Stacks and Queues

Queue from Two Stacks

Implement queue behavior with an input stack and an output stack.

Algorithm

The replay uses the same three values in every language, so this PHP DSA implementation can be compared directly with the rest of the DSA track.

input stack Enqueue pushes new values onto the input stack.
output stack When the output stack is empty, transferring all input values reverses them into dequeue order.

Visual walkthrough

The two-stack queue keeps cheap enqueues in the input stack, then reverses that stack only when dequeue needs the output stack.

Step 1 - Enqueue pushes onto the input stack

After enqueueing 10, 20, 30, the newest input value is on top of the input stack.

After enqueues: input top is 30; output is empty.input stack top -> bottomoutput stack top -> bottomremoved30(empty)(empty)2010

Step 2 - Transfer reverses into output order

Moving every input value to the output stack turns 10 into the next pop.

After transfer: output top is 10, so dequeue returns the oldest value.input stackoutput stack top -> bottomremoved(empty)10(empty)2030

Step 3 - Dequeue pops from output

The output stack pops 10 first while 20 becomes the next front.

After one dequeue: removed is 10; output top is now 20.input stackoutput stack top -> bottomremoved(empty)201030

Basic Implementation

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

Complexity

  • Time: O(1) amortized per operation
  • Space: O(n)

Implementation notes

  • $inStack = [] and $outStack = [] are plain PHP arrays used as stacks; the trace begins with both empty.
  • Enqueue uses foreach ([10, 20, 30] as $value) { $inStack[] = $value; }, so values append to the back of $inStack.
  • After enqueue, the replay shows $inStack as [10, 20, 30] and $outStack still empty.
  • The transfer loop runs while count($inStack) > 0 and moves values with $outStack[] = array_pop($inStack).
  • Because array_pop removes the last appended value, the transfer reverses the stack into $outStack = [30, 20, 10] and leaves $inStack = [].
  • $removed = [] records dequeued values separately.
  • The dequeue loop uses $removed[] = array_pop($outStack), so popping the output stack returns 10, then 20, then 30.
  • The trace ends with $removed = [10, 20, 30] and $outStack = [].
  • render_values($removed) joins the dequeued order with " -> ", and echo ... . PHP_EOL prints 10 -> 20 -> 30.