Tree Diameter, Balanced Check & LCA

Tree Metrics & LCA

Tree Diameter: Longest path between any two nodes. $Diameter = LeftHeight + RightHeight$.

Production Code Example:

public class LcaDemo {
    public TreeTraversals.TreeNode lowestCommonAncestor(TreeTraversals.TreeNode root, TreeTraversals.TreeNode p, TreeTraversals.TreeNode q) {
        if (root == null || root == p || root == q) return root;
        TreeTraversals.TreeNode left = lowestCommonAncestor(root.left, p, q);
        TreeTraversals.TreeNode right = lowestCommonAncestor(root.right, p, q);
        if (left != null && right != null) return root;
        return left != null ? left : right;
    }
}

Key Complexity & Algorithmic Takeaways:

When implementing Tree Diameter, Balanced Check & LCA in coding interviews and production applications, keep these core guidelines in mind:

• Time Complexity Analysis: Always evaluate best-case, average-case, and worst-case time complexities ($O(1)$, $O(\log n)$, $O(n)$, $O(n \log n)$, $O(n^2)$).
• Space Complexity & Memory Bounds: Account for auxiliary memory usage, call stack frame recursion overhead, and heap allocations.
• Edge Cases & Validation: Test empty inputs, null pointers, single-element collections, duplicate values, and integer overflow bounds.
• Optimal vs Naive Solutions: Start with a clear brute-force solution, then optimize using techniques like Hashing, Two Pointers, Windowing, or Dynamic Programming.

Summary Takeaway:

Mastering Tree Diameter, Balanced Check & LCA provides the foundational problem-solving skills needed to pass technical coding interviews at top tech companies and write ultra-performant software systems.