Question

Explain how to find the structure of an M-ary tree when given information about the number of leaves and the height.

Answer 1

To find the structure of an M-ary tree given the number of leaves and the height, follow these steps: calculate the number of nodes, calculate the number of internal nodes, and divide the number of internal nodes by the number of branches. Example calculation provided.

Step-by-step explanation:

To find the structure of an M-ary tree given the number of leaves and the height, you can follow these steps:

1. Start by determining the number of nodes in the tree. For an M-ary tree, the number of nodes can be calculated using the formula (M^(h+1)-1)/(M-1), where M is the number of children each node can have and h is the height of the tree.
2. Next, calculate the number of internal nodes in the tree by subtracting the number of leaves from the total number of nodes.
3. Finally, divide the number of internal nodes by the number of branches each node has (M) to determine the structure of the tree.

For example, let's say we have an M-ary tree with 5 leaves and a height of 2. Using the formula, we can calculate the number of nodes as (M^(h+1)-1)/(M-1) = (5^(2+1)-1)/(M-1) = 31. Subtracting the number of leaves, we get 31 - 5 = 26 internal nodes. Since this is an M-ary tree, each internal node has M branches, so the structure of the tree is 26 / M.