Binarytree Module in Python
A binary tree is a data structure in which every node or vertex has atmost two children. In Python, a binary tree can be represented in different ways with different data structures(dictionary, list) and class representation for a node. However, binarytree library helps to directly implement a binary tree. It also supports heap and binary search tree(BST). This module does not come pre-installed with Python’s standard utility module. To install it type the below command in the terminal.
pip install binarytree
Creating Node
The node class represents the structure of a particular node in the binary tree. The attributes of this class are values, left, right.
Syntax: binarytree.Node(value, left=None, right=None)
Parameters:
value: Contains the data for a node. This value must be number.
left: Conatins the details of left node child.
right: Contains details of the right node child.
Note: If left or right child node is not an instance of binarytree.Node class then binarytree.exceptions.NodeTypeError is raised and if the node value is not a number then binarytree.exceptions.NodeValueError is raised.
Example:
from binarytree import Node root = Node(3) root.left = Node(6) root.right = Node(8) # Getting binary tree print('Binary tree :', root) # Getting list of nodes print('List of nodes :', list(root)) # Getting inorder of nodes print('Inorder of nodes :', root.inorder) # Checking tree properties print('Size of tree :', root.size) print('Height of tree :', root.height) # Get all properties at once print('Properties of tree : \n', root.properties) |
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Output:
Binary tree :
3
/ \
6 8List of nodes : [Node(3), Node(6), Node(8)]
Inorder of nodes : [Node(6), Node(3), Node(8)]
Size of tree : 3
Height of tree : 1
Properties of tree :
{‘height’: 1, ‘size’: 3, ‘is_max_heap’: False, ‘is_min_heap’: True, ‘is_perfect’: True, ‘is_strict’: True, ‘is_complete’: True, ‘leaf_count’: 2, ‘min_node_value’: 3, ‘max_node_value’: 8, ‘min_leaf_depth’: 1, ‘max_leaf_depth’: 1, ‘is_bst’: False, ‘is_balanced’: True, ‘is_symmetric’: False}
Build a binary tree from the List
Instead of using the Node method repeatedly, we can use build() method to convert a list of values into a binary tree.
Here, a given list contains the nodes of tree such that the element at index i has its left child at index 2*i+1, the right child at index 2*i+2 and parent at (i - 1)//2. The elements at index j for j>len(list)//2 are leaf nodes. None indicates the absence of a node at that index. We can also get the list of nodes back after building a binary tree using values attribute.
Syntax: binarytree.build(values)
Parameters:
values: List representation of the binary tree.Returns: root of the binary tree.
Example:
# Creating binary tree # from given list from binarytree import build # List of nodes nodes =[3, 6, 8, 2, 11, None, 13] # Builidng the binary tree binary_tree = build(nodes) print('Binary tree from list :\n', binary_tree) # Getting list of nodes from # binarytree print('\nList from binary tree :', binary_tree.values) |
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Output:
Binary tree from list :
___3
/ \
6 8
/ \ \
2 11 13
List from binary tree : [3, 6, 8, 2, 11, None, 13]
Build a random binary tree
tree() generates a random binary tree and returns its root node.
Syntax: binarytree.tree(height=3, is_perfect=False)
Parameters:
height: It is the height of the tree and its value can be between the range 0-9 (inclusive)
is_perfect: If set True a perfect binary is created.Returns: Root node of the binary tree.
Example:
from binarytree import tree # Create a random binary # tree of any height root = tree() print("Binary tree of any height :") print(root) # Create a random binary # tree of given height root2 = tree(height = 2) print("Binary tree of given height :") print(root2) # Create a random perfect # binary tree of given height root3 = tree(height = 2, is_perfect = True) print("Perfect binary tree of given height :") print(root3) |
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Output:
Binary tree of any height :
14____
/ \
2 5__
/ / \
6 1 13
/ / / \
7 9 4 8
Binary tree of given height :
1__
/ \
5 2
/ \
4 3
Perfect binary tree of given height :
__3__
/ \
2 4
/ \ / \
6 0 1 5
Building a BST
The binary search tree is a special type of tree data structure whose inorder gives a sorted list of nodes or vertices. In Python, we can directly create a BST object using binarytree module. bst() generates a random binary search tree and return its root node.
Syntax: binarytree.bst(height=3, is_perfect=False)
Parameters:
height: It is the height of the tree and its value can be between the range 0-9 (inclusive)
is_perfect: If set True a perfect binary is created.Returns: Root node of the BST.
Example:
from binarytree import bst # Create a random BST # of any height root = bst() print('BST of any height : \n', root) # Create a random BST of # given height root2 = bst(height = 2) print('BST of given height : \n', root2) # Create a random perfect # BST of given height root3 = bst(height = 2, is_perfect = True) print('Perfect BST of given height : \n', root3) |
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Output:
BST of any height :
____9______
/ \
__5__ ____12___
/ \ / \
2 8 10 _14
/ \ / \ /
1 4 7 11 13
BST of given height :
5
/ \
4 6
/
3
Perfect BST of given height :
__3__
/ \
1 5
/ \ / \
0 2 4 6
Importing heap
Heap is a tree data structure that can be of two types –
- max heap
- min heap
Using the heap() method of binarytree library, we can generate a random maxheap and return its root node. To generate minheap, we need to set the is_max attribute as False.
Syntax: binarytree.heap(height=3, is_max=True, is_perfect=False)
Parameters:
height: It is the height of the tree and its value can be between the range 0-9 (inclusive)
is_max: If set True generates a max heap else min heap.
is_perfect: If set True a perfect binary is created.Returns: Root node of the heap.
from binarytree import heap # Create a random max-heap root = heap() print('Max-heap of any height : \n', root) # Create a random max-heap # of given height root2 = heap(height = 2) print('Max-heap of given height : \n', root2) # Create a random perfect # min-heap of given height root3 = heap(height = 2, is_max = False, is_perfect = True) print('Perfect min-heap of given height : \n', root3) |
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Output:
Max-heap of any height :
_______14______
/ \
___12__ __13__
/ \ / \
10 8 3 9
/ \ / \ / \ /
1 5 4 6 0 2 7
Max-heap of given height :
__6__
/ \
4 5
/ \ / \
2 0 1 3
Perfect min-heap of given height :
__0__
/ \
1 3
/ \ / \
2 6 4 5
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