Draw the stack after each operation

Updated Oct 7, 2026

Before coding, write the stack (bottom to top) after every push, pop, or pop-while step on a 3–5 item example. If you cannot, you do not yet know the invariant. Each line of code should match one arrow on that trace.

What to focus on

Include tops, sizes, and any extra pair fields. Nested bracket traces and next-greater traces are the two drawings you will reuse most.

Worked examples

a = [], push 4, push 1, pop, push 9

s = "([])"

a = [2, 1, 3]

Try it

Write drawOps(). No arguments. Print the stack after every step in the three traces. Push 4, push 1, pop, push 9: [4] then [4, 1] then [4] then [4, 9]. a = [], push 4, push 1, pop, push 9 → four drawings. s = \"([])\" → four drawings. a = [2, 1, 3] → index stack drawings.

Every pop happens on a non-empty stack. "([])" is well-formed. a may be empty. Draw the snapshots.