Stacks and Queues

Queue Enqueue/Dequeue

Enqueue values at the back and dequeue them from the front in first-in, first-out order.

Algorithm

Basic Implementation

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

void main() {
  final queue = <int>[];
  for (final value in [10, 20, 30]) { queue.add(value); }
  final removed = <int>[];
  while (queue.isNotEmpty) { removed.add(queue.removeAt(0)); }
  print(render(removed));
}

The queue keeps the oldest value at the front and adds new values at the back.

Step 1 - Enqueue 10, 20, 30

New values join at the back. The oldest value, 10, stays at the front.

Queue after three enqueues: front 10, then 20, then back 30.nextnext10front2030back

Step 2 - Dequeue removes 10

Removing from the front returns 10 and makes 20 the new front.

After one dequeue: removed is 10; front moves to 20.next10removed20front30back

Complexity

  • Time: O(1) per operation with a real queue
  • 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.
front The front is the oldest value still waiting in the queue.
FIFO A queue removes values in first-in, first-out order.