Level-Order Traversal

Visit a tree breadth-first with a queue.

Algorithm

The canonical tree is 4(2(1,3),6(5,7)), so this PHP DSA implementation can be compared directly with the rest of the DSA track.

Basic Implementation

basic.php

<?php
class Node {
    public int $value;
    public ?Node $left;
    public ?Node $right;
    public function __construct(int $value, ?Node $left = null, ?Node $right = null) {
        $this->value = $value; $this->left = $left; $this->right = $right;
    }
}
function render_tree(?Node $node): string {
    if ($node === null) return "_";
    if ($node->left === null && $node->right === null) return (string)$node->value;
    return $node->value . "(" . render_tree($node->left) . "," . render_tree($node->right) . ")";
}
function sample_tree(): Node {
    return new Node(4, new Node(2, new Node(1), new Node(3)), new Node(6, new Node(5), new Node(7)));
}
function list_string(array $values): string { return "[" . implode(", ", $values) . "]"; }
$queue = [sample_tree()];
$output = [];
while ($queue) { $node = array_shift($queue); $output[] = $node->value; if ($node->left !== null) $queue[] = $node->left; if ($node->right !== null) $queue[] = $node->right; }
echo list_string($output) . PHP_EOL;
?>

Complexity

Time: O(n)
Space: O(w) queue space

Implementation notes

Render tree structure explicitly instead of printing node objects.
The replay highlights the node, traversal state, queue, path, or search cursor that changes at each step.

level order Level-order traversal uses a queue to visit shallower nodes first.