Lecture 267:- Height vs Node of Strict Binary Tree

In a strict binary tree, the height of the tree and the number of nodes are related to each other based on the properties of a binary tree.

For a strict binary tree:

1. Minimum Number of Nodes:
   • The minimum number of nodes in a strict binary tree of height h is h+1.
   • This occurs when the tree is a complete binary tree, with each level (except the last) having the maximum number of nodes (i.e., 2^h nodes).
2. Maximum Number of Nodes:
   • The maximum number of nodes in a strict binary tree of height h is 2^(h+1) - 1.
   • This occurs when the tree is a full binary tree, with every internal node having exactly two children.
3. Height and Nodes Relationship:
   • The height h of a strict binary tree with n nodes can be calculated using the formula: h = log2(n+1) - 1.
   • Similarly, the number of nodes n in a strict binary tree with height h can be calculated using the formula: n = 2^(h+1) - 1.

In summary, the height of a strict binary tree is logarithmic with respect to the number of nodes. As the number of nodes increases, the height of the tree increases logarithmically, making it an efficient data structure for certain operations.

It's important to note that a strict binary tree is a specific type of binary tree where each internal node has exactly two children. In contrast, a general binary tree may have nodes with zero, one, or two children, and the height and number of nodes in a general binary tree are not as strictly related as in a strict binary tree.