Explain what is meant by the height of a binary tree. Let us assume that in a fully populated binary tree, there are 15 internal (non terminal) vertices. What is the height of the tree? Is there a relationship between height of a tree and maximum number of nodes? Solution The height of a tree is the length of the path from the root to the leave of the tree. A (rooted) tree with only one node (the root) has a height of zero. heigh = 0, node = 1, internal vertices = 0 heigh = 1, node = 2, internal vertices = 1 heigh = 2, node = 4, internal vertices = 3 heigh = 3, node = 8, internal vertices = 7 heigh = 4, node = 16, internal vertices = 15 therefore, the height of the tree with 15 internal vertices is 4. relationship: max nodes = (2(Height + 1)) - 1.

1. Explain what is meant by the height of a binary tree. Let us assume that in a fully populated
binary tree, there are 15 internal (non terminal) vertices. What is the height of the tree? Is there a
relationship between height of a tree and maximum number of nodes?
Solution
The height of a tree is the length of the path from the root to the leave of the tree. A (rooted) tree
with only one node (the root) has a height of zero.
heigh = 0, node = 1, internal vertices = 0
heigh = 1, node = 2, internal vertices = 1
heigh = 2, node = 4, internal vertices = 3
heigh = 3, node = 8, internal vertices = 7
heigh = 4, node = 16, internal vertices = 15
therefore, the height of the tree with 15 internal vertices is 4.
relationship:
max nodes = (2(Height + 1)) - 1