Introduction to Stacks & Queues

[!NOTE] This module explores the core principles of Introduction to Stacks & Queues, deriving solutions from first principles and hardware constraints to build world-class, production-ready expertise.

1. The Hook: Rules of the Road

We’ve learned Arrays (random access) and Linked Lists (flexible size). But sometimes, unlimited power leads to bugs.

Stacks and Queues are not new data structures. They are Linear Data Structures with strict rules on how you add and remove data. By restricting access, we gain architectural safety and performance guarantees.

2. The 4 Pillars of Stack & Queue Mastery

Pillar Focus Why it matters
1. Intuition Rules over Access Knowing when to use LIFO vs FIFO.
2. Rigor Amortized Analysis Proving why nested Monotonic loops are O(N).
3. Hardware The Call Stack Understanding stack frames and recursion depth.
4. Patterns Monotonic & Deques Optimizing range queries from O(N2) to O(N).

3. The Stack: Last In, First Out (LIFO)

Think of a Stack of Plates.

  • You put a new plate on top.
  • You can only remove the plate from the top.
  • The first plate you put down is the last one you’ll get back.

Real World Analogy: Browser History

  1. Visit google.com. (Push google)
  2. Click link to wikipedia.org. (Push wiki)
  3. Click link to react.dev. (Push react)
  4. Hit Back button. (Pop react → Return to wiki)

4. The Queue: First In, First Out (FIFO)

Think of a Line at Starbucks.

  • You join the line at the back (Enqueue).
  • The barista serves the person at the front (Dequeue).
  • First person to arrive is the first to get coffee.

Real World Analogy: Printer Spool

  1. User A sends doc1.pdf. (Enqueue doc1)
  2. User B sends image.png. (Enqueue image)
  3. Printer finishes current job.
  4. Printer asks: “Who’s next?” (Dequeue doc1).

5. Interactive: Structure Visualizer

See the difference in data flow.

Stack (LIFO)

↑ Top

Queue (FIFO)

← Front      Back ←
Ready.

6. Hardware Reality: The Call Stack

The most famous Stack is inside your CPU. Every time you call a function, a Stack Frame is pushed.

What’s in a Stack Frame?

  1. Return Address: Where the CPU should go after the function finishes.
  2. Parameters: Values passed to the function.
  3. Local Variables: Temporary data used inside the function.

The Recursion Connection

Recursion is just a series of Push operations. If your recursion goes too deep:

  1. The Stack grows until it hits the memory limit.
  2. The CPU throws a Stack Overflow error.
  3. This is why recursive space complexity is O(\text{depth}).

Next Steps

Now that you know the rules, let’s learn how to implement these structures with maximum efficiency.

Next: Stack Operations