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A tree in which each node has at most two children, which are referred to as the left child and the right child.
There we can say that a binary tree node contains the following parts:
Data
Pointer to the left child
Pointer to the right child
Properties of Binary Tree:
Property_01: Minimum number of nodes in the binary tree of height H = H+1
2. Property_02:
Maximum no of nodes in a binary tree of height H = 2^(H+1)-1
Example:
Maximum number of nodes in a binary tree of height 2
= 2^(2+1) - 1
= 8 - 1
= 7
Thus, in a Binary tree of height = 2, the maximum number of nodes that can be inserted = 7.
3. Property_03:
Total number of leaf nodes in a Binary Tree
= Total number of nodes with 2 children + 1
Example:
Consider the following binary tree-
Here,
Number of leaf nodes = 4
Number of nodes with 2 children = 3
Clearly, the number of leaf nodes is greater than the number of nodes with 2 children.
4. Property_04:
Maximum number of nodes at any level 'L' in a binary tree = 2^L
Example:
The maximum number of nodes at level 2 in a binary tree.
= 2^2
= 4
Thus, in a binary tree, the maximum number of nodes that can be present at level 2 = 4
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