Listas Ligadas e Pilhas
Beyond Arrays - Dynamic Data
Arrays are brilliant when you know the size of your data upfront. But what happens when data arrives unpredictably - a stream of sensor readings, a queue of tasks for an AI to process, or a conversation history that grows with every message? You need structures that grow and shrink gracefully.
Enter linked lists, stacks, and queues - the dynamic trio.
Linked Lists - Nodes and Pointers
A linked list stores items as a chain of nodes. Each node holds two things: the data itself, and a pointer (reference) to the next node in the chain.
[data: "A" | next: →] → [data: "B" | next: →] → [data: "C" | next: null]
Unlike arrays, linked list nodes don't sit side by side in memory. They can be scattered anywhere - the pointer simply tells you where to find the next one.
Linked Lists vs Arrays
| Operation | Array | Linked List | |-----------|-------|-------------| | Access by index | O(1) ⚡ | O(n) 🐢 | | Insert at beginning | O(n) 🐢 | O(1) ⚡ | | Insert in middle | O(n) 🐢 | O(1)* ⚡ | | Delete from middle | O(n) 🐢 | O(1)* ⚡ | | Memory usage | Compact | Extra (pointers) |
*Once you've found the position - finding it is still O(n).
When Linked Lists Win
- Frequent insertions and deletions: If you're constantly adding and removing items from the middle of a collection, linked lists avoid the costly shifting that arrays require.
- Unknown size: When you don't know how many items you'll store, linked lists grow one node at a time without needing to resize.
- Building other structures: Stacks, queues, and more complex structures are often built on top of linked lists.
Your browser's tab bar lets you open, close, and rearrange tabs freely. Would an array or a linked list be a better fit for managing the list of open tabs? Consider what happens when you close a tab in the middle.
Stacks - Last In, First Out (LIFO)
A stack works exactly like a stack of plates: you add to the top and remove from the top. The last item placed on the stack is the first one taken off.
Push "A" → [A]
Push "B" → [A, B]
Push "C" → [A, B, C]
Pop → [A, B] (removed "C")
Pop → [A] (removed "B")
Two operations define a stack:
- Push: Add an item to the top.
- Pop: Remove the item from the top.
Both are O(1) - instant, regardless of stack size.
Stacks in the Real World
- Undo/Redo: Every text editor maintains a stack of actions. Press Ctrl+Z and the most recent action is popped off and reversed.
- Browser back button: Your browsing history is a stack. Each new page is pushed; clicking "back" pops the current page.
- Call stacks: When your code calls a function, that function is pushed onto the call stack. When it finishes, it's popped off. This is how programmes keep track of where they are.
When you see a "stack overflow" error, it literally means the call stack has run out of space - usually because a function keeps calling itself without stopping (infinite recursion). The famous developer Q&A site Stack Overflow is named after this very error.
Stacks in AI
- Expression evaluation: AI compilers and interpreters use stacks to evaluate mathematical expressions in neural network computation graphs.
- Backtracking algorithms: When an AI explores possible solutions (like solving a maze), it uses a stack to remember where it's been so it can backtrack.
- Depth-first search: Traversing trees and graphs depth-first naturally uses a stack - we'll explore this in the next lesson.
You're implementing an 'undo' feature for a drawing application. Which data structure best models the history of actions?
Queues - First In, First Out (FIFO)
A queue works like a queue at a shop: the first person to join is the first person served. Items are added at the back and removed from the front.
Enqueue "A" → [A]
Enqueue "B" → [A, B]
Enqueue "C" → [A, B, C]
Dequeue → [B, C] (removed "A")
Dequeue → [C] (removed "B")
Two operations define a queue:
- Enqueue: Add an item to the back.
- Dequeue: Remove the item from the front.
Queues in the Real World
- Print queues: Documents are printed in the order they're submitted.
- Task scheduling: Operating systems use queues to manage which processes run next.
- Message queues: Web applications use queues (like RabbitMQ or Kafka) to handle thousands of requests without dropping any.
Queues in AI
- Breadth-first search (BFS): Exploring a graph level by level uses a queue - we'll see this in the trees and graphs lesson.
- Training data pipelines: Training data is loaded into queues so the GPU always has the next batch ready, preventing idle time.
- Request handling: When thousands of users query an AI API simultaneously, requests enter a queue and are processed in order.
An AI API receives 10,000 requests per second. Which structure ensures requests are processed in the order they arrive?
There's also a priority queue, where items are dequeued based on priority rather than arrival order. AI systems use priority queues to process urgent tasks first - for example, a self-driving car might prioritise obstacle detection over route planning.
Real AI Use: Sequence Processing and Memory Management
Sequence Processing
Language models process text as sequences. Under the hood, frameworks like PyTorch and TensorFlow use linked-list-like structures to build computation graphs - chains of operations where each step points to the next.
Memory Management in ML Frameworks
When training a neural network, memory is constantly allocated and freed as tensors (multi-dimensional arrays) are created and destroyed. Memory allocators often use linked lists of free memory blocks, finding suitable spaces for new tensors.
A chatbot needs to remember the last 10 messages in a conversation but discard older ones. Would you use a stack, a queue, or something else? What happens when the 11th message arrives?
Which statement about linked lists is FALSE?
The undo history in most applications has a limit - typically 100 to 1,000 actions. Without this limit, the stack would consume ever-growing memory. Some advanced systems use a combination of a stack and a queue (a "deque") to keep the most recent actions whilst discarding the oldest.
Key Takeaways
- Linked lists excel at dynamic data with frequent insertions and deletions, but sacrifice direct index access.
- Stacks (LIFO) power undo systems, backtracking, and depth-first traversal.
- Queues (FIFO) ensure fair ordering in task scheduling, BFS, and request handling.
- These structures often work behind the scenes in AI frameworks, managing memory and processing sequences.
- Choosing between arrays and linked structures depends on your access patterns - random access favours arrays, dynamic modification favours linked lists.