarks
Time O(h) where h is tree height.
Inherited from BST._floorByKey
- Defined in data-structures/binary-tree/bst.ts:1474

`Protected`_floorByPredicate

_floorByPredicate(predicate, iterationType): undefined | BSTNode<K, V>
(Protected) In-order traversal search for floor by predicate. Falls back to linear in-order traversal when predicate-based search is required. Returns the last node that satisfies the predicate function.
Parameters
- predicate: NodePredicate<BSTNode<K, V>>
  The predicate function to test nodes.
- iterationType: IterationType
  The iteration type (RECURSIVE or ITERATIVE).
Returns undefined | BSTNode<K, V>
The last node satisfying predicate (highest key), or undefined if none found.

Remarks
Time Complexity: O(n) since it may visit every node. Space Complexity: O(h) for recursion, O(h) for iterative stack.
Inherited from BST._floorByPredicate
- Defined in data-structures/binary-tree/bst.ts:1527

`Protected`_getIterator

_getIterator(node?): IterableIterator<[K, undefined | V], any, any>
(Protected) Gets the iterator for the tree (default in-order).
Parameters
- Optionalnode: null | BinaryTreeNode<K, V> = ...
  The node to start iteration from.
Returns IterableIterator<[K, undefined | V], any, any>
An iterator for [key, value] pairs.

Remarks
Time O(N) for full iteration. O(H) to get the first element. Space O(H) for the iterative stack. O(H) for recursive stack.
Inherited from BST._getIterator
- Defined in data-structures/binary-tree/binary-tree.ts:2074

`Protected`_insert

_insert(node): CRUD
(Protected) Standard BST insert followed by red-black fix-up.
Parameters
- node: RedBlackTreeNode<K, V>
  Node to insert.
Returns CRUD
Status string: 'CREATED' or 'UPDATED'.

Remarks
Time O(log n), Space O(1)
- Defined in data-structures/binary-tree/red-black-tree.ts:521

`Protected`_insertFixup

_insertFixup(z): void
(Protected) Restore red-black properties after insertion (recolor/rotate).
Parameters
- z: undefined | RedBlackTreeNode<K, V>
  Recently inserted node.
Returns void
void

Remarks
Time O(log n), Space O(1)
- Defined in data-structures/binary-tree/red-black-tree.ts:585

`Protected`_isPredicate

_isPredicate(p): p is NodePredicate<BinaryTreeNode<K, V>>
(Protected) Checks if an item is a predicate function.
Parameters
- p: any
  The item to check.
Returns p is NodePredicate<BinaryTreeNode<K, V>>
True if it's a function.

Remarks
Time O(1)
Inherited from BST._isPredicate
- Defined in data-structures/binary-tree/binary-tree.ts:2440

`Protected`_keyValueNodeOrEntryToNodeAndValue

_keyValueNodeOrEntryToNodeAndValue(keyNodeOrEntry, value?): [OptNode<BSTNode<K, V>>, undefined | V]
(Protected) Converts a key, node, or entry into a standardized [node, value] tuple.
Parameters
- keyNodeOrEntry:
      | undefined
      | null
      | K
      | BSTNode<K, V>
      | [undefined | null | K, undefined | V]
  The input item.
- Optionalvalue: V
  An optional value (used if input is just a key).
Returns [OptNode<BSTNode<K, V>>, undefined | V]
A tuple of [node, value].

Remarks
Time O(1)
Inherited from BST._keyValueNodeOrEntryToNodeAndValue
- Defined in data-structures/binary-tree/bst.ts:1932

`Protected`_leftRotate

_leftRotate(x): void
(Protected) Perform a left rotation around x.
Parameters
- x: undefined | RedBlackTreeNode<K, V>
  Pivot node to rotate around.
Returns void
void

Remarks
Time O(1), Space O(1)
- Defined in data-structures/binary-tree/red-black-tree.ts:709

`Protected`_lowerByKey

_lowerByKey(key, iterationType): undefined | BSTNode<K, V>
(Protected) Binary search for lower by key with pruning optimization. Performs standard BST binary search, choosing left or right subtree based on comparator result. Finds first node where key < target.
Parameters
- key: K
  The target key to search for.
- iterationType: IterationType
  The iteration type (RECURSIVE or ITERATIVE).
Returns undefined | BSTNode<K, V>
The first node with key < target, or undefined if none exists.

Remarks
Time O(h) where h is tree height.
Inherited from BST._lowerByKey
- Defined in data-structures/binary-tree/bst.ts:1592

`Protected`_lowerByPredicate

_lowerByPredicate(predicate, iterationType): undefined | BSTNode<K, V>
(Protected) In-order traversal search for lower by predicate. Falls back to linear in-order traversal when predicate-based search is required. Returns the node that satisfies the predicate and appears last in in-order traversal.
Parameters
- predicate: NodePredicate<BSTNode<K, V>>
  The predicate function to test nodes.
- iterationType: IterationType
  The iteration type (RECURSIVE or ITERATIVE).
Returns undefined | BSTNode<K, V>
The last node satisfying predicate (highest key < target), or undefined if none found.

Remarks
Time Complexity: O(n) since it may visit every node. Space Complexity: O(h) for recursion, O(h) for iterative stack.
Inherited from BST._lowerByPredicate
- Defined in data-structures/binary-tree/bst.ts:1645

`Protected`_replaceNode

_replaceNode(oldNode, newNode): RedBlackTreeNode<K, V>
(Protected) Replaces a node in the tree with a new node, maintaining children and parent links.
Parameters
- oldNode: RedBlackTreeNode<K, V>
  The node to be replaced.
- newNode: RedBlackTreeNode<K, V>
  The node to insert.
Returns RedBlackTreeNode<K, V>
The newNode.

Remarks
Time O(1)
Overrides BST._replaceNode
- Defined in data-structures/binary-tree/red-black-tree.ts:505

`Protected`_rightRotate

_rightRotate(y): void
(Protected) Perform a right rotation around y.
Parameters
- y: undefined | RedBlackTreeNode<K, V>
  Pivot node to rotate around.
Returns void
void

Remarks
Time O(1), Space O(1)
- Defined in data-structures/binary-tree/red-black-tree.ts:742

`Protected`_setRoot

_setRoot(v): void
(Protected) Sets the root node and clears its parent reference.
Parameters
- v: undefined | RedBlackTreeNode<K, V>
  The node to set as root.
Returns void
Remarks
Time O(1)
Overrides BST._setRoot
- Defined in data-structures/binary-tree/red-black-tree.ts:498

`Protected`_setValue

_setValue(key, value): false | Map<K, undefined | V>
(Protected) Sets a value in the external store (Map mode).
Parameters
- key: undefined | null | K
  The key.
- value: undefined | V
  The value.
Returns false | Map<K, undefined | V>
True if successful.

Remarks
Time O(1) (average for Map.set).
Inherited from BST._setValue
- Defined in data-structures/binary-tree/binary-tree.ts:2472

`Protected`_snapshotOptions

_snapshotOptions<TK, TV, TR>(): BSTOptions<TK, TV, TR>
(Protected) Snapshots the current BST's configuration options.
Type Parameters
- TK = K
- TV = V
- TR = R
Returns BSTOptions<TK, TV, TR>
The options object.

Remarks
Time O(1)
Inherited from BST._snapshotOptions
- Defined in data-structures/binary-tree/bst.ts:1917

`Protected`_swapProperties

_swapProperties(srcNode, destNode): undefined | BinaryTreeNode<K, V>
(Protected) Swaps the key/value properties of two nodes.
Parameters
- srcNode:
      | undefined
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>
  The source node.
- destNode:
      | undefined
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>
  The destination node.
Returns undefined | BinaryTreeNode<K, V>
The destNode (now holding srcNode's properties).

Remarks
Time O(1)
Inherited from BST._swapProperties
- Defined in data-structures/binary-tree/binary-tree.ts:2319

`Protected`_transplant

_transplant(u, v): void
(Protected) Transplant a subtree in place of another during deletion.
Parameters
- u: RedBlackTreeNode<K, V>
  Node to replace.
- v: undefined | RedBlackTreeNode<K, V>
  Replacement subtree root (may be undefined).
Returns void
void

Remarks
Time O(1), Space O(1)
- Defined in data-structures/binary-tree/red-black-tree.ts:564

[iterator]

[iterator](...args): IterableIterator<[K, undefined | V], any, any>
Default iterator yielding [key, value] entries.
Parameters
- Rest...args: any[]
Returns IterableIterator<[K, undefined | V], any, any>
Iterator of [K, V].

Remarks
Time O(n) to iterate, Space O(1)
Implementation of IBinaryTree.[iterator]
Inherited from BST.[iterator]
- Defined in data-structures/base/iterable-entry-base.ts:22

add

add(keyNodeOrEntry, value?): boolean
Insert or replace an entry using BST order and red-black fix-up.
Parameters
- keyNodeOrEntry:
      | undefined
      | null
      | K
      | RedBlackTreeNode<K, V>
      | [undefined | null | K, undefined | V]
  Key, node, or [key, value] entry to insert.
- Optionalvalue: V
  See parameter type for details.
Returns boolean
True if inserted or updated; false if ignored.

Remarks
Time O(log n), Space O(1)
Implementation of IBinaryTree.add
Overrides BST.add
- Defined in data-structures/binary-tree/red-black-tree.ts:353

addMany

addMany(keysNodesEntriesOrRaws, values?, isBalanceAdd?, iterationType?): boolean[]
Adds multiple items to the tree.
Parameters
- keysNodesEntriesOrRaws: Iterable<R | BTNRep<K, V, BSTNode<K, V>>, any, any>
  An iterable of items to add.
- Optionalvalues: Iterable<undefined | V, any, any>
  An optional parallel iterable of values.
- OptionalisBalanceAdd: boolean = true
  If true, builds a balanced tree from the items.
- OptionaliterationType: IterationType = ...
  The traversal method for balanced add (recursive or iterative).
Returns boolean[]
An array of booleans indicating the success of each individual add operation.

Remarks
If isBalanceAdd is true, sorts the input and builds a balanced tree. Time O(N log N) (due to sort and balanced add). If false, adds items one by one. Time O(N * H), which is O(N^2) worst-case. Space O(N) for sorting and recursion/iteration stack.
Implementation of IBinaryTree.addMany
Inherited from BST.addMany
- Defined in data-structures/binary-tree/bst.ts:779

bfs

bfs(): (undefined | K)[]
Returns (undefined | K)[]
Implementation of IBinaryTree.bfs
Inherited from BST.bfs
- Defined in data-structures/binary-tree/bst.ts:488
bfs<C>(callback, startNode?, iterationType?): ReturnType<C>[]
Type Parameters
- C extends NodeCallback<BSTNode<K, V>>
Parameters
- callback: C
- OptionalstartNode:
      | null
      | K
      | BSTNode<K, V>
      | [undefined | null | K, undefined | V]
- OptionaliterationType: IterationType
Returns ReturnType<C>[]
Implementation of IBinaryTree.bfs
Inherited from BST.bfs
- Defined in data-structures/binary-tree/bst.ts:489

ceiling

ceiling(keyNodeEntryOrPredicate): undefined | K
Returns the first key with a value >= target. Equivalent to Java TreeMap.ceiling. Time Complexity: O(log n) average, O(h) worst case. Space Complexity: O(h) for recursion, O(1) for iteration.
Parameters
- keyNodeEntryOrPredicate:
      | undefined
      | null
      | K
      | BSTNode<K, V>
      | [undefined | null | K, undefined | V]
      | NodePredicate<BSTNode<K, V>>
Returns undefined | K
Inherited from BST.ceiling
- Defined in data-structures/binary-tree/bst.ts:876
ceiling<C>(keyNodeEntryOrPredicate, callback, iterationType?): ReturnType<C>
Returns the first node with a key >= target and applies callback. Time Complexity: O(log n) average, O(h) worst case. Space Complexity: O(h) for recursion, O(1) for iteration.
Type Parameters
- C extends NodeCallback<BSTNode<K, V>>
Parameters
- keyNodeEntryOrPredicate:
      | undefined
      | null
      | K
      | BSTNode<K, V>
      | [undefined | null | K, undefined | V]
      | NodePredicate<BSTNode<K, V>>
- callback: C
- OptionaliterationType: IterationType
Returns ReturnType<C>
Inherited from BST.ceiling
- Defined in data-structures/binary-tree/bst.ts:891

clear

clear(): void
Remove all nodes and clear the key→value store (if in map mode).

Returns void
void

Remarks
Time O(n), Space O(1)
Implementation of IBinaryTree.clear
Overrides BST.clear
- Defined in data-structures/binary-tree/red-black-tree.ts:341

clone

clone(): this
Clones the tree.

Returns this
A new, cloned instance of the tree.

Remarks
Time O(N * M), where N is the number of nodes and M is the tree size during insertion (due to bfs + add, and add is O(M)). Space O(N) for the new tree and the BFS queue.
Implementation of IBinaryTree.clone
Inherited from BST.clone
- Defined in data-structures/binary-tree/binary-tree.ts:1837

createNode

createNode(key, value?, color?): RedBlackTreeNode<K, V>
Create a red-black node for the given key/value (value ignored in map mode).
Parameters
- key: K
  See parameter type for details.
- Optionalvalue: V
  See parameter type for details.
- color: RBTNColor = 'BLACK'
  See parameter type for details.
Returns RedBlackTreeNode<K, V>
A new RedBlackTreeNode instance.

Remarks
Time O(1), Space O(1)
Implementation of IBinaryTree.createNode
Overrides BST.createNode
- Defined in data-structures/binary-tree/red-black-tree.ts:318

createTree

createTree(options?): this
Creates a new, empty tree of the same type and configuration.
Parameters
- Optionaloptions: Partial<BinaryTreeOptions<K, V, R>>
  Optional overrides for the new tree's options.
Returns this
A new, empty tree instance.

Remarks
Time O(1) (excluding options cloning), Space O(1)
Implementation of IBinaryTree.createTree
Inherited from BST.createTree
- Defined in data-structures/binary-tree/binary-tree.ts:483

delete

delete(keyNodeOrEntry): BinaryTreeDeleteResult<RedBlackTreeNode<K, V>>[]
Delete a node by key/node/entry and rebalance as needed.
Parameters
- keyNodeOrEntry:
      | undefined
      | null
      | K
      | RedBlackTreeNode<K, V>
      | [undefined | null | K, undefined | V]
  Key, node, or [key, value] entry identifying the node to delete.
Returns BinaryTreeDeleteResult<RedBlackTreeNode<K, V>>[]
Array with deletion metadata (removed node, rebalancing hint if any).

Remarks
Time O(log n), Space O(1)
Implementation of IBinaryTree.delete
Overrides BST.delete
- Defined in data-structures/binary-tree/red-black-tree.ts:386

deleteWhere

deleteWhere(keyNodeEntryOrPredicate, onlyOne?, startNode?, iterationType?): BinaryTreeDeleteResult<BSTNode<K, V>>[]
Deletes nodes that match a key, node, entry, predicate, or range.
Parameters
- keyNodeEntryOrPredicate:
      | undefined
      | null
      | K
      | BSTNode<K, V>
      | [undefined | null | K, undefined | V]
      | NodePredicate<BSTNode<K, V>>
      | Range<K>
  The search criteria. Can be one of:
  - A key (type K): searches for exact key match using the comparator.
  - A BSTNode: searches for the matching node in the tree.
  - An entry tuple: searches for the key-value pair.
  - A NodePredicate function: tests each node and returns true for matches.
  - A Range object: searches for nodes whose keys fall within the specified range (inclusive/exclusive based on range settings).
  - null or undefined: treated as no match, returns empty results.
- onlyOne: boolean = false
  If true, stops the search after finding the first match and only deletes that one node. If false (default), searches for and deletes all matching nodes.
- startNode:
      | undefined
      | null
      | K
      | BSTNode<K, V>
      | [undefined | null | K, undefined | V] = ...
  The node to start the search from. Can be:
  - A key, node, or entry: the method resolves it to a node and searches from that subtree.
  - null or undefined: defaults to the root, searching the entire tree.
  - Default value: this._root (the tree's root).
- iterationType: IterationType = ...
  Controls the internal traversal implementation:
  - 'RECURSIVE': uses recursive function calls for traversal.
  - 'ITERATIVE': uses explicit stack-based iteration.
  - Default: this.iterationType (the tree's default iteration mode).
Returns BinaryTreeDeleteResult<BSTNode<K, V>>[]
A Map<K, boolean> containing the deletion results:
- Key: the matched node's key.
- Value: true if the deletion succeeded, false if it failed (e.g., key not found during deletion phase).
- If no nodes match the search criteria, the returned map is empty.
Remarks
Time Complexity: O(N) for search + O(M log N) for M deletions, where N is tree size. Space Complexity: O(M) for storing matched nodes and result map.
Inherited from BST.deleteWhere
- Defined in data-structures/binary-tree/bst.ts:1413

dfs

dfs(): (undefined | K)[]
Returns (undefined | K)[]
Implementation of IBinaryTree.dfs
Inherited from BST.dfs
- Defined in data-structures/binary-tree/bst.ts:456
dfs<C>(callback, pattern?, onlyOne?, startNode?, iterationType?): ReturnType<C>[]
Type Parameters
- C extends NodeCallback<BSTNode<K, V>>
Parameters
- callback: C
- Optionalpattern: DFSOrderPattern
- OptionalonlyOne: boolean
- OptionalstartNode:
      | null
      | K
      | BSTNode<K, V>
      | [undefined | null | K, undefined | V]
- OptionaliterationType: IterationType
Returns ReturnType<C>[]
Implementation of IBinaryTree.dfs
Inherited from BST.dfs
- Defined in data-structures/binary-tree/bst.ts:458

ensureNode

ensureNode(keyNodeOrEntry, iterationType?): OptNode<BSTNode<K, V>>
Ensures the input is a node. If it's a key or entry, it searches for the node.
Parameters
- keyNodeOrEntry:
      | undefined
      | null
      | K
      | BSTNode<K, V>
      | [undefined | null | K, undefined | V]
  The item to resolve to a node.
- OptionaliterationType: IterationType = ...
  The traversal method to use if searching.
Returns OptNode<BSTNode<K, V>>
The resolved node, or undefined if not found.

Remarks
Time O(log N) (height of the tree), O(N) worst-case.
Inherited from BST.ensureNode
- Defined in data-structures/binary-tree/bst.ts:425

entries

entries(): IterableIterator<[K, undefined | V], any, any>
Iterate over [key, value] pairs (may yield undefined values).

Returns IterableIterator<[K, undefined | V], any, any>
Iterator of [K, V | undefined].

Remarks
Time O(n), Space O(1)
Implementation of IBinaryTree.entries
Inherited from BST.entries
- Defined in data-structures/base/iterable-entry-base.ts:31

every

every(predicate, thisArg?): boolean
Test whether all entries satisfy the predicate.
Parameters
- predicate: EntryCallback<K, undefined | V, boolean>
  (key, value, index, self) => boolean.
- OptionalthisArg: any
  Optional this for callback.
Returns boolean
true if all pass; otherwise false.

Remarks
Time O(n), Space O(1)
Implementation of IBinaryTree.every
Inherited from BST.every
- Defined in data-structures/base/iterable-entry-base.ts:66

filter

filter(predicate, thisArg?): this
Creates a new tree containing only the entries that satisfy the predicate.
Parameters
- predicate: EntryCallback<K, undefined | V, boolean>
  A function to test each [key, value] pair.
- OptionalthisArg: unknown
  this context for the predicate.
Returns this
A new, filtered tree.

Remarks
Time O(N * M), where N is nodes in this tree, and M is size of the new tree during insertion (O(N) iteration + O(M) add for each item). Space O(N) for the new tree.
Implementation of IBinaryTree.filter
Inherited from BST.filter
- Defined in data-structures/binary-tree/binary-tree.ts:1851

find

find(callbackfn, thisArg?): undefined | [K, undefined | V]
Find the first entry that matches a predicate.
Parameters
- callbackfn: EntryCallback<K, undefined | V, boolean>
  (key, value, index, self) => boolean.
- OptionalthisArg: any
  Optional this for callback.
Returns undefined | [K, undefined | V]
Matching [key, value] or undefined.

Remarks
Time O(n), Space O(1)
Implementation of IBinaryTree.find
Inherited from BST.find
- Defined in data-structures/base/iterable-entry-base.ts:114

floor

floor(keyNodeEntryOrPredicate): undefined | K
Returns the first key with a value <= target. Equivalent to Java TreeMap.floor. Time Complexity: O(log n) average, O(h) worst case. Space Complexity: O(h) for recursion, O(1) for iteration.
Parameters
- keyNodeEntryOrPredicate:
      | undefined
      | null
      | K
      | BSTNode<K, V>
      | [undefined | null | K, undefined | V]
      | NodePredicate<BSTNode<K, V>>
Returns undefined | K
Inherited from BST.floor
- Defined in data-structures/binary-tree/bst.ts:1006
floor<C>(keyNodeEntryOrPredicate, callback, iterationType?): ReturnType<C>
Returns the first node with a key <= target and applies callback. Time Complexity: O(log n) average, O(h) worst case. Space Complexity: O(h) for recursion, O(1) for iteration.
Type Parameters
- C extends NodeCallback<BSTNode<K, V>>
Parameters
- keyNodeEntryOrPredicate:
      | undefined
      | null
      | K
      | BSTNode<K, V>
      | [undefined | null | K, undefined | V]
      | NodePredicate<BSTNode<K, V>>
- callback: C
- OptionaliterationType: IterationType
Returns ReturnType<C>
Inherited from BST.floor
- Defined in data-structures/binary-tree/bst.ts:1021

forEach

forEach(callbackfn, thisArg?): void
Visit each entry, left-to-right.
Parameters
- callbackfn: EntryCallback<K, undefined | V, void>
  (key, value, index, self) => void.
- OptionalthisArg: any
  Optional this for callback.
Returns void
Remarks
Time O(n), Space O(1)
Implementation of IBinaryTree.forEach
Inherited from BST.forEach
- Defined in data-structures/base/iterable-entry-base.ts:99

get

get(keyNodeEntryOrPredicate, startNode?, iterationType?): undefined | V
Gets the value associated with a key.
Parameters
- keyNodeEntryOrPredicate:
      | undefined
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>
  The key, node, or entry to get the value for.
- OptionalstartNode:
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V> = ...
  The node to start searching from (if not in Map mode).
- OptionaliterationType: IterationType = ...
  The traversal method (if not in Map mode).
Returns undefined | V
The associated value, or undefined.

Remarks
Time O(log N), For BST, Red-Black Tree, and AVL Tree subclasses, the worst-case time is O(log N). Time O(1) if in Map mode. O(N) if not in Map mode (uses getNode). Space O(1) if in Map mode. O(H) or O(N) otherwise.
Implementation of IBinaryTree.get
Inherited from BST.get
- Defined in data-structures/binary-tree/binary-tree.ts:1020

getDepth

getDepth(dist, startNode?): number
Gets the depth of a node (distance from startNode).
Parameters
- dist:
      | undefined
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>
  The node to find the depth of.
- OptionalstartNode:
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V> = ...
  The node to measure depth from (defaults to root).
Returns number
The depth (0 if dist is startNode).

Remarks
Time O(H), where H is the depth of the dist node relative to startNode. O(N) worst-case. Space O(1).
Implementation of IBinaryTree.getDepth
Inherited from BST.getDepth
- Defined in data-structures/binary-tree/binary-tree.ts:1159

getHeight

getHeight(startNode?, iterationType?): number
Gets the maximum height of the tree (longest path from startNode to a leaf).
Parameters
- OptionalstartNode:
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V> = ...
  The node to start measuring from.
- OptionaliterationType: IterationType = ...
  The traversal method.
Returns number
The height ( -1 for an empty tree, 0 for a single-node tree).

Remarks
Time O(N), as it must visit every node. Space O(H) for recursive stack (O(N) worst-case) or O(N) for iterative stack (storing node + depth).
Implementation of IBinaryTree.getHeight
Inherited from BST.getHeight
- Defined in data-structures/binary-tree/binary-tree.ts:1184

getLeftMost

getLeftMost(): undefined | K
Returns undefined | K
Implementation of IBinaryTree.getLeftMost
Inherited from BST.getLeftMost
- Defined in data-structures/binary-tree/binary-tree.ts:1311
getLeftMost<C>(callback, startNode?, iterationType?): ReturnType<C>
Type Parameters
- C extends NodeCallback<undefined | BinaryTreeNode<K, V>>
Parameters
- callback: C
- OptionalstartNode:
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>
- OptionaliterationType: IterationType
Returns ReturnType<C>
Implementation of IBinaryTree.getLeftMost
Inherited from BST.getLeftMost
- Defined in data-structures/binary-tree/binary-tree.ts:1313

getMinHeight

getMinHeight(startNode?, iterationType?): number
Gets the minimum height of the tree (shortest path from startNode to a leaf).
Parameters
- OptionalstartNode:
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V> = ...
  The node to start measuring from.
- OptionaliterationType: IterationType = ...
  The traversal method.
Returns number
The minimum height (-1 for empty, 0 for single node).

Remarks
Time O(N), as it must visit every node. Space O(H) for recursive stack (O(N) worst-case) or O(N) for iterative (due to depths Map).
Implementation of IBinaryTree.getMinHeight
Inherited from BST.getMinHeight
- Defined in data-structures/binary-tree/binary-tree.ts:1226

getNode

getNode(keyNodeEntryOrPredicate, startNode?, iterationType?): OptNode<BSTNode<K, V>>
Gets the first node matching a predicate.
Parameters
- keyNodeEntryOrPredicate:
      | undefined
      | null
      | K
      | BSTNode<K, V>
      | [undefined | null | K, undefined | V]
      | NodePredicate<BSTNode<K, V>>
  The key, node, entry, or predicate function to search for.
- OptionalstartNode: BSTNOptKeyOrNode<K, BSTNode<K, V>> = ...
  The node to start the search from.
- OptionaliterationType: IterationType = ...
  The traversal method.
Returns OptNode<BSTNode<K, V>>
The first matching node, or undefined if not found.

Remarks
Time O(log N) if searching by key, O(N) if searching by predicate. Space O(log N) or O(N).
Implementation of IBinaryTree.getNode
Inherited from BST.getNode
- Defined in data-structures/binary-tree/bst.ts:548

getNodes

getNodes(keyNodeEntryOrPredicate, onlyOne?, startNode?, iterationType?): BinaryTreeNode<K, V>[]
Gets all nodes matching a predicate.
Parameters
- keyNodeEntryOrPredicate:
      | undefined
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>
      | NodePredicate<BinaryTreeNode<K, V>>
  The key, node, entry, or predicate function to search for.
- OptionalonlyOne: boolean
  If true, stops after finding the first match.
- OptionalstartNode:
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>
  The node to start the search from.
- OptionaliterationType: IterationType
  The traversal method.
Returns BinaryTreeNode<K, V>[]
An array of matching nodes.

Remarks
Time O(N) (via search). Space O(H) or O(N) (via search).
Inherited from BST.getNodes
- Defined in data-structures/binary-tree/binary-tree.ts:960

getPathToRoot

getPathToRoot(beginNode): (undefined | K)[]
Parameters
- beginNode:
      | undefined
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>
Returns (undefined | K)[]
Implementation of IBinaryTree.getPathToRoot
Inherited from BST.getPathToRoot
- Defined in data-structures/binary-tree/binary-tree.ts:1273
getPathToRoot<C>(beginNode, callback, isReverse?): ReturnType<C>[]
Type Parameters
- C extends NodeCallback<undefined | BinaryTreeNode<K, V>>
Parameters
- beginNode:
      | undefined
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>
- callback: C
- OptionalisReverse: boolean
Returns ReturnType<C>[]
Implementation of IBinaryTree.getPathToRoot
Inherited from BST.getPathToRoot
- Defined in data-structures/binary-tree/binary-tree.ts:1277

getPredecessor

getPredecessor(node): BinaryTreeNode<K, V>
Gets the Morris traversal predecessor (rightmost node in the left subtree, or node itself).
Parameters
- node: BinaryTreeNode<K, V>
  The node to find the predecessor for.
Returns BinaryTreeNode<K, V>
The Morris predecessor.

Remarks
This is primarily a helper for Morris traversal. Time O(H), where H is the height of the left subtree. O(N) worst-case. Space O(1).
Inherited from BST.getPredecessor
- Defined in data-structures/binary-tree/binary-tree.ts:1411

getRightMost

getRightMost(): undefined | K
Returns undefined | K
Implementation of IBinaryTree.getRightMost
Inherited from BST.getRightMost
- Defined in data-structures/binary-tree/binary-tree.ts:1358
getRightMost<C>(callback, startNode?, iterationType?): ReturnType<C>
Type Parameters
- C extends NodeCallback<undefined | BinaryTreeNode<K, V>>
Parameters
- callback: C
- OptionalstartNode:
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>
- OptionaliterationType: IterationType
Returns ReturnType<C>
Implementation of IBinaryTree.getRightMost
Inherited from BST.getRightMost
- Defined in data-structures/binary-tree/binary-tree.ts:1360

getSuccessor

getSuccessor(x?): undefined | null | BinaryTreeNode<K, V>
Gets the in-order successor of a node in a BST.
Parameters
- Optionalx: null | K | BinaryTreeNode<K, V>
  The node to find the successor of.
Returns undefined | null | BinaryTreeNode<K, V>
The successor node, or null/undefined if none exists.

Remarks
Time O(H), where H is the tree height. O(N) worst-case. Space O(H) (due to getLeftMost stack).
Inherited from BST.getSuccessor
- Defined in data-structures/binary-tree/binary-tree.ts:1432

has

has(keyNodeEntryOrPredicate?, startNode?, iterationType?): boolean
Checks if a node matching the predicate exists in the tree.
Parameters
- OptionalkeyNodeEntryOrPredicate:
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>
      | NodePredicate<BinaryTreeNode<K, V>>
  The key, node, entry, or predicate to check for.
- OptionalstartNode:
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>
  The node to start the search from.
- OptionaliterationType: IterationType
  The traversal method.
Returns boolean
True if a matching node exists, false otherwise.

Remarks
Time O(log N), For BST, Red-Black Tree, and AVL Tree subclasses, the worst-case time is O(log N). Time O(N) in the worst case (via search). Space O(H) or O(N) (via search).
Implementation of IBinaryTree.has
Inherited from BST.has
- Defined in data-structures/binary-tree/binary-tree.ts:1042

hasValue

hasValue(value): boolean
Whether there exists an entry with the given value.
Parameters
- value: undefined | V
  Value to test.
Returns boolean
true if found; otherwise false.

Remarks
Time O(n), Space O(1)
Implementation of IBinaryTree.hasValue
Inherited from BST.hasValue
- Defined in data-structures/base/iterable-entry-base.ts:143

higher

higher(keyNodeEntryOrPredicate): undefined | K
Returns the first key with a value > target. Equivalent to Java TreeMap.higher. Time Complexity: O(log n) average, O(h) worst case. Space Complexity: O(h) for recursion, O(1) for iteration.
Parameters
- keyNodeEntryOrPredicate:
      | undefined
      | null
      | K
      | BSTNode<K, V>
      | [undefined | null | K, undefined | V]
      | NodePredicate<BSTNode<K, V>>
Returns undefined | K
Inherited from BST.higher
- Defined in data-structures/binary-tree/bst.ts:941
higher<C>(keyNodeEntryOrPredicate, callback, iterationType?): ReturnType<C>
Returns the first node with a key > target and applies callback. Time Complexity: O(log n) average, O(h) worst case. Space Complexity: O(h) for recursion, O(1) for iteration.
Type Parameters
- C extends NodeCallback<BSTNode<K, V>>
Parameters
- keyNodeEntryOrPredicate:
      | undefined
      | null
      | K
      | BSTNode<K, V>
      | [undefined | null | K, undefined | V]
      | NodePredicate<BSTNode<K, V>>
- callback: C
- OptionaliterationType: IterationType
Returns ReturnType<C>
Inherited from BST.higher
- Defined in data-structures/binary-tree/bst.ts:956

isAVLBalanced

isAVLBalanced(iterationType?): boolean
Checks if the tree meets the AVL balance condition (height difference <= 1).
Parameters
- OptionaliterationType: IterationType = ...
  The traversal method.
Returns boolean
True if the tree is AVL balanced, false otherwise.

Remarks
Time O(N), as it must visit every node to compute height. Space O(log N) for recursion or O(N) for iterative map.
Inherited from BST.isAVLBalanced
- Defined in data-structures/binary-tree/bst.ts:1306

isBST

isBST(startNode?, iterationType?): boolean
Checks if the tree is a valid Binary Search Tree (BST).
Parameters
- OptionalstartNode:
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V> = ...
  The node to start checking from.
- OptionaliterationType: IterationType = ...
  The traversal method.
Returns boolean
True if it's a valid BST, false otherwise.

Remarks
Time O(N), as it must visit every node. Space O(H) for the call stack (recursive) or explicit stack (iterative), where H is the tree height (O(N) worst-case).
Implementation of IBinaryTree.isBST
Inherited from BST.isBST
- Defined in data-structures/binary-tree/binary-tree.ts:1108

isEmpty

isEmpty(): boolean
Checks if the tree is empty.

Returns boolean
True if the tree has no nodes, false otherwise.

Remarks
Time O(1), Space O(1)
Implementation of IBinaryTree.isEmpty
Inherited from BST.isEmpty
- Defined in data-structures/binary-tree/binary-tree.ts:1083

isEntry

isEntry(keyNodeOrEntry): keyNodeOrEntry is BTNEntry<K, V>
Checks if the given item is a [key, value] entry pair.
Parameters
- keyNodeOrEntry:
      | undefined
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>
  The item to check.
Returns keyNodeOrEntry is BTNEntry<K, V>
True if it's an entry, false otherwise.

Remarks
Time O(1), Space O(1)
Inherited from BST.isEntry
- Defined in data-structures/binary-tree/binary-tree.ts:620

isLeaf

isLeaf(keyNodeOrEntry): boolean
Checks if a node is a leaf (has no real children).
Parameters
- keyNodeOrEntry:
      | undefined
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>
  The node to check.
Returns boolean
True if the node is a leaf, false otherwise.

Remarks
Time O(N) if a key/entry is passed (due to ensureNode). O(1) if a node is passed. Space O(1) or O(H) (from ensureNode).
Inherited from BST.isLeaf
- Defined in data-structures/binary-tree/binary-tree.ts:606

isNIL

isNIL(keyNodeOrEntry): boolean
Checks if the given item is the sentinel NIL node.
Parameters
- keyNodeOrEntry:
      | undefined
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>
  The item to check.
Returns boolean
True if it's the NIL node, false otherwise.

Remarks
Time O(1), Space O(1)
Inherited from BST.isNIL
- Defined in data-structures/binary-tree/binary-tree.ts:575

isNode

isNode(keyNodeOrEntry): keyNodeOrEntry is RedBlackTreeNode<K, V>
Type guard: check whether the input is a RedBlackTreeNode.
Parameters
- keyNodeOrEntry:
      | undefined
      | null
      | K
      | RedBlackTreeNode<K, V>
      | [undefined | null | K, undefined | V]
  See parameter type for details.
Returns keyNodeOrEntry is RedBlackTreeNode<K, V>
True if the value is a RedBlackTreeNode.

Remarks
Time O(1), Space O(1)
Overrides BST.isNode
- Defined in data-structures/binary-tree/red-black-tree.ts:329

isPerfectlyBalanced

isPerfectlyBalanced(startNode?): boolean
Checks if the tree is perfectly balanced.
Parameters
- OptionalstartNode:
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V> = ...
  The node to start checking from.
Returns boolean
True if perfectly balanced, false otherwise.

Remarks
A tree is perfectly balanced if the difference between min and max height is at most 1. Time O(N), as it requires two full traversals (getMinHeight and getHeight). Space O(H) or O(N) (from height calculation).
Implementation of IBinaryTree.isPerfectlyBalanced
Inherited from BST.isPerfectlyBalanced
- Defined in data-structures/binary-tree/binary-tree.ts:1094

isRange

isRange(keyNodeEntryOrPredicate): keyNodeEntryOrPredicate is Range<K>
Checks if the given item is a Range object.
Parameters
- keyNodeEntryOrPredicate:
      | undefined
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>
      | NodePredicate<BinaryTreeNode<K, V>>
      | Range<K>
  The item to check.
Returns keyNodeEntryOrPredicate is Range<K>
True if it's a Range, false otherwise.

Remarks
Time O(1), Space O(1)
Inherited from BST.isRange
- Defined in data-structures/binary-tree/binary-tree.ts:586

isRaw

isRaw(keyNodeEntryOrRaw): keyNodeEntryOrRaw is R
Checks if the given item is a raw data object (R) that needs conversion via toEntryFn.
Parameters
- keyNodeEntryOrRaw:
      | undefined
      | null
      | K
      | R
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>
  The item to check.
Returns keyNodeEntryOrRaw is R
True if it's a raw object, false otherwise.

Remarks
Time O(1), Space O(1)
Inherited from BST.isRaw
- Defined in data-structures/binary-tree/binary-tree.ts:535

isRealNode

isRealNode(keyNodeOrEntry): keyNodeOrEntry is BinaryTreeNode<K, V>
Checks if the given item is a "real" node (i.e., not null, undefined, or NIL).
Parameters
- keyNodeOrEntry:
      | undefined
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>
  The item to check.
Returns keyNodeOrEntry is BinaryTreeNode<K, V>
True if it's a real node, false otherwise.

Remarks
Time O(1), Space O(1)
Inherited from BST.isRealNode
- Defined in data-structures/binary-tree/binary-tree.ts:548

isRealNodeOrNull

isRealNodeOrNull(keyNodeOrEntry): keyNodeOrEntry is null | BinaryTreeNode<K, V>
Checks if the given item is either a "real" node or null.
Parameters
- keyNodeOrEntry:
      | undefined
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>
  The item to check.
Returns keyNodeOrEntry is null | BinaryTreeNode<K, V>
True if it's a real node or null, false otherwise.

Remarks
Time O(1), Space O(1)
Inherited from BST.isRealNodeOrNull
- Defined in data-structures/binary-tree/binary-tree.ts:562

isValidKey

isValidKey(key): key is K
Checks if the given key is valid (comparable).
Parameters
- key: any
  The key to validate.
Returns key is K
True if the key is valid, false otherwise.

Remarks
Time O(1)
Inherited from BST.isValidKey
- Defined in data-structures/binary-tree/bst.ts:452

keys

keys(): IterableIterator<K, any, any>
Iterate over keys only.

Returns IterableIterator<K, any, any>
Iterator of keys.

Remarks
Time O(n), Space O(1)
Implementation of IBinaryTree.keys
Inherited from BST.keys
- Defined in data-structures/base/iterable-entry-base.ts:42

leaves

leaves(): (undefined | K)[]
Returns (undefined | K)[]
Implementation of IBinaryTree.leaves
Inherited from BST.leaves
- Defined in data-structures/binary-tree/binary-tree.ts:1577
leaves<C>(callback, startNode?, iterationType?): ReturnType<C>[]
Type Parameters
- C extends NodeCallback<BinaryTreeNode<K, V>>
Parameters
- callback: C
- OptionalstartNode:
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>
- OptionaliterationType: IterationType
Returns ReturnType<C>[]
Implementation of IBinaryTree.leaves
Inherited from BST.leaves
- Defined in data-structures/binary-tree/binary-tree.ts:1579

lesserOrGreaterTraverse

lesserOrGreaterTraverse(): (undefined | K)[]
Returns (undefined | K)[]
Inherited from BST.lesserOrGreaterTraverse
- Defined in data-structures/binary-tree/bst.ts:1210
lesserOrGreaterTraverse<C>(callback, lesserOrGreater?, targetNode?, iterationType?): ReturnType<C>[]
Type Parameters
- C extends NodeCallback<BSTNode<K, V>>
Parameters
- callback: C
- OptionallesserOrGreater: number
- OptionaltargetNode:
      | null
      | K
      | BSTNode<K, V>
      | [undefined | null | K, undefined | V]
- OptionaliterationType: IterationType
Returns ReturnType<C>[]
Inherited from BST.lesserOrGreaterTraverse
- Defined in data-structures/binary-tree/bst.ts:1212

listLevels

listLevels(): (undefined | K)[][]
Returns (undefined | K)[][]
Implementation of IBinaryTree.listLevels
Inherited from BST.listLevels
- Defined in data-structures/binary-tree/bst.ts:513
listLevels<C>(callback, startNode?, iterationType?): ReturnType<C>[][]
Type Parameters
- C extends NodeCallback<BSTNode<K, V>>
Parameters
- callback: C
- OptionalstartNode:
      | null
      | K
      | BSTNode<K, V>
      | [undefined | null | K, undefined | V]
- OptionaliterationType: IterationType
Returns ReturnType<C>[][]
Implementation of IBinaryTree.listLevels
Inherited from BST.listLevels
- Defined in data-structures/binary-tree/bst.ts:515

lower

lower(keyNodeEntryOrPredicate): undefined | K
Returns the first key with a value < target. Equivalent to Java TreeMap.lower. Time Complexity: O(log n) average, O(h) worst case. Space Complexity: O(h) for recursion, O(1) for iteration.
Parameters
- keyNodeEntryOrPredicate:
      | undefined
      | null
      | K
      | BSTNode<K, V>
      | [undefined | null | K, undefined | V]
      | NodePredicate<BSTNode<K, V>>
Returns undefined | K
Inherited from BST.lower
- Defined in data-structures/binary-tree/bst.ts:1111
lower<C>(keyNodeEntryOrPredicate, callback, iterationType?): ReturnType<C>
Returns the first node with a key < target and applies callback. Time Complexity: O(log n) average, O(h) worst case. Space Complexity: O(h) for recursion, O(1) for iteration.
Type Parameters
- C extends NodeCallback<BSTNode<K, V>>
Parameters
- keyNodeEntryOrPredicate:
      | undefined
      | null
      | K
      | BSTNode<K, V>
      | [undefined | null | K, undefined | V]
      | NodePredicate<BSTNode<K, V>>
- callback: C
- OptionaliterationType: IterationType
Returns ReturnType<C>
Inherited from BST.lower
- Defined in data-structures/binary-tree/bst.ts:1126

map

map<MK, MV, MR>(callback, options?, thisArg?): RedBlackTree<MK, MV, MR>
Transform entries into a like-kind red-black tree with possibly different key/value types.
Type Parameters
- MK = K
- MV = V
- MR = any
Parameters
- callback: EntryCallback<K, undefined | V, [MK, MV]>
  Mapping function from (key, value, index, tree) to a new [key, value].
- Optionaloptions: Partial<RedBlackTreeOptions<MK, MV, MR>>
  See parameter type for details.
- OptionalthisArg: unknown
  See parameter type for details.
Returns RedBlackTree<MK, MV, MR>
A new RedBlackTree with mapped entries.

Remarks
Time O(n), Space O(n)
Implementation of IBinaryTree.map
Overrides BST.map
- Defined in data-structures/binary-tree/red-black-tree.ts:463

merge

merge(anotherTree): void
Merges another tree into this one by adding all its nodes.
Parameters
- anotherTree: BinaryTree<K, V, R>
  The tree to merge.
Returns void
Remarks
Time O(N * M), same as addMany, where N is the size of anotherTree and M is the size of this tree. Space O(M) (from add).
Implementation of IBinaryTree.merge
Inherited from BST.merge
- Defined in data-structures/binary-tree/binary-tree.ts:776

morris

morris(): (undefined | K)[]
Returns (undefined | K)[]
Implementation of IBinaryTree.morris
Inherited from BST.morris
- Defined in data-structures/binary-tree/binary-tree.ts:1713
morris<C>(callback?, pattern?, startNode?): ReturnType<C>[]
Type Parameters
- C extends NodeCallback<BinaryTreeNode<K, V>>
Parameters
- Optionalcallback: C
- Optionalpattern: DFSOrderPattern
- OptionalstartNode:
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>
Returns ReturnType<C>[]
Implementation of IBinaryTree.morris
Inherited from BST.morris
- Defined in data-structures/binary-tree/binary-tree.ts:1715

perfectlyBalance

perfectlyBalance(iterationType?): boolean
Rebuilds the tree to be perfectly balanced.
Parameters
- OptionaliterationType: IterationType = ...
  The traversal method for the initial node export.
Returns boolean
True if successful, false if the tree was empty.

Remarks
Time O(N) (O(N) for DFS, O(N) for sorted build). Space O(N) for node array and recursion stack.
Inherited from BST.perfectlyBalance
- Defined in data-structures/binary-tree/bst.ts:1274

print

print(options?, startNode?): void
Prints a visual representation of the tree to the console.
Parameters
- Optionaloptions: BinaryTreePrintOptions
  Options to control the output.
- OptionalstartNode:
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V> = ...
  The node to start printing from.
Returns void
Remarks
Time O(N) (via toVisual). Space O(N*H) or O(N^2) (via toVisual).
Inherited from BST.print
- Defined in data-structures/binary-tree/binary-tree.ts:1922

rangeSearch

rangeSearch(range): (undefined | K)[]
Parameters
- range: Range<K> | [K, K]
Returns (undefined | K)[]
Inherited from BST.rangeSearch
- Defined in data-structures/binary-tree/bst.ts:685
rangeSearch<C>(range, callback, startNode?, iterationType?): ReturnType<C>[]
Type Parameters
- C extends NodeCallback<BSTNode<K, V>>
Parameters
- range: Range<K> | [K, K]
- callback: C
- OptionalstartNode:
      | null
      | K
      | BSTNode<K, V>
      | [undefined | null | K, undefined | V]
- OptionaliterationType: IterationType
Returns ReturnType<C>[]
Inherited from BST.rangeSearch
- Defined in data-structures/binary-tree/bst.ts:687

reduce

reduce<U>(callbackfn, initialValue): U
Reduce entries into a single accumulator.
Type Parameters
- U
Parameters
- callbackfn: ReduceEntryCallback<K, undefined | V, U>
  (acc, value, key, index, self) => acc.
- initialValue: U
  Initial accumulator.
Returns U
Final accumulator.

Remarks
Time O(n), Space O(1)
Implementation of IBinaryTree.reduce
Inherited from BST.reduce
- Defined in data-structures/base/iterable-entry-base.ts:171

refill

refill(keysNodesEntriesOrRaws, values?): void
Clears the tree and refills it with new items.
Parameters
- keysNodesEntriesOrRaws: Iterable<
      | undefined
      | null
      | K
      | R
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>, any, any>
  An iterable of items to add.
- Optionalvalues: Iterable<undefined | V, any, any>
  An optional parallel iterable of values.
Returns void
Remarks
Time O(N) (for clear) + O(N * M) (for addMany) = O(N * M). Space O(M) (from addMany).
Implementation of IBinaryTree.refill
Inherited from BST.refill
- Defined in data-structures/binary-tree/binary-tree.ts:787

search

search(keyNodeEntryOrPredicate, onlyOne?): (undefined | K)[]
Parameters
- keyNodeEntryOrPredicate:
      | undefined
      | null
      | K
      | BSTNode<K, V>
      | [undefined | null | K, undefined | V]
      | NodePredicate<BSTNode<K, V>>
      | Range<K>
- OptionalonlyOne: boolean
Returns (undefined | K)[]
Implementation of IBinaryTree.search
Inherited from BST.search
- Defined in data-structures/binary-tree/bst.ts:562
search<C>(keyNodeEntryOrPredicate, onlyOne, callback, startNode?, iterationType?): ReturnType<C>[]
Type Parameters
- C extends NodeCallback<BSTNode<K, V>>
Parameters
- keyNodeEntryOrPredicate:
      | undefined
      | null
      | K
      | BSTNode<K, V>
      | [undefined | null | K, undefined | V]
      | NodePredicate<BSTNode<K, V>>
      | Range<K>
- onlyOne: boolean
- callback: C
- OptionalstartNode:
      | null
      | K
      | BSTNode<K, V>
      | [undefined | null | K, undefined | V]
- OptionaliterationType: IterationType
Returns ReturnType<C>[]
Implementation of IBinaryTree.search
Inherited from BST.search
- Defined in data-structures/binary-tree/bst.ts:574

set

set(keyNodeOrEntry, value?): boolean
Adds or updates a new node to the tree.
Parameters
- keyNodeOrEntry:
      | undefined
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>
  The key, node, or entry to add or update.
- Optionalvalue: V
  The value, if providing just a key.
Returns boolean
True if the addition was successful, false otherwise.

Remarks
Time O(log N), For BST, Red-Black Tree, and AVL Tree subclasses, the worst-case time is O(log N). This implementation adds the node at the first available position in a level-order (BFS) traversal. This is NOT a Binary Search Tree insertion. Time O(N), where N is the number of nodes. It must traverse level-by-level to find an empty slot. Space O(N) in the worst case for the BFS queue (e.g., a full last level).
Implementation of IBinaryTree.set
Inherited from BST.set
- Defined in data-structures/binary-tree/binary-tree.ts:709

setMany

setMany(keysNodesEntriesOrRaws, values?): boolean[]
Adds or updates multiple items to the tree.
Parameters
- keysNodesEntriesOrRaws: Iterable<
      | undefined
      | null
      | K
      | R
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V>, any, any>
  An iterable of items to add or update.
- Optionalvalues: Iterable<undefined | V, any, any>
  An optional parallel iterable of values.
Returns boolean[]
An array of booleans indicating the success of each individual add operation.

Remarks
Time O(N * M), where N is the number of items to add and M is the size of the tree at insertion (due to O(M) add operation). Space O(M) (from add) + O(N) (for the inserted array).
Inherited from BST.setMany
- Defined in data-structures/binary-tree/binary-tree.ts:761

some

some(predicate, thisArg?): boolean
Test whether any entry satisfies the predicate.
Parameters
- predicate: EntryCallback<K, undefined | V, boolean>
  (key, value, index, self) => boolean.
- OptionalthisArg: any
  Optional this for callback.
Returns boolean
true if any passes; otherwise false.

Remarks
Time O(n), Space O(1)
Implementation of IBinaryTree.some
Inherited from BST.some
- Defined in data-structures/base/iterable-entry-base.ts:83

toArray

toArray(): [K, undefined | V][]
Converts data structure to [key, value] pairs.

Returns [K, undefined | V][]
Array of entries.

Remarks
Time O(n), Space O(n)
Inherited from BST.toArray
- Defined in data-structures/base/iterable-entry-base.ts:186

toVisual

toVisual(startNode?, options?): string
Generates a string representation of the tree for visualization.
Parameters
- OptionalstartNode:
      | null
      | K
      | [undefined | null | K, undefined | V]
      | BinaryTreeNode<K, V> = ...
  The node to start printing from.
- Optionaloptions: BinaryTreePrintOptions
  Options to control the output (e.g., show nulls).
Returns string
The string representation of the tree.

Remarks
Time O(N), visits every node. Space O(N*H) or O(N^2) in the worst case, as the string width can grow significantly.
Inherited from BST.toVisual
- Defined in data-structures/binary-tree/binary-tree.ts:1889

values

values(): IterableIterator<undefined | V, any, any>
Iterate over values only.

Returns IterableIterator<undefined | V, any, any>
Iterator of values.

Remarks
Time O(n), Space O(1)
Implementation of IBinaryTree.values
Inherited from BST.values
- Defined in data-structures/base/iterable-entry-base.ts:53

Class RedBlackTree<K, V, R>

Remarks

Example

Example

Example

Example

Type Parameters

Hierarchy (view full)

Implements

Index

Properties

Accessors

Methods

Properties

Protected_comparator

Remarks

Accessors

comparator

Returns Comparator<K>

Remarks

isDuplicate

Returns boolean

Remarks

isMapMode

Returns boolean

Remarks

NIL

Returns BinaryTreeNode<K, V>

Remarks

root

Returns undefined | RedBlackTreeNode<K, V>

Remarks

size

Returns number

Remarks

store

Returns Map<K, undefined | V>

Remarks

toEntryFn

Returns undefined | ToEntryFn<K, V, R>

Remarks

Methods

Protected_bound

Parameters

Returns undefined | BSTNode<K, V>

Protected_boundByKey

Parameters

Returns undefined | BSTNode<K, V>

Protected_boundByPredicate

Parameters

Returns undefined | BSTNode<K, V>

Protected_clearNodes

Returns void

Remarks

Protected_clearValues

Returns void

Remarks

Protected_clone

Parameters

Returns void

Remarks

Protected_compare

Parameters

Returns number

Remarks

Protected_createDefaultComparator

Returns Comparator<K>

Remarks

Protected_createInstance

Type Parameters

Parameters

Returns this

Remarks

Protected_createLike

Type Parameters

Parameters

Returns RedBlackTree<TK, TV, TR>

Remarks

Protected_DEFAULT_NODE_CALLBACK

Parameters

`Protected`_comparator

`Protected`_bound

`Protected`_boundByKey

`Protected`_boundByPredicate

`Protected`_clearNodes

`Protected`_clearValues

`Protected`_clone

`Protected`_compare

`Protected`_createDefaultComparator

`Protected`_createInstance

`Protected`_createLike

`Protected`_DEFAULT_NODE_CALLBACK

`Protected`_deleteByKey

`Protected`_deleteFixup

`Protected`_dfs

`Protected`_displayAux

`Protected`_ensurePredicate

`Protected`_extractKey

`Protected`_floorByKey

`Protected`_floorByPredicate

`Protected`_getIterator

`Protected`_insert

`Protected`_insertFixup

`Protected`_isPredicate

`Protected`_keyValueNodeOrEntryToNodeAndValue

`Protected`_leftRotate

`Protected`_lowerByKey