Maximum Depth of Nary Tree
To find the maximum depth of an nary tree, we can use a recursive function that explores all the children of a node.
Code


Explanation
 Base Case: If the root is
None
, the depth is 0.  Recursive Case: For each child of the root, call the
maxDepth
function recursively.  Calculate Maximum Depth: Keep track of the maximum depth returned from the children, and add 1 for the current node.
 Return Result: Return the calculated maximum depth.
The time complexity of this approach is O(N), where N is the total number of nodes in the tree, as we visit each node once. The space complexity is O(H), where H is the height of the tree, due to the recursive call stack.
Define the Terms
Nary Tree: A node can have many children.
Define the Interface Input: root reference of the nary tree Output: integer
Analyze the Input and Output Edge case : 0 nodes, return 0
Identify the Invariants
Identify the constraints
 The depth of the nary tree is less than or equal to 1000.
 The total number of nodes is between [0, 10^4].
Search the Problem Space
Classify the Problem
Analyze the Examples
Solve the Problem by Hand
Describe the Pattern
Distill the Observations to Create Insights
Brute Force Approach
Analyze Time and Space Complexity
Time: O( ) Space: O( )
Outline the Solution
Keep track of two things:
 depth (current depth)
 maximum depth (the final answer) Start from the root. current_depth = 1 Get all the children of the root. current_depth += 1 (the root must have at least one child) Iterate over all the children Which child will give
Recursive Approach
The base case is when the root is null, return 0
Loop through the children (root.children)
 Update the current_depth by one more than its previous
 Update the max_depth
We can either have the max_depth as global variable or as a parameter
Before the loop begins, ans = max(current_depth, max_depth) max_depth can be global
If I am a leaf node, check the max and if my depth is higher update the depth otherwise, return from the recursive call.
Unit of Work
 Updating the max depth we have seen so far.








Problem Classification
This problem is related to Trees. It deals with the traversal and analysis of a nary tree, which is a form of hierarchical data structure where each node can have n number of children.
‘What’ components of this problem are:
Nary Tree: A nary tree is a tree data structure where each node can have no more than n children.
Maximum Depth: This is the length of the longest path from the root node down to the furthest leaf node.
NaryTree Input Serialization: The problem states that the input is represented as a level order traversal of the tree, where each group of children is separated by the null value.
The problem can further be classified into the Tree Traversal subdomain within Data Structures. It requires understanding and implementing tree traversal algorithms to identify and return the maximum depth of the tree. It implies using a depthfirst search (DFS) or breadthfirst search (BFS) traversal approach to explore all paths from the root to the leaf nodes, tracking the length of each path and returning the maximum length.
 Domain: Trees, Tree Traversal
 Main components: Nary tree, Maximum depth, Tree traversal (level order traversal represented by NaryTree Input Serialization)
Language Agnostic Coding Drills
 Dissect the Code
Here are the distinct concepts and subconcepts contained in the code:
a. Function Definitions: The syntax and structure of defining a function in a programming language.
b. Base Case Handling: Checking the root of the tree to see if it’s null, and returning an appropriate value (0 in this case) if it is.
c. Usage of Data Structures: The implementation uses a queue to handle the traversal of the tree nodes. Understanding and implementing queues are fundamental here.
d. Looping: The use of a while loop to traverse through all elements until the condition is no longer met.
e. Unpacking: The concept of unpacking a data structure into multiple variables in a single line.
f. Conditional Checking: Checking if a node has children, using an if statement.
g. Traversing Children Nodes: The ability to traverse through the children of a node.
h. Updating Data Structures: Adding elements to the end of a queue.
i. Keeping Track of Depth: The concept of keeping track of the maximum depth by storing the value of the maximum depth encountered during the traversal.
Ordered List of Concepts
a. Function Definitions (Easy): Fundamental to all programming tasks.
b. Base Case Handling (Easy): An important concept in recursion and when dealing with trees, but fairly straightforward.
c. Usage of Data Structures  Queues (Intermediate): Understanding queues is a fundamental part of data structures, but applying them effectively can be challenging.
d. Looping (Easy): Looping is a fundamental concept in programming.
e. Unpacking (Easy): Unpacking is a helpful tool in many languages that makes code cleaner and easier to read.
f. Conditional Checking (Easy): Fundamental concept used in all forms of programming.
g. Traversing Children Nodes (Intermediate): This requires understanding of the tree data structure and how to iterate over it.
h. Updating Data Structures  Adding to Queue (Easy): Basic understanding of how to interact with data structures.
i. Keeping Track of Depth (Intermediate): While not complex, this concept does require an understanding of the problem domain and some foresight to implement effectively.
Problemsolving Approach
The solution uses a breadthfirst search (BFS) approach, which is a common method for tree traversal. Each node of the tree is paired with its depth level in a tuple and added to a queue. The BFS proceeds by dequeuing a node and its depth, then enqueuing all its children paired with the updated depth (parent’s depth + 1).
In a BFS traversal, the queue always contains nodes at the current level before any nodes at the next level. So, the last node dequeued is guaranteed to be the one at the maximum depth, i.e., the deepest node encountered during the traversal. By keeping track of this node’s depth, we effectively track the maximum depth of the tree.
This approach ensures that each node is visited exactly once and that its depth compared to the root is properly computed. This leads us to the final solution: the maximum depth of the nary tree.
Targeted Drills in Python
 Pythonbased Coding Drills
Let’s write Pythonbased coding drills to encapsulate each identified concept.
a. Function Definitions


b. Base Case Handling


c. Usage of Data Structures  Queues


d. Looping


e. Unpacking


f. Conditional Checking


g. Traversing Children Nodes


h. Updating Data Structures  Adding to Queue


i. Keeping Track of Depth


 Problemspecific Drills
For this particular problem, we need to understand how to traverse an nary tree using BreadthFirst Search (BFS).


 Integration of Drills
To solve the problem, we integrate the above drills in the following way:
 We start with a function definition
maxDepth
that takes the root of the tree as an argument.  We handle the base case by checking if the root is
None
. If so, we return 0.  We initialize a queue and add the root node and its depth (1) to the queue.
 We enter a loop that continues until the queue is empty. In each iteration:
 We dequeue a node and its depth (using unpacking).
 We update our maximum depth.
 We check if the node has children (conditional checking).
 If it has children, we append each child and its depth (parent’s depth + 1) to the queue (updating data structures).
 Once the loop is finished, we return the maximum depth we’ve recorded. This integrates the ‘keeping track of depth’ drill.