A tree is a complex data structure used to store data (nodes) in a “parent/child” relationship. The top node of a tree (the node with no parent) is called the root. Each node of a tree can have 0, 1 or several child nodes. In a Binary Tree, each node can have a maximum of two child nodes.
The Breadth-First Traversal of a tree is used to read all the values of a tree, one level at a time, from the top level (root node) to the bottom level:
In this blog post will first:
- Investigate how to use Python to create a binary tree data structure,
- Use our binary tree data structure to initialise different binary trees,
- Use an algorithm to implement a breadth-first traversal of our tree,
Using a Node Class to create a Binary Tree
The following Python code is all what’s needed to create a Node/Tree structure.
#A class to implement a Node / Tree class Node: def __init__(self, value, left=None, right=None): self.value = value self.left = left self.right = right
Initialising the values of a Binary Tree
In order to initialise the above Binary Tree (Tree #1) we will need the following Python code:
tree = Node(47) #The root node of our binary tree tree.left = Node(36) tree.right = Node(66) tree.left.left = Node(25) tree.left.right = Node(39) tree.left.right.left = Node(38) tree.left.right.right = Node(42) tree.right.left = Node(63) tree.right.left.right = Node(64) tree.right.right = Node(68)
Note that we have included other trees (#2 and #3) for you to initialise in Python for testing purposes.
Breadth-First Traversal of a Binary Tree
In order to implement a Breadth-First Traversal of a Binary Tree, we will need to use a queue data structure and we will base our algorithm on the following steps:
- Initialise the queue by enqueuing the root node of the tree to traverse
- While the queue is not empty:
- Dequeue a node from the queue,
- Output the value of this node,
- Enqueue the left and right node of this node to the queue.
In Python, a queue can be implemented as a simple list:
- Enqueuing an element to a list is done using the following instruction:
- Dequeuing an element from a list is done by removing its first element using the following instruction: node = list.pop(0)
- Checking if a queue is empty can be done by checking if the length of the list is equal to 0:
Full Python code for the Breadth-First Traversal of a Binary Tree
Tweak the above code to perform a breadth-first traversal of the two other binary trees provided in the above tabs.