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Intro to Binary Trees and Breadth First Traversal

In this video, we provide a comprehensive overview of what trees are, common tree terminology, how binary trees are unique, applications of trees, how to implement a binary tree explore various applications of breadth first traversals across a binary tree.


  • 0:15 Learning objectives
  • 0:30 What’s a tree & common terminology
  • 2:58 Not a tree
  • 5:22 Practical applications of trees
  • 6:14 Binary trees
  • 7:23 Implementing a binary tree
  • 9:35 Conceptual overview of breadth-first traversal using a queue
  • 16:17 Implementing breadth-first search
  • 18:25 Summing all values in a tree
  • 20:06 Time and space complexity
  • 21:03 Recap


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Intro to Binary Trees and Breadth First Traversal
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Mix Order Traversal of a Binary Tree

Given a Binary Tree consisting of** N** nodes, the task is to print its Mix Order Traversal.

Mix Order Traversal_ is a tree traversal technique, which involves any two of the existing traversal techniques like Inorder, Preorder and Postorder Traversal. Any two of them can be performed or alternate levels of given tree and a mix traversal can be obtained._


_Input: _N = 6

_Output: __7 4 5 1 3 6 _


_Inorder-Preorder Mix Traversal is applied to the given tree in the following order: _

_Inorder Traversal is applied at level 0 _

_Preorder Traversal is applied at level 1 _

Inorder Traversal at level 2.

_Output: __4 5 7 1 6 3 _

#data structures #recursion #tree #inorder traversal #postorder traversal #preorder traversal #tree traversals

Check if all the Nodes in a Binary Tree having common values are at least D distance apart

Given a Binary Tree and an integer D, the task is to check if the distance between all pairs of same node values in the Tree is ? D or not. If found to be true, then print Yes. Otherwise, print No.


Input:_ D = 7 _

              /   \ 
             2     3
            / \   /  \ 
           4   3  4   4

Output:_ Yes _


_The repeated value of nodes are 3 and 4. _

_The distance between the two nodes valued 3, is 3. _

_The maximum distance between any pair of nodes valued 4 is 4. _

Therefore, none of the distances exceed 7

Input:_ D = 1 _

         / \
        3   3

Output:_ No _

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

**Approach: **

The idea is to observe that the problem is similar to finding the distance between two nodes of a tree. But there can be multiple pairs of nodes for which we have to find the distance. Follow the steps below:

  1. Perform the Post Order Traversal of the given tree and find the distance between the repeated pairs of nodes.
  2. Find the nodes that are repeated in the tree using unordered_map.
  3. For each repeated node of a particular value, find the maximum possible distance between any pair.
  4. If that distance is > D, print “No”.
  5. If no such node value is found having a pair containing that value, exceeding **D, **then print “Yes”.

#greedy #recursion #searching #tree #binary tree #frequency-counting #postorder traversal #tree-traversal

Construct a Maximum Binary Tree from two given Binary Trees

Given two Binary Trees, the task is to create a Maximum Binary Tree from the two given binary trees and print the Inorder Traversal of that tree.

What is the maximum Binary Tree?

_The __maximum binary __is constructed in the following manner: _

_In the case of both the Binary Trees having two corresponding nodes, the maximum of the two values is considered as the node value of the Maximum Binary Tree. _

_If any of the two nodes is NULL and if the other node is not null, insert that value on that node of the Maximum Binary Tree. _


Tree 1                Tree 2
   3                    5 
  / \                  / \
 2   6                1   8 
/                      \   \ 
20                      2   8 
Output: 20 2 2 5 8 8
         / \
        2   8
       / \   \
      20   2   8

To construct the required Binary Tree,
Root Node value: Max(3, 5) = 5
Root->left value: Max(2, 1) = 2
Root->right value: Max(6, 8) = 8
Root->left->left value: 20
Root->left->right value: 2
Root->right->right value: 8

       Tree 1            Tree 2 
         9                 5
        / \               / \
       2   6             1   8
      / \                 \   \
     20  3                 2   8
Output:  20 2 3 9 8 8
         / \
        2   8
       / \   \
      20  3   8

#data structures #mathematical #recursion #tree #preorder traversal #tree traversals

Double Order Traversal of a Binary Tree

Given a Binary Tree consisting of** N** nodes, the task is to print its Double Order Traversal.

Double Order Traversal_ is a tree traversal technique in which every node is traversed twice in the following order: _

  • Visit the Node.
  • Traverse the Left Subtree.
  • Visit the Node.
  • Traverse the Right Subtree.


      /   \
     7     3
    / \   /
   4   5 6
Output: 1 7 4 4 7 5 5 1 3 6 6 3 

      /   \
     7     3
    / \     \
   4   5     6
Output: 1 7 4 4 7 5 5 1 3 3 6 6

Recommended: Please try your approach on {IDE} first, before moving on to the solution.


The idea is to perform Inorder Traversal recursively on the given Binary Tree and print the node value on **visiting a vertex **and after the recursive call to the left subtree during the traversal.

Follow the steps below to solve the problem:

#data structures #recursion #tree #binary tree #inorder traversal #data analysis