This page assumes you have seen nothing. Before you meet a single algorithm in the parent topic, every word, symbol, and picture it leans on is built here, one on top of the next.
Think of the difference between a queue at a shop (first person in line served first) and a pile of books on your desk (you grab the top one). Same items, opposite access rule. The topic ahead lives entirely inside the "pile of books" rule.
The picture above is the whole subject in one image: a vertical pile. You add to the top, you remove from the top. Nowhere else.
The parent note opens with the phrase LIFO. Let's earn every letter.
The picture: imagine dropping plates onto a spring-loaded dispenser. The plate you drop last sits on top, so it is the plate you take first. The very first plate is buried at the bottom and leaves last.
The algorithms are written using two verbs, push and pop. If those are new, everything else is unreadable — so here they are from zero.
Look at the figure: the left board pushesC — it lands above B. The right board pops — C leaves, revealing B again. Notice we never reach A at the bottom until everything above is gone. That "buried" feeling is LIFO.
Everything above lives in one prerequisite note: Stack — ADT and Implementation. ADT means Abstract Data Type — a promise about what operations do (push/pop/empty) without caring how they're built inside.
The top row of the figure shows proper nesting as boxes cleanly inside boxes. The bottom row shows crossing — the [ box and ( box slice through each other, which no physical container can do. That impossibility is exactly why ([)] is called unbalanced, and why a mere count of brackets can't detect it: counting ignores this box-inside-box order.
The parent's second application converts between two ways of writing math. Both are just word orders for the same calculation.
The figure shows the same expression a + b in both layouts. In infix the + sits in the gap; in postfix it waits at the end, after it has both its operands lined up.
prec(^)>prec(×,÷)>prec(+,−)
You'll meet these ranking rules in full detail in Operator Precedence and Associativity, and you'll use the postfix result in Postfix Evaluation Algorithm and Expression Trees and Evaluation.
The parent contrasts stacks with queues to sharpen your intuition: nesting needs reverse order (LIFO), a fair line needs arrival order (FIFO). See Queues for the full picture.
Recall One-line contrast to lock it in
Stack vs Queue in one sentence? ::: A stack reverses order (last in, first out); a queue preserves order (first in, first out).
