If k is a positive integer and T is a full binary tree with k internal vertices. then T has a total of _____ vertices and has leaves.
To fill the blanks in the statement, “If is a positive integer and is a full binary tree with internal vertices, then has a total of _____ vertices and has _____ leaves.”
In the full binary tree , there are number of internal vertices.
In a full binary tree, every vertex has a parent vertex except the root vertex. Hence, the total number of vertices are one greater than the number of all vertices that have a parent. Since every parent has exactly two children vertices, for number of internal vertices, we can obtain number of vertices that have a parent.
Then, the total number of vertices are .
Also, the terminal vertices in a rooted tree are called as leaves. Then, from among all he vertices in a full binary tree, there are only internal vertices or terminal vertices(leaves).
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