Trees

BST Search

Search a binary search tree for one present and one absent value.

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) . "]"; }
function search_tree(?Node $root, int $target): bool { $node = $root; while ($node !== null) { if ($target === $node->value) return true; $node = $target < $node->value ? $node->left : $node->right; } return false; }
$root = sample_tree();
echo (search_tree($root, 5) ? "5 found" : "5 not found") . PHP_EOL;
echo (search_tree($root, 8) ? "8 found" : "8 not found") . PHP_EOL;
?>

Complexity

  • Time: O(h) per search
  • Space: O(1) iterative

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.
search path A comparison chooses one subtree at each step, so whole branches are skipped.