1110. Delete Nodes And Return Forest

[mah-shamim]

Given the root of a binary tree, each node in the tree has a distinct value.

After deleting all nodes with a value in to_delete, we are left with a forest (a disjoint union of trees).

Return the roots of the trees in the remaining forest. You may return the result in any order.

Example 1:

• Input: root = [1,2,3,4,5,6,7], to_delete = [3,5]
• Output: [[1,2,null,4],[6],[7]]

Example 2:

• Input: root = [1,2,4,null,3], to_delete = [3]
• Output: [[1,2,4]]

Constraints:

• The number of nodes in the given tree is at most 1000.
• Each node has a distinct value between 1 and 1000.
• to_delete.length <= 1000
• to_delete contains distinct values between 1 and 1000.

[mah-shamim]

To solve this problem, we can follow these steps:

1. Traverse the tree using a helper function.
2. If a node is marked for deletion, add its children to the result forest if they are not null.
3. Recursively delete nodes and adjust the tree accordingly.
4. Return the list of root nodes of the remaining forest.

Let's implement this solution in PHP: 1110. Delete Nodes And Return Forest

<?PHP

class TreeNode {
    public $val = null;
    public $left = null;
    public $right = null;

    public function __construct($val = 0, $left = null, $right = null) {
        $this->val = $val;
        $this->left = $left;
        $this->right = $right;
    }
}

class Solution {

    /**
     * @param TreeNode $root
     * @param Integer[] $to_delete
     * @return TreeNode[]
     */
    function delNodes($root, $to_delete) {
        $to_delete_set = array_flip($to_delete);
        $forest = [];

        $root = $this->helper($root, $forest, $to_delete_set);
        if ($root !== null) {
            $forest[] = $root;
        }

        return $forest;
    }

    /**
     * @param $node
     * @param $forest
     * @param $to_delete_set
     * @return mixed|null
     */
    function helper($node, &$forest, $to_delete_set) {
        if ($node === null) {
            return null;
        }

        $node->left = self::helper($node->left, $forest, $to_delete_set);
        $node->right = self::helper($node->right, $forest, $to_delete_set);

        if (isset($to_delete_set[$node->val])) {
            if ($node->left !== null) {
                $forest[] = $node->left;
            }
            if ($node->right !== null) {
                $forest[] = $node->right;
            }
            return null;
        }
        return $node;
    }
}
// Helper function to build a binary tree from a list
function buildTree($nodes) {
    if (empty($nodes)) {
        return null;
    }
    $root = new TreeNode($nodes[0]);
    $queue = [$root];
    $i = 1;
    while ($i < count($nodes)) {
        $current = array_shift($queue);
        if ($nodes[$i] !== null) {
            $current->left = new TreeNode($nodes[$i]);
            $queue[] = $current->left;
        }
        $i++;
        if ($i < count($nodes) && $nodes[$i] !== null) {
            $current->right = new TreeNode($nodes[$i]);
            $queue[] = $current->right;
        }
        $i++;
    }
    return $root;
}


// Example usage:
$root = buildTree([1, 2, 3, 4, 5, 6, 7]);
$to_delete = [3, 5];
$forestRoot = new Solution();

$forest = $forestRoot->delNodes($root, $to_delete);

function printForest($forest) {
    foreach ($forest as $tree) {
        printTree($tree);
        echo "\n";
    }
}

function printTree($node) {
    if ($node === null) {
        return;
    }
    echo $node->val . " ";
    printTree($node->left);
    printTree($node->right);
}

printForest($forest);
?>

Explanation:

1. TreeNode Class: Defines the structure of a tree node.
2. delNodes Function: Main function to delete specified nodes and return the forest.
   • $to_delete_set: Converts the list of nodes to delete into a set for quick lookups.
   • helper Function: Recursively processes each node, checking if it should be deleted. If a node is deleted, its children are added to the forest.
3. buildTree Function: Helper function to build a binary tree from a list representation (used for testing).
4. printForest Function: Helper function to print the trees in the forest (used for testing).

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