Stacks and Queues

Stack Push/Pop

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

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.

top The top is the most recently pushed value.
LIFO A stack removes values in last-in, first-out order.

Visual walkthrough

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

Basic Implementation

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

Complexity

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

Implementation notes

  • $stack = [] starts as an empty PHP array, and the trace records that empty stack before any pushes.
  • The push loop is foreach ([10, 20, 30] as $value) { $stack[] = $value; }, so each value appends to the top end of the array.
  • After the pushes, the replayed stack state is [10, 20, 30], with 30 at the pop end.
  • $popped = [] stores the values in removal order.
  • The pop loop runs while count($stack) > 0 and uses $popped[] = array_pop($stack).
  • array_pop($stack) removes and returns the last array value, so the first pop returns 30 and leaves [10, 20].
  • The remaining pops return 20 and then 10, ending with $popped = [30, 20, 10] and $stack = [].
  • render_values($popped) joins the LIFO order with " -> ", and echo ... . PHP_EOL prints 30 -> 20 -> 10.