# Inorder traversal in binary tree | Data structures

In the inorder traversal of the binary tree, we first visit the left subtree of the root node, and then we visit the root node and after that, we visit the right subtree of the root node.

### Properties of Inorder traversal

• Traverse the left subtree of the root in inorder
• Visit the root node
• Traverse the right subtree of the root in inorder

let's understand it with an example

let's say we have a binary tree as you see in the image given below. First, we need to divide the whole tree into subtrees like as you see in the given image above. and then we start traversing the tree.

as you see first we visit the left subtree of the root node in inorder. so the root node is P and it's left subtree is B but in the subtree B, there is also a left subtree D so we first start traversing with subtree D.

In the subtree, there is no left subtree so we first visit the left node and then the root node and then the right node.

so the inorder traversal of subtree D is T S Q and inorder of subtree B is D A E and substitute the value of subtree D so the inorder is

T S Q A E P F C

now find the inorder of subtree E and the inorder of E is E D so the inorder is

T S Q A E D P F C

now go to the root node P so the inorder is

T S Q A E D P F C

now find the inorder of subtree C but in the subtree C, there is also left subtree F and right subtree G.

so first we need to find the inorder of F subtree because it's a left subtree and in inorder, the left subtree comes first and then root node and right node.

so the inorder of subtree F is M so the inorder of subtree C is

M X G

now we find the inorder of subtree G so the inorder of subtree is C R
so the inorder of subtree C is

M X C R

now we substitute the inorder of right subtree C into the so the inorder of the binary tree is

T S Q A E D P M X C R

#### Program to find the inorder of binary tree using the python programming language.

```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())

```