Specific Level Order Traversal of Binary Tree

Given a Binary Tree, the task is to perform Specific Level Order Traversal of the tree such that at each level print 1st element then the last element, then 2nd element and 2nd last element, until all elements of that level is printed and so on.

Examples:

Input: Below is the given tree:

Output: 1 8 3 4 7 5 6
Explanation:
1st level:    1(root)
2nd level:   8(left),    3(right)
3rd level:    4(left),     7(right),    5(left),    6(right)

Input: Below is the given tree:

Output: 20 8 22 4 12 10 14
Explanation:
1st level:    20(root)
2nd level:   8(left),    22(right)
3rd level:    4(left),     12(right)
4th level:    10(left),    14(right)

Approach: The idea is to the Level Order Traversal of the given Binary Tree and convert this tree into Perfect Binary Tree. While traversing if any node whose child Node doesn’t exist then append NULL node as the child node in the queue. Below are the steps:



  1. Perform the level order traversal of the given tree.
  2. During traveral if any node whose child Node doesn’t exist then append NULL node as the child node in the queue
  3. During traversal for each level do the following:
    • Maintain two queues to store the nodes for the two half of each level.
    • For first half of the level store nodes in left to right manner.
    • For second half of the level store nodes in right to left manner.
    • Iterate the above two queues formed and print in an alternate manner for specific level order traversal.

Below is the implementation of the above approach:

Python3

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# Python program for the above approach
from queue import Queue
  
# A binary tree node
class Node:
  
    # A constructor for making
    # a new node
    def __init__(self, key):
        self.data = key
        self.left = None
        self.right = None
      
# Function to find the height of tree    
def Height(root):
    if root == None:
        return 0
    return 1 + max(Height(root.left), Height(root.right))
  
  
# Given a perfect binary tree 
# print its node in Specific order
def printSpecificLevelOrder(A, B, height):
  
    while height != 0:
  
        # Get each one front 
        # element of both queue
        X = A.get()
        Y = B.get()
  
        # Check if X exist or not  
        if X == None
            # Assume is has and put
            # their both child as none
            A.put(None)
            A.put(None)
        else:        
            # print the data and store 
            # their child first left 
            # then right
            print(X.data, end =" ")
            A.put(X.left)
            A.put(X.right)
          
        # Check Y exist or not    
        if Y == None:       
            # Assume is has and put
            # their both child as none
            B.put(None)
            B.put(None)    
        else:
            # print the data and store their
            # child first left then right
            print(Y.data, end =" ")
            B.put(Y.right)
            B.put(Y.left)
        # Decrease by 1 unit    
        height-= 1 
  
        
# Driver Code
  
# Given Tree
root = Node(1)
  
root.left = Node(2)
root.right = Node(3)
  
  
root.left.left = Node(4)
root.left.right = Node(5)
root.right.right = Node(7)
  
root.left.left.left = Node(8)
root.left.left.right = Node(9)
root.left.right.left = Node(10)
root.left.right.right = Node(11)
root.right.right.left = Node(14)
root.right.right.right = Node(15)
  
root.left.left.left.left = Node(16)
root.left.left.left.right = Node(17)
root.left.left.right.left = Node(18)
root.left.left.right.right = Node(19)
root.left.right.left.left = Node(20)
root.left.right.left.right = Node(21)
root.left.right.right.left = Node(22)
root.left.right.right.right = Node(23)
root.right.right.left.left = Node(28)
root.right.right.left.right = Node(29)
root.right.right.right.left = Node(30)
root.right.right.right.right = Node(31)
  
# Initialise Queue
A = Queue(100)
B = Queue(100)
  
# Check top root manually
if root != None:  
    print(root.data, end =" ")
  
    A.put(root.left)
    B.put(root.right)
      
    height = Height(root)
    height = 2**(height-1)-1
  
# Function Call
    printSpecificLevelOrder(A, B, height)

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Output:

1 2 3 4 7 5 8 15 9 14 10 11 16 31 17 30 18 29 19 28 20 21 22 23


Time Complexity: O(N), N is the number of nodes
Auxiliary Space: O(N), N is the number of nodes

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