Foundation Module

Advanced Data Structures

Beyond arrays and linked lists: heaps, balanced trees, hash tables, and union-find - the building blocks of efficient algorithms.

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12 hours

5 key concepts

Key Principles

Core Concepts

Right Tool for the Job

Each data structure excels at specific operations. Choosing the right one can change O(n) to O(1).

Trade-offs

No structure is best at everything. Fast lookups often mean slower inserts. Understand the trade-offs.

Abstract vs Concrete

Distinguish between abstract types (Stack, Queue) and concrete implementations (Array, Linked List).

Linear Structures

Array

Contiguous memory, random access

access: O(1)search: O(n)insert: O(n)delete: O(n)

Linked List

Node-based, efficient insertions

access: O(n)search: O(n)insert: O(1)delete: O(1)

Stack

LIFO - Last In, First Out

push: O(1)pop: O(1)peek: O(1)

Queue

FIFO - First In, First Out

enqueue: O(1)dequeue: O(1)peek: O(1)

Trees

Binary Search Tree

Ordered binary tree

search: O(log n)insert: O(log n)delete: O(log n)

AVL Tree

Self-balancing BST

search: O(log n)insert: O(log n)delete: O(log n)

Red-Black Tree

Balanced with color properties

search: O(log n)insert: O(log n)delete: O(log n)

B-Tree

Multi-way tree for disk access

search: O(log n)insert: O(log n)delete: O(log n)

Heaps & Priority Queues

Binary Heap

Complete binary tree with heap property

insert: O(log n)extractMin: O(log n)peek: O(1)

Fibonacci Heap

Amortized efficient operations

insert: O(1)extractMin: O(log n)decreaseKey: O(1)

Hash-Based

Hash Table

Average case with good hash function

search: O(1)insert: O(1)delete: O(1)

Hash Set

Unique elements, fast membership

contains: O(1)add: O(1)remove: O(1)

Specialized

Trie

Prefix tree for strings (m = key length)

search: O(m)insert: O(m)prefix: O(m)

Union-Find

Disjoint set with path compression

find: O(α(n))union: O(α(n))

Segment Tree

Range queries and updates

query: O(log n)update: O(log n)

Data Structures in AI Coding

Ask AI with Context

"Use a heap for..." or "We need O(1) lookup so use a hash map" guides AI to generate efficient code.

Verify Complexity

When AI generates code, check if it's using the right data structure. A list where a set is needed can tank performance.

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