In Data Structures and Algorithms to

let's take an example to understand how to represent a binary tree using an array.

to do this first we need to convert a binary tree into a full binary tree.

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 one node in 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.

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

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

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**represent**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 represent a binary tree using an array.

to do this first we need to convert a binary tree into a full binary tree.

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

**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.**__Note:__####
__Program to implement binary tree using python programming__

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())

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- What are Data Structures and algorithms
- Algorithm design and analysis
- Classification of algorithms
- How to calculate the running time of an algorithm.
- Worst Average and Best-case analysis of the algorithm.
- Big o notation
- Big o notation examples
- Linked List in Data Structures
- Traversing in Linked list
- Operations on the linked list
- Insertion in the linked list
- Deletion in a linked list
- Reversing a linked list
- Sorting a linked list
- Find and remove the loop in the linked list
- Doubly linked list
- Insertion in the doubly linked list
- Deletion in the doubly linked list
- Reversing a doubly linked list
- Circular linked list
- Insertion in the circular linked list
- Deletion in the circular linked list
- Merge two linked list
- Header linked list
- Sorted linked list
- Stack in data structures
- Queue in data structures
- Circular queue
- Dequeue in the data structure
- Priority queue
- Polish notation
- Tree in the data structure
- Binary tree
- linked representation of a binary tree
- Traversing in the binary tree
- Inorder traversal in the binary tree
- Preorder traversal in the binary tree
- Postorder traversal in the binary tree
- Level order traversal in the binary tree
- Binary search tree
- Insertion in the binary search tree
- Deletion in the binary search tree
- Heap in data structures

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