Traversing a binary tree means visiting each node of the tree exactly once. and as we know the nodes of the tree are arranged in a hierarchical order so there are different ways to traverse a binary tree.
we have three main tasks to traverse in the tree.
- visiting the root node.
- visiting the left subtree.
- visiting the right subtree.
Types of traversing in a binary tree.
- Preorder
- Postorder
- In order
- Level order
Preorder Traversing
In preorder traversing first, we
visit the root node.
then we traverse the left subtree of the root node in preorder
then we traverse the right subtree of the root node in preorder
In order Traversing
In inorder traversing first, we
Traverse the left subtree of the root node in inorder
then we visit the root node
then we traverse the right subtree of the root in order
Postorder traversing
In postorder traversing first, we
Traverse the left subtree of the root node in postorder
Traverse the right subtree of the root node in postorder
visit the root node.
Level order Traversing
In level order traversing nodes are traversed level by level. so we have a binary tree as you see in the given below image.
so the Preorder traversing is – P A S T Q E D X M R C
Postorder traversing – T Q S D E A M C R X P
In order traversing – T S Q A E D P M X C R
Level order traversing – P A X T Z M G Y L F C
Program to implement traversing in the binary tree using 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())
