Stacks and Queues

Stack Push/Pop

Push values onto a stack and pop them back in last-in, first-out order.

Algorithm

Basic Implementation

basic.dart 
String render(List<int> values) => values.join(' -> ');

void main() {
  final stack = <int>[];
  for (final value in [10, 20, 30]) { stack.add(value); }
  final popped = <int>[];
  while (stack.isNotEmpty) { popped.add(stack.removeLast()); }
  print(render(popped));
}

The same three values from the trace are shown as stack states. The top cell is the next value a pop removes.

Step 1 - Start empty

There is no top value yet.

Empty stack before any push.top of stack(empty)

Step 2 - Push 10, then 20, then 30

Each push places the new value above the previous top.

After push 10, push 20, push 30: 30 is on top.top -> bottom302010

Step 3 - Pop removes 30 first

The top cell leaves first, so the remaining stack starts with 20.

After one pop: popped is 30; 20 is now on top.top -> bottompopped203010

Complexity

  • Time: O(1) per push/pop
  • Space: O(n)

Implementation notes

  • Keep the explicit stack/queue operations. Library shortcuts that only produce the final list hide the data-structure behavior this lesson is meant to replay.
  • The final output uses a deterministic a -> b -> c format for cross-language comparison.
top The top is the most recently pushed value.
LIFO A stack removes values in last-in, first-out order.