Balanced Dressing Room

Ever wondered why computers need a stack to check if parentheses are balanced? Let’s see it in action with a metaphor that makes it impossible to forget.

Slide 1 — The Dressing Room Rule

You try on clothes in layers. You can only take off the last one you put on.

With a single type of clothing, a simple counter tells us if the sequence is valid: just track how many items are on.

Slide 2 — A Valid Sequence

All garments come on and off in the correct order. Notice the counter going up and down.

✅ We never try to remove a garment that wasn’t on top.

Slide 3 — The Impossible Sequence

What happens when we try to remove a garment that’s not on top?

With only one type, the counter catches this: we go negative! But what if we have multiple types?

Slide 4 — Multiple Types: T-Shirt, Sweater, Jacket

Now we introduce different garment types. Each has a different shape:

• T - T-Shirt (basic)
• S - Sweater (long sleeves)
• J - Jacket (open front)

With multiple types, we need to remember WHAT was put on last, not just count!

Slide 5 — The Tricky Example

Here’s the catch: the count per type might look balanced, but the sequence is impossible.

❌ You can’t remove the T-Shirt when the Sweater is on top!

The counters say everything is fine (1 T, 1 S on), but order matters.

Slide 6 — The Final Reveal: Parentheses!

Now watch the labels transform…

The sequence ([{}]) is the same as putting on T-Shirt, Sweater, Jacket and taking them off in reverse!

• ( = PUT T-Shirt → ) = TAKE OFF T-Shirt
• [ = PUT Sweater → ] = TAKE OFF Sweater
• { = PUT Jacket → } = TAKE OFF Jacket

The Insight

Balancing parentheses is exactly like getting dressed in layers without breaking the laws of physics.

A counter works for a single type, but with multiple types (like (), [], {}), you need a stack to remember the order.

That’s why the classic “balanced parentheses” algorithm uses a stack: it’s simulating a dressing room! 🧥