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
  • Inorder
  • 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 inorder

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.

traversing in binary tree in data structures


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 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())