---
sidebar_label: "OVERVIEW"
description: "Complete overview of all 20+ data structures: trees, heaps, graphs, queues, linked lists, hash maps, and more."
title: "Data Structures Overview — Trees, Heaps, Graphs, Queues"
keywords: ["typescript data structures overview", "red black tree", "heap", "priority queue", "trie", "graph", "deque", "treemap", "treeset"]
---
# OVERVIEW

A quick-reference guide to all structures, common operations, and usage patterns. For complete API details with method signatures and examples, see the **[Full API Docs](https://data-structure-typed-docs.vercel.app/)**.

**[Back to README](/docs/guide/quick-start) • [API Docs](https://data-structure-typed-docs.vercel.app/) • [Real-World Examples](/guide/guides.md) • [Performance](/guide/performance.md)**

---

## Table of Contents

1. [Quick Reference Table](#quick-reference-table)
2. [All Data Structures](#all-data-structures)
3. [CRUD Operations](#crud-operations)
4. [Common Methods](#common-methods)
5. [TypeScript Support](#typescript-support)

---

## Quick Reference Table

| Data Structure    | Best Use Case             | Time Complexity          | Space  |
|-------------------|---------------------------|--------------------------|--------|
| **Array**         | Direct indexed access     | O(n) insert/delete       | O(n)   |
| **Linked List**   | Dynamic size, fast insert | O(n) search, O(1) insert | O(n)   |
| **Stack**         | Undo/redo, DFS            | O(1) all                 | O(n)   |
| **Queue**         | FIFO processing           | O(1) all                 | O(n)   |
| **Deque**         | Head/tail operations      | O(1) all                 | O(n)   |
| **Binary Tree**   | Hierarchical data         | O(n) avg                 | O(n)   |
| **BST**           | Sorted search             | O(log n) avg             | O(n)   |
| **RedBlackTree**  | Guaranteed sorted         | O(log n) guaranteed      | O(n)   |
| **AVL Tree**      | Balanced sorted           | O(log n) guaranteed      | O(n)   |
| **Heap**          | Priority queue            | O(log n) add/remove      | O(n)   |
| **PriorityQueue** | Task scheduling           | O(log n) add/poll        | O(n)   |
| **Trie**              | Prefix search                         | O(m+k) search                | O(26n)     |
| **Graph**             | Networks, paths                       | Varies                       | O(V+E)     |
| **SkipList**          | Sorted KV (probabilistic)             | O(log n) avg all ops         | O(n log n) |
| **SegmentTree**       | Range queries (sum/min/max/custom)    | O(log n) query/update        | O(n)       |
| **BinaryIndexedTree** | Prefix sums, frequency counting       | O(log n) query/update        | O(n)       |
| **Matrix**            | 2D grid arithmetic                    | O(n²) add, O(n³) multiply    | O(n²)      |

---

## All Data Structures

### Stack Structure

#### Stack

```typescript
import { Stack } from 'data-structure-typed';

const stack = new Stack<number>([1, 2]);
stack.push(3);                // add to top
const top = stack.pop();      // Remove from top - O(1)
const peek = stack.peek();    // View top
stack.print();                // [1, 2]
```



### Linear Structures

#### Queue

```typescript
import { Queue } from 'data-structure-typed';

const queue = new Queue<number>([1, 2]);
queue.push(3);                   // add to back
const first = queue.shift();     // Remove from front - O(1)
const length = queue.length;     // Current length
queue.print();                   // [2, 3]
```

#### Deque

```typescript
import { Deque } from 'data-structure-typed';

const deque = new Deque<number>([1, 2]);
deque.push(3);               // Add to back
deque.unshift(0);            // Add to front
deque.pop();                 // Remove from back - O(1)
deque.shift();               // Remove from front - O(1)
deque.print();               // [1, 2]
```

#### Linked Lists

```typescript
import { SinglyLinkedList, DoublyLinkedList } from 'data-structure-typed';

const singly = new SinglyLinkedList<number>([1, 2]);
const doubly = new DoublyLinkedList<number>([1, 2]);

singly.push(3);              // Add to end
singly.addAt(1, 99);         // Insert at index - O(n)
singly.deleteAt(2);          // Delete at index - O(n)
singly.print();              // [1, 99, 3]

doubly.push(3);              // Add to end
doubly.addAt(1, 99);         // Insert at index - O(n)
doubly.deleteAt(2);          // Delete at index - O(n)
doubly.print();              // [1, 99, 3]
```

### Tree Structures

#### Binary Search Tree (BST)

```typescript
import { BST } from 'data-structure-typed';

const bst = new BST<number>([1, 3, 5, 8, 6, 2, 4, 7]);
bst.add(9);                   // Add elements
bst.has(5);                  // Check existence - O(log n) avg
bst.delete(1);               // Remove - O(log n) avg
bst.print();                 // Visual representation
//      ___4___
//     /       \
//    2_       _6_
//      \     /   \
//       3    5    7_
//                   \
//                    8_
//                      \ 
//                      9 
```

#### Red-Black Tree

```typescript
import { RedBlackTree } from 'data-structure-typed';

const rbTree = new RedBlackTree<number, string>([[1, 'Alice'], [2, 'Bob'], [3, 'Chris']]);
rbTree.set(4, 'Dan');               // Add key-value
rbTree.get(1);                      // 'Alice'
rbTree.delete(2);                   // Remove - O(log n) guaranteed
console.log([...rbTree.values()]);  // ['Alice', 'Chris', 'Dan'] Automatically sorted
rbTree.print()
//   _3_
//  /   \
//  1    4

```

#### AVL Tree

```typescript
import {AVLTree} from 'data-structure-typed';

const avl = new AVLTree<number>([5, 4, 3, 8, 1]);
avl.add(9);
avl.isAVLBalanced();         // Check balance
avl.delete(3);               // Auto-rebalances
avl.print()
//    ___5_    
//   /     \   
//   1_     8_  
//     \      \ 
//      4      9 
```

#### TreeMap (Ordered Map)

```typescript
import { TreeMap } from 'data-structure-typed';

const tm = new TreeMap<number, string>([[3, 'c'], [1, 'a'], [2, 'b']]);
tm.set(4, 'd');                    // Set key-value - O(log n)
tm.get(2);                         // 'b' - O(log n)
tm.has(3);                         // true
tm.delete(1);                      // Remove - O(log n)

// Navigation — Java NavigableMap-style
tm.first();                        // [2, 'b'] — smallest entry
tm.last();                         // [4, 'd'] — largest entry
tm.ceiling(3);                     // [3, 'c'] — smallest >= 3
tm.floor(2);                       // [2, 'b'] — largest <= 2
tm.higher(2);                      // [3, 'c'] — strictly > 2
tm.lower(3);                       // [2, 'b'] — strictly < 3

// Iteration (sorted order)
console.log([...tm.keys()]);       // [2, 3, 4]
console.log([...tm.values()]);     // ['b', 'c', 'd']

// Bulk operations
tm.setMany([[5, 'e'], [6, 'f']]);  // Set multiple at once

// Functional
const filtered = tm.filter((v, k) => k > 2);
const mapped = tm.map((v, k) => [k * 10, v!.toUpperCase()] as [number, string]);
```

#### TreeSet (Ordered Set)

```typescript
import { TreeSet } from 'data-structure-typed';

const ts = new TreeSet<number>([5, 3, 8, 1]);
ts.add(4);                         // Add - O(log n)
ts.has(3);                         // true
ts.delete(5);                      // Remove - O(log n)

// Navigation
ts.first();                        // 1
ts.last();                         // 8
ts.ceiling(4);                     // 4 — smallest >= 4
ts.floor(6);                       // 4 — largest <= 6
ts.higher(3);                      // 4 — strictly > 3
ts.lower(4);                       // 3 — strictly < 4

// Iteration (sorted order)
console.log([...ts.keys()]);       // [1, 3, 4, 8]

// Bulk operations
ts.addMany([10, 20, 30]);          // Add multiple at once
```

#### Order-Statistic Tree (Rank Queries)

Enable `enableOrderStatistic: true` on any tree-based structure to get O(log n) rank operations:

```typescript
import { RedBlackTree, TreeMap, TreeSet } from 'data-structure-typed';

// Works with RedBlackTree, TreeMap, TreeSet, TreeMultiMap, TreeMultiSet
const tree = new RedBlackTree<number, string>(
  [[100, 'Alice'], [85, 'Bob'], [92, 'Charlie'], [78, 'Diana']],
  { comparator: (a, b) => b - a, enableOrderStatistic: true }
);

// getByRank(k) — element at position k in tree order, O(log n)
tree.getByRank(0);                 // 100 (1st in tree order)
tree.getByRank(2);                 // 92  (3rd in tree order)

// getRank(key) — count of elements before key in tree order, O(log n)
tree.getRank(92);                  // 2

// rangeByRank(start, end) — elements between positions, O(log n + k)
tree.rangeByRank(0, 2);           // [100, 92, 85] — positions 0..2

// Also works with wrapper classes
const tm = new TreeMap<number, string>([], { enableOrderStatistic: true });
tm.set(10, 'a'); tm.set(20, 'b'); tm.set(30, 'c');
tm.getByRank(1);                   // [20, 'b']
tm.getRank(20);                    // 1

const ts = new TreeSet<number>([], { enableOrderStatistic: true });
ts.addMany([10, 20, 30]);
ts.getByRank(0);                   // 10
ts.getRank(30);                    // 2
```

### Heap & Priority Queue

#### Heap

```typescript
import { MinHeap, MaxHeap } from 'data-structure-typed';

const minHeap = new MinHeap<number>([5, 3, 8]);
minHeap.add(1);               // Add element - O(log n)
const min = minHeap.poll();   // Get minimum - O(log n)
const peek = minHeap.peek();  // View minimum - O(1)
```

#### Priority Queue

```typescript
import { MaxPriorityQueue } from 'data-structure-typed';

const pq = new MaxPriorityQueue<Task>([], {
  comparator: (a, b) => b.priority - a.priority
});
pq.add({ id: 1, priority: 5 });  // Add - O(log n)
const task = pq.poll();          // Remove highest - O(log n)
const size = pq.size;            // Current size
```

### Special Structures

#### Trie (Prefix Tree)

```typescript
import { Trie } from 'data-structure-typed';

const trie = new Trie(['apple', 'app', 'banana']);
trie.add('apply');
trie.getWords('app');        // ['apple', 'apply', 'app'] - O(m+k)
trie.has('apple');           // true
trie.hasPrefix('ap');        // true
```

#### Graph

```typescript
import { DirectedGraph, UndirectedGraph } from 'data-structure-typed';

const graph = new DirectedGraph<string>();
graph.addVertex('A');
graph.addVertex('B');
graph.addEdge('A', 'B', 1);  // Add edge with weight
graph.hasEdge('A', 'B');     // true
const {
  distMap, distPaths, preMap, seen, paths, minDist, minPath
} = graph.dijkstra('A', 'B', true, true)!; 
const order = graph.topologicalSort();
console.log(distMap)
console.log(distPaths)
console.log(preMap)
console.log(seen)
console.log(paths)
console.log(minDist)
console.log(minPath)  // Shortest path
console.log(order)    // DAG order
```

---

## CRUD Operations

### Create (Add)

```typescript
const tree = new RedBlackTree<number, string>();
tree.set(1, 'Alice');
tree.setMany([[2, 'Bob'], [3, 'Charlie']]);

// Heap
const heap = new MaxHeap<number>([10, 20]);
heap.add(15);

// Trie
const trie = new Trie(['hello']);
trie.add('world');

// Graph
const graph = new DirectedGraph<string>();
graph.addVertex('A');
graph.addEdge('A', 'B', 1);
```

### Read (Query)

```typescript
// Tree
tree.get(1);               // 'Alice'
tree.has(1);               // true
tree.size;                 // Number of elements

// Heap
heap.peek();               // Highest priority element
heap.size;                 // Current size

// Trie
trie.has('hello');            // true
trie.hasPrefix('hel');    // true

// Graph
graph.hasVertex('A');      // true
graph.hasEdge('A', 'B');   // true
graph.getNeighbors('A');   // Connected vertices
```

### Update (Modify)

```typescript
// Tree
tree.set(1, 'Alice Updated'); // Update value
tree.delete(1);               // Remove

// Heap
heap.pop();                    // Remove highest

// Graph
graph.deleteEdge('A', 'B');   // Remove edge
graph.deleteVertex('A');      // Remove vertex
```

### Delete

```typescript
// All structures support:
structure.clear();             // Remove all elements
structure.delete(key);         // Remove specific

// Conditional delete (BST-family and Deque)
tree.deleteWhere(node => node.key < 10);           // Delete all matching
tree.deleteWhere(node => node.key < 10, true);     // Delete first match only
tree.deleteWhere(new Range(5, 15));                 // Delete by range
deque.deleteWhere((val, idx) => val > 100);        // Deque predicate delete
```

---

## Common Methods

### Available on All Structures

```typescript
// Iteration
structure.forEach((value, key) => {
});
for (const item of structure) {
}

// Conversion
[...structure];                // Spread
Array.from(structure);         // Array conversion

// Array methods
structure.map((v, k) => v * 2);
structure.filter((v, k) => v > 5);
structure.reduce((acc, v) => acc + v, 0);
structure.find((v, k) => v === 5);
structure.some((v, k) => v > 10);
structure.every((v, k) => v > 0);

// Properties
structure.size;                // Element count
structure.isEmpty();           // Check empty
```

### Raw Data Mapping

Pass raw objects directly — no `.map()` pre-processing needed:

```typescript
// toElementFn — extract a field, store only that (Heap, Queue, Stack, LinkedList, Trie)
const heap = new MinHeap<number, User>(users, {
  toElementFn: u => u.age
});

// toEntryFn — split into key-value pairs (TreeMap, HashMap, SkipList)
const map = new TreeMap<number, User, User>(users, {
  toEntryFn: u => [u.id, u]
});

// comparator — store full objects, sort by a field (all sorted structures)
const set = new TreeSet<User>(users, {
  comparator: (a, b) => a.id - b.id
});
```

### Structure-Specific Methods

#### Trees

```typescript
tree.height;                   // Tree height (getter)
tree.isAVLBalanced();         // Balance check
tree.getNode(key);            // Get node object
tree.getHeight(key);          // Node height
tree.getLeftMost();           // Leftmost node
tree.getRightMost();          // Rightmost node
```

#### Deque

```typescript
deque.first;                  // View front (getter)
deque.last;                   // View back (getter)
deque.shift();                // Remove front - O(1)
deque.pop();                  // Remove back - O(1)
```

#### Graph

```typescript
graph.topologicalSort();      // DAG order
graph.dijkstra(start, end);   // Shortest path
graph.dfs(vertex);            // Depth-first traversal
graph.bfs(vertex);            // Breadth-first traversal
```

---

## TypeScript Support

### Full Generic Support

```typescript
// Custom type safety
const tree = new RedBlackTree<number, User>();
tree.set(1, { name: 'Alice', age: 30 });

const value = tree.get(1);  // Type: User | undefined

// Automatic inference
const numbers = new Deque<number>([1, 2]);
numbers.push(3);

// Custom comparators
const descending = new RedBlackTree<number, string>([], {
    comparator: (a, b) => b - a  // Sort descending
  });
```

### Type Safety Examples

```typescript
interface Task {
  id: string;
  priority: number;
  action: Promise<void>;
}

const pq = new MaxPriorityQueue<Task>(
  {
    comparator: (a, b) => a.priority - b.priority
  }
);

pq.add({
  id: '1', priority: 5, action: async () => {
  }
});

// Type checking catches errors
const task = pq.poll();
if (task) {
  // task is guaranteed to be Task
  await task.action;
}
```

---

## Complexity Chart

| Operation | Array | LinkedList | BST      | RBTree   | Heap     | Trie |
|-----------|-------|------------|----------|----------|----------|------|
| Access    | O(1)  | O(n)       | O(log n) | O(log n) | O(n)     | N/A  |
| Search    | O(n)  | O(n)       | O(log n) | O(log n) | O(n)     | O(m) |
| Insert    | O(n)  | O(1)       | O(log n) | O(log n) | O(log n) | O(m) |
| Delete    | O(n)  | O(1)       | O(log n) | O(log n) | O(log n) | O(m) |

---

## Common Patterns

### Iterator Pattern

```typescript
const tree = new RedBlackTree([5, 2, 8]);

// Works everywhere
const arr = [...tree.keys()];           // Spread
const set = new Set(tree.keys());       // Set constructor
for (const val of tree.values()) {
}      // for...of
const [first, ...rest] = tree.keys();   // Destructuring
```

### Filtering Pattern

```typescript
const tree = new RedBlackTree([
  [1, { active: true }],
  [2, { active: false }],
  [3, { active: true }]
]);

const inactive = tree
  .filter((val) => val?.active ?? false)
  .map((val, key) => [key, !val]);

console.log(...inactive);
```

### Sorting Pattern

```typescript
const data = [64, 34, 25, 12, 22, 11, 90];
const sorted = [...new RedBlackTree(data).keys()]; // Instant sort!
```

---

## SkipList

Probabilistic sorted containers. Interchangeable with `TreeMap`/`TreeSet`.

```typescript
import { SkipList } from 'data-structure-typed';

// Same API as TreeMap — drop-in replacement
const sl = new SkipList<number, string>([[3, 'c'], [1, 'a'], [2, 'b']]);
sl.set(4, 'd');                    // upsert — returns this (chainable)
sl.get(2);                         // 'b'
sl.has(5);                         // false
sl.delete(1);                      // true

// Navigation
sl.first();                        // [2, 'b']
sl.last();                         // [4, 'd']
sl.ceiling(2);                     // [2, 'b'] — smallest >= 2
sl.floor(3);                       // [3, 'c'] — largest <= 3
sl.higher(2);                      // [3, 'c'] — strictly > 2
sl.lower(3);                       // [2, 'b'] — strictly < 3
sl.rangeSearch([2, 4]);            // [[2,'b'],[3,'c'],[4,'d']]
sl.pollFirst();                    // [2, 'b'] — remove+return first

// Iteration (sorted order)
for (const [k, v] of sl) console.log(k, v);
[...sl.keys()];   // [3, 4]
[...sl.values()]; // ['c', 'd']

// Functional
sl.filter((v, k) => k > 2).toArray();   // [[3,'c'],[4,'d']]
sl.map((v, k) => [k * 10, v]);          // new SkipList
sl.reduce((acc, v) => acc + v!, '');    // 'cd'

// Custom comparator
const reversed = new SkipList<number, string>([], {
  comparator: (a, b) => b - a
});

// From objects via toEntryFn
type User = { id: number; name: string };
const users = new SkipList<number, User, User>(data, {
  toEntryFn: u => [u.id, u]
});
```

---

## SegmentTree

Range queries with any associative merge operation.

```typescript
import { SegmentTree } from 'data-structure-typed';

// Convenience factories (covers 90% of use cases)
const sumTree = SegmentTree.sum([1, 3, 5, 7, 9]);
const minTree = SegmentTree.min([5, 2, 8, 1, 9]);
const maxTree = SegmentTree.max([5, 2, 8, 1, 9]);

// Range query O(log n)
sumTree.query(1, 3);   // 15 (3+5+7)
minTree.query(0, 4);   // 1
maxTree.query(0, 2);   // 8

// Point update O(log n)
sumTree.update(2, 10); // replaces 5 with 10
sumTree.query(1, 3);   // 20 (3+10+7)

// Single element access O(1)
sumTree.get(2);        // 10

// Custom merge (gcd, product, etc.)
const gcd = (a: number, b: number): number => b === 0 ? a : gcd(b, a % b);
const gcdTree = new SegmentTree([12, 8, 6, 18], { merger: gcd, identity: 0 });
gcdTree.query(0, 3);   // 2

// Binary search on tree (ACL-style)
// maxRight(l, pred): find max r where pred(query(l, r)) is true
sumTree.maxRight(0, s => s <= 10);  // rightmost index where prefix ≤ 10

// Standard interface
[...sumTree];          // leaf values as array
sumTree.toArray();     // same
sumTree.size;          // 5
sumTree.clone();       // independent copy
```

---

## BinaryIndexedTree (Fenwick Tree)

Prefix sums and point updates in O(log n). Lighter than SegmentTree; use when you only need sums.

```typescript
import { BinaryIndexedTree } from 'data-structure-typed';

// Construct from size or array
const bit = new BinaryIndexedTree(6);
const bit2 = new BinaryIndexedTree([1, 3, 5, 7, 9, 11]);

// Point update: add delta
bit2.update(2, 4);    // index 2 += 4 → value becomes 9

// Point set: absolute value
bit2.set(0, 100);     // index 0 = 100

// Point query
bit2.get(2);          // 9

// Prefix sum [0..i]
bit2.query(3);        // sum of [0..3]

// Range sum [start..end]
bit2.queryRange(1, 3); // sum of [1..3]

// Binary search — requires non-negative values
bit2.lowerBound(10);  // smallest i where prefix sum [0..i] >= 10
bit2.upperBound(10);  // smallest i where prefix sum [0..i] > 10

// Standard interface
[...bit2];            // point values as array
bit2.toArray();       // same
bit2.size;            // 6
bit2.clone();
bit2.clear();
```

---

## Matrix

2D grid arithmetic. Correct, minimal — not competing with NumPy.

```typescript
import { Matrix } from 'data-structure-typed';

// Construction
const m = new Matrix([[1, 2, 3], [4, 5, 6]]);
Matrix.zeros(3, 4);       // 3×4 zero matrix
Matrix.identity(3);       // 3×3 identity matrix
Matrix.from([[1, 2], [3, 4]]); // from plain array

// Element access
m.get(0, 1);              // 2
m.set(0, 1, 99);          // returns boolean
m.size;                   // [2, 3]
m.rows;                   // 2
m.cols;                   // 3

// Arithmetic (returns new Matrix)
a.add(b);
a.subtract(b);
a.multiply(b);            // matrix multiplication
a.dot(b);                 // dot product
a.transpose();            // supports rectangular matrices
a.inverse();              // square matrices only

// Standard interface
[...m];                   // array of rows (copies)
m.toArray();              // deep copy as number[][]
m.flatten();              // [1,2,3,4,5,6] row-major
m.forEach((v, r, c) => ...);
m.map(v => v * 2);        // new Matrix
m.clone();                // independent copy
m.isEmpty();              // true if 0 rows or 0 cols
```

---

**Need details?** Check [GUIDES.md](/guide/guides.md) for real-world examples.

**Performance curious?** See [PERFORMANCE.md](/guide/performance.md) for benchmarks.