Trees

BST Insert

Insert values into a binary search tree by comparing at each node.

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 insert_node(?Node $root, int $value): Node { if ($root === null) return new Node($value); if ($value < $root->value) $root->left = insert_node($root->left, $value); else $root->right = insert_node($root->right, $value); return $root; }
$root = null;
foreach ([4, 2, 6, 1, 3, 5, 7] as $value) $root = insert_node($root, $value);
echo render_tree($root) . PHP_EOL;
?>

Complexity

  • Time: O(h) per insert
  • Space: O(n)

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.
binary search tree Values smaller than a node go left; larger values go right.