Readme.md

Table of content

• Binary Tree
• Height of the binary tree
  • Algorithm
  • Output for height of the binary tree
  • Properties
• Number of leaf nodes in Binary Tree
  • Algorithm
  • Output for number of leaf nodes in binary tree
  • Properties

Binary Tree:

• A tree whose elements have at most 2 children is called a binary tree.
• Each element of a binary tree can have only 2 children, we name them the left and right child.

Height of the binary tree

• The height of a binary tree is equal to the largest number of edges from the root to the most distant leaf node.

Algorithm

begin height(root)
If node is NULL 
  then return 0
Else 
  If left child and right child nodes are NULL 
    return 1
Else 
  take two integers let 'l' and 'r' to store value of left child and right child recursively
  by using formula:
    height_of_a_tree = 1 + (which-one is bigger from 'l' & 'r')
 end height

Output for height of the binary tree

100
 \
  120
     \
     130
        \
        140
           \
           150
             \
             160
                \
                170

Height of tree: 7

                 100
           /              \
        30                150
     /    \             /      \
  20       50          122      188

Height of tree: 3

Properties

• Time Complexity: O(n)
• Space Complexity: O(n)

Number of leaf nodes in binary tree

• A node is a leaf node if both left child and right child nodes of its are NULL.
• We are using Recursion to count nodes.

Algorithm

begin leaf_count(root)
If node is NULL 
  then return 0
Else 
  If left child and right child nodes are NULL 
    return 1
Else 
  recursively calculate leaf count of the tree using formula:
    Leaf_count_of_tree = Leaf_count_of_left_subtree + Leaf_count_of_right_subtree
 end leaf_count

Output for number of leaf nodes in binary tree

100
  \
   120
      \
      130
         \
         140
            \
            150
              \
              160
                 \
                 170

No. of leaf nodes of tree: 1

                 30
           /              \
        20                40
     /    \             /      \
  10       25          35      45

No. of leaf nodes in tree: 4

Properties

• Time Complexity: O(n)
• Space Complexity: O(n)