N-ary Tree Preorder Traversal

Here’s the code to perform a preorder traversal on an n-ary tree.

The preorder traversal in an n-ary tree is similar to the binary tree, but instead of traversing just left and right children, you need to traverse all the children of a node.

You can achieve this by recursively traversing the children of each node in the tree and adding their values to the result.

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class Solution:
    def preorder(self, root: 'Node') -> List[int]:
        if root is None:
            return []

        result = []
        result.append(root.val) # Process the current node's value first

        # Then recursively traverse the children
        for child in root.children:
            result.extend(self.preorder(child))

        return result

Explanation

  • If the root is None, return an empty list, as there is nothing to traverse.
  • For each node, add its value to the result first.
  • Then recursively call the preorder function for each of its children, extending the result with the values returned.
  • Finally, return the result.

This code follows the preorder traversal pattern where you process the current node before its children and maintains the order of children as they appear in the n-ary tree.

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class Solution(object):
    def preorder(self, root):
        output = []
        self.traverse(root, output)
        return output
    def traverse(self, root, output):
        if root is None: return

        output.append(root.val)

        for child in root.children:
            self.traverse(child, output)

Problem Classification

The problem is based on Trees, and more specifically on N-ary Trees. The problem involves understanding tree traversals and in this case, the concept of preorder traversal.

‘What’ Components:

  • Given: The root of an N-ary tree. The nodes of this tree are represented in level order traversal, where each group of children is separated by a null value.
  • Task: The task is to return the preorder traversal of the node values of the given tree. In preorder traversal, each node is processed before (i.e., “pre”) any of its children. This means that a node will be processed the first time the algorithm visits it, as opposed to the second time for in-order traversal or the last time for post-order traversal.

This can be categorized as a traversal problem with a focus on preorder traversal of an N-ary tree. This problem requires a good understanding of N-ary trees and how tree traversal algorithms work. It is a problem that tests algorithmic thinking and depth-first search traversal implementation.

This is about understanding how an N-ary tree can be traversed in a specific order (preorder). The task is to find a specific ordering of the nodes, which makes it a traversal problem. The complexity arises from the fact that the tree is an N-ary tree, where each node can have more than two children, and thus the traversal isn’t as straightforward as it would be for binary trees.

Language Agnostic Coding Drills

  1. Dissecting the Code:

Here are the individual coding concepts in this piece of software:

a) Defining Classes: The first line of code defines a new class, Solution. Classes allow us to bundle data and functionalities together. Creating a new class creates a new type of object, allowing new instances of that type to be made.

b) Defining Methods: Inside the class Solution, two methods are defined: preorder and traverse. Methods are a kind of function that are defined within a class and are used to define the behaviors of an object.

c) Working with Lists: The output list is initialized and manipulated using methods like append(). Understanding list operations is crucial for building complex algorithms.

d) Recursion: The traverse function is called recursively to traverse through the tree nodes. Recursion is a concept where a function calls itself in its definition.

e) Conditional Statements: if statements are used to control the flow of the program based on specific conditions.

f) Tree Traversal: The code traverses an n-ary tree in a pre-order fashion. This involves depth-first search and the handling of tree data structure.

  1. Listing Coding Concepts by Increasing Difficulty:

    a) Defining Classes (Easy): This is a basic concept in most object-oriented programming languages. The class serves as a blueprint for creating objects (a particular data structure).

    b) Defining Methods (Easy): Another basic concept of object-oriented programming. Methods determine what type of functionality a class has.

    c) Working with Lists (Easy): Operations with lists are common in many programming tasks.

    d) Conditional Statements (Easy): These are used to control the flow of most programs and are a fundamental concept in programming.

    e) Recursion (Medium): While the basic idea is simple, recursion can get complex when used in more involved scenarios, such as tree traversal in this case.

    f) Tree Traversal (Hard): This concept is more advanced as it requires a deep understanding of tree data structures and the logic behind depth-first search. The difficulty comes in handling the traversal order and ensuring all nodes are covered.

  2. Problem-solving Approach:

The problem involves returning a list of values of an N-ary tree in preorder. The solution first defines a helper function traverse to visit each node in a pre-order manner using recursion. Starting from the root, it adds the current node’s value to the output list, then recursively calls the traverse function for each of its children. This process is repeated until all nodes have been visited.

Each identified coding concept contributes to the final solution. Defining classes and methods provide the structure of the solution. Working with lists allows storing the traversal result. Conditional statements control the recursion termination, while the concept of recursion enables the traversal through the tree. Finally, the understanding of tree traversal is the key to correctly implement the preorder traversal.

Targeted Drills in Python

  1. Python-based coding drills:

    a) Defining Classes:

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    class MyClass:
    pass
my_instance = MyClass()

    b) Defining Methods:

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    class MyClass:
    def my_method(self):
        print("Hello, World!")
my_instance = MyClass()
my_instance.my_method()

    c) Working with Lists:

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    my_list = []
my_list.append(1)
my_list.append(2)
print(my_list)

    d) Conditional Statements:

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    x = 10
if x > 5:
    print("x is greater than 5")

    e) Recursion:

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    def factorial(n):
    if n == 1:
        return 1
    else:
        return n * factorial(n-1)
print(factorial(5))

    f) Tree Traversal (Specific Concept for the Problem):

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    class Node:
    def __init__(self, val=None, children=None):
        self.val = val
        self.children = children if children is not None else []

def preorder(node):
    if node is None:
        return []
    result = [node.val]
    for child in node.children:
        result.extend(preorder(child))
    return result

root = Node(1, [Node(3, [Node(5), Node(6)]), Node(2), Node(4)])
print(preorder(root))  # Prints: [1, 3, 5, 6, 2, 4]

  2. Problem-Specific Concepts:

The most relevant problem-specific concept for this problem is tree traversal, specifically pre-order traversal for an N-ary tree. Understanding this concept is crucial because the problem involves returning a list of values of an N-ary tree in preorder.

  1. Integrating the Drills:

We begin by defining the class and its methods, creating the structure of our solution (drill a and drill b). Then, we initialize a list to store the traversal result (drill c). We use recursion (drill e) to traverse through the tree in a pre-order fashion, starting from the root node. During each recursive call, we check if the current node is not None (drill d), and if it’s not, we add its value to the list and call the recursion on its children (problem-specific drill f). The recursion and tree traversal together form the backbone of our solution. After all nodes have been visited, we return the final list of node values in pre-order traversal. This way, all identified drills contribute to building up to the final solution.