Validate Binary Tree Nodes

Problem Description

You have n binary tree nodes numbered from 0 to n - 1 where node i has two children leftChild[i] and rightChild[i], return true if and only if all the given nodes form exactly one valid binary tree. If node i has no left child then leftChild[i] will equal -1, similarly for the right child.

Key Insights

• Each node can have at most one parent, ensuring that there are no cycles.
• The total number of nodes must equal the number of unique nodes that have parents, plus the root node.
• A valid binary tree must have exactly one root node, which is the only node that does not appear as a child of any other node.
• The input constraints ensure that the child indices are valid and within bounds.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(n)

Solution

To determine if the given nodes form a valid binary tree, we can use the following approach:

1. Create an array to keep track of the number of parents for each node.
2. Iterate through the leftChild and rightChild arrays to populate the parent count for each node.
3. Check if there is exactly one node with zero parents (the root).
4. Ensure that there are no cycles by confirming that no node has more than one parent.

We will use an array to count parents and a single loop for checking conditions.

Code Solutions