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
Given information:
In the full binary tree
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
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).
Hence,