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.php 
<?php
function render_values(array $values): string { return implode(" -> ", $values); }
$queue = [];
foreach ([10, 20, 30] as $value) { $queue[] = $value; }
$removed = [];
while (count($queue) > 0) { $removed[] = array_shift($queue); }
echo render_values($removed) . PHP_EOL;

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

  • $queue = [] starts as an empty PHP array, and the trace records that exact empty state first.
  • The enqueue loop is foreach ([10, 20, 30] as $value) { $queue[] = $value; }, so each value is appended at the back of the same array.
  • After enqueue, the replayed queue state is [10, 20, 30].
  • $removed = [] collects the dequeue order separately from the live queue.
  • The dequeue loop runs while count($queue) > 0 and uses array_shift($queue) to remove the front element.
  • In PHP, array_shift mutates the array by removing the first value; with these numeric positions, the remaining values slide forward in queue order.
  • That makes the source easy to replay for three pinned values, but it is not the scalable PHP queue shape; a larger queue would keep a head index or use a real queue container instead of shifting the array each time.
  • The first dequeue moves 10 into $removed, leaving $queue as [20, 30].
  • The remaining dequeues produce $removed = [10, 20, 30] and $queue = [].
  • render_values($removed) joins values with " -> ", and echo ... . PHP_EOL prints 10 -> 20 -> 30.
front The front is the oldest value still waiting in the queue.
FIFO A queue removes values in first-in, first-out order.