Lesson notes
These notes explain the problem and current implementation. They are a reading companion, not a verbatim transcript of the recording.
A stack processes values in last-in, first-out order. Pushing adds a new top, popping removes that top, and peeking reads it without removal. The recording connects this behavior to function calls and interview problems. Once you can track the top after each operation, bracket matching and explicit depth-first worklists become easier to explain.
Follow the most recent unfinished work
Push A, B, then C. The next pop returns C, leaving B at the top. A later push of D makes D the next returned item. A trace should track order and size, including the transition from one item to empty. Reading an empty stack needs a defined result or error behavior.
Bracket matching uses the stack to remember openings whose closings have not appeared yet. A closing bracket must match the most recent opening. Remembering only the counts of each bracket type loses nesting order: equal counts do not make ([)] valid. That example explains why the stack stores ordered unfinished obligations.
Distinguish the data structure from the call stack
Function execution also retains unfinished work. A caller may need local values and a return location after a nested call completes. Recursive algorithms build a chain of such frames. A stack overflow means that this call stack exceeds its available capacity; it does not imply that the entire computer has no memory remaining.
An explicit stack can move the algorithm's worklist into ordinary program storage and make its processing order visible. That does not automatically reduce total memory. A deep traversal still needs somewhere to retain its unfinished branches, and the chosen representation determines the associated overhead.
Explain endpoint and growth costs
A linked stack changes a fixed number of references per push or pop. A dynamic array is also a convenient stack representation at its end. Appending may have amortized constant cost because an occasional resize copies existing entries. Removing from the front would use the wrong endpoint for that representation.
Continue with Implement a Stack for the link updates, Valid Brackets for nesting, and Max Min Stack for an augmented stack that retains extrema. For each example, state exactly what the stored entries mean after every operation rather than only naming the container.