Array Representation of Binary Tree

In Data Structures and Algorithms to make a representation of a binary tree using an array first, we need to convert a binary tree into a full binary tree. and then we give the number to each node and store it in their respective locations.

let’s take an example to understand how to do the representation of a binary tree using an array. to do this first we need to convert a binary tree into a full binary tree.

sequential Array representation of Binary tree in data structures

here in the above example to convert this binary tree into a full binary tree, we need to add nodes that don’t have child nodes till the last level of the tree.

So now the tree becomes a full binary tree. after that to represent it using an array we need to give the numbers to each and every node but level by level.

after giving the number to each and every node now we need to create an array of size 15 + 1.

after that store each node in an array in their respective index points. like D has number 1 then we store it in the array at index 1 and E has number 2 then we store it at index 2 in the array.

so this is the array representation of a binary tree.

Important terms to represent a binary tree in sequential order.

The root is always stored at index 1 in the array.

if any node is stored at the K position then the left child of a node is stored at index 2k and the right child has stored at index 2K + 1 and the parent of a node is stored at the floor(K/2) index.

Note: The size of an array to represent a binary tree of height H is equal to the maximum number of nodes possible in a binary tree of height H.

Program to implement binary tree in Python

from collections import deque


class Node:
    def __init__(self, value):
        self.info = value
        self.lchild = None
        self.rchild = None

class BinaryTree:
    def __init__(self):
        self.root = None
    def is_empty(self):
        return self.root is None
    def display(self):
        self._display(self.root, 0)
        print()

    def _display(self,p,level):
        if p is None:
            return        self._display(p.rchild, level+1)
        print()

        for i in range(level):
            print(" ", end='')
        print(p.info)
        self._display(p.lchild, level+1)

    def preorder(self):
        self._preorder(self.root)
        print()

    def _preorder(self,p):
        if p is None:
            return        print(p.info, " ", end='')
        self._preorder(p.lchild)
        self._preorder(p.rchild)

    def inorder(self):
        self._inorder(self.root)
        print()

    def _inorder(self,p):
        if p is None:
            return        self._inorder(p.lchild)
        print(p.info," ", end='')
        self._inorder(p.rchild)

    def postorder(self):
        self._postorder(self.root)
        print()

    def _postorder(self,p):
        if p is None:
            return        self._postorder(p.lchild)
        self._postorder(p.rchild)
        print(p.info," ",end='')

    def level_order(self):
        if self.root is None:
            print("Tree is empty")
            return
        qu = deque()
        qu.append(self.root)

        while len(qu) != 0:
            p = qu.popleft()
            print(p.info + " ", end='')
            if p.lchild is not None:
                qu.append(p.lchild)
            if p.rchild is not None:
                qu.append(p.rchild)

    def height(self):
        return self._height(self.root)

    def _height(self,p):
        if p is None:
            return 0
        hL = self._height(p.lchild)
        hR = self._height(p.rchild)

        if hL > hR:
            return 1 + hL
        else:
            return 1 + hR

    def create_tree(self):
        self.root = Node('p')
        self.root.lchild = Node('Q')
        self.root.rchild = Node('R')
        self.root.lchild.lchild = Node('A')
        self.root.lchild.rchild = Node('B')
        self.root.rchild.lchild = Node('X')


##########################
bt = BinaryTree()

bt.create_tree()

bt.display()
print()

print("Preorder : ")
bt.preorder()
print("")

print("Inorder : ")
bt.inorder()
print()

print("Postorder : ")
bt.postorder()
print()

print("Level order : ")
bt.level_order()
print()

print("Height of tree is ", bt.height())