2196. Create Binary Tree From Descriptions

[mah-shamim]

You are given a 2D integer array descriptions where descriptions[i] = [parenti, childi, isLefti] indicates that parenti is the parent of childi in a binary tree of unique values. Furthermore,

• If isLefti == 1, then childi is the left child of parenti.
• If isLefti == 0, then childi is the right child of parenti.

Construct the binary tree described by descriptions and return its root.

The test cases will be generated such that the binary tree is valid.

Example 1:

• Input: descriptions = [[20,15,1],[20,17,0],[50,20,1],[50,80,0],[80,19,1]]
• Output: [50,20,80,15,17,19]
• Explanation: The root node is the node with value 50 since it has no parent.
  The resulting binary tree is shown in the diagram.

Example 2:

• Input: descriptions = [[1,2,1],[2,3,0],[3,4,1]]
• Output: [1,2,null,null,3,4]
• Explanation: The root node is the node with value 1 since it has no parent.
  The resulting binary tree is shown in the diagram.

Constraints:

• 1 <= descriptions.length <= 104
• descriptions[i].length == 3
• 1 <= parenti, childi <= 105
• 0 <= isLefti <= 1
• The binary tree described by descriptions is valid.

Hint:

1. Could you represent and store the descriptions more efficiently?
2. Could you find the root node?
3. The node that is not a child in any of the descriptions is the root node.

[mah-shamim]

To solve this problem, we can follow these steps:

1. Create a class to represent the tree nodes.
2. Parse the descriptions array to build the tree.
3. Find the root node (the node that is not a child of any other node).
4. Return the root node.

Let's implement this solution in PHP: 2196. Create Binary Tree From Descriptions

<?php
// Definition for a binary tree node.
class TreeNode {
    public $val = null;
    public $left = null;
    public $right = null;
    public function __construct($value) { $this->val = $value; }
}

function createBinaryTree($descriptions) {
    $nodes = [];
    $children = [];

    // Create nodes and build the tree
    foreach ($descriptions as $description) {
        $parentVal = $description[0];
        $childVal = $description[1];
        $isLeft = $description[2];

        if (!isset($nodes[$parentVal])) {
            $nodes[$parentVal] = new TreeNode($parentVal);
        }
        if (!isset($nodes[$childVal])) {
            $nodes[$childVal] = new TreeNode($childVal);
        }

        if ($isLeft) {
            $nodes[$parentVal]->left = $nodes[$childVal];
        } else {
            $nodes[$parentVal]->right = $nodes[$childVal];
        }

        $children[$childVal] = true;
    }

    // Find the root node (node that is not a child of any other node)
    foreach ($nodes as $val => $node) {
        if (!isset($children[$val])) {
            return $node;
        }
    }

    return null;
}

// Example usage:
$descriptions1 = [[20,15,1],[20,17,0],[50,20,1],[50,80,0],[80,19,1]];
$descriptions2 = [[1,2,1],[2,3,0],[3,4,1]];

$root1 = createBinaryTree($descriptions1);
$root2 = createBinaryTree($descriptions2);

function printTree($node) {
    if ($node == null) {
        return null;
    }
    $result = [$node->val];
    $result[] = printTree($node->left);
    $result[] = printTree($node->right);
    return $result;
}

print_r(printTree($root1)); // Output: [50, [20, [15], [17]], [80, [19]]]
print_r(printTree($root2)); // Output: [1, [2, null, [3, [4]]]]

?>

This code defines a TreeNode class to represent each node in the binary tree. The createBinaryTree function constructs the tree based on the descriptions provided and finds the root node by identifying the node that is not a child of any other node. The printTree function is used to print the tree structure for verification.