Consider the set T of binary trees which are recursively defined by the following. If T...
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Consider the set T of binary trees which are recursively defined by the following. If T = (V, E), T2 = (V2, E) are trees, then we can make a new tree Tree (T1, T) in the following way. As vertex set we take the vertices in T, T and add a new vertex r. This vertex r' is the root of the new tree and is the tail of 2 new edges with head r, with 1 i 2, the root of T. All other edges come from T and T. The set of finite trees is then defined by: o the tree on a single vertex is in T; o if T and T are in T, then Tree (T, T) is in T. A leaf of a tree is a vertex with outdegree 0. Denote by I the number of leaves in a tree . Then 7 (v+1)/2 where u is the number of vertices. = Prove this using structural induction. Consider the set T of binary trees which are recursively defined by the following. If T = (V, E), T2 = (V2, E) are trees, then we can make a new tree Tree (T1, T) in the following way. As vertex set we take the vertices in T, T and add a new vertex r. This vertex r' is the root of the new tree and is the tail of 2 new edges with head r, with 1 i 2, the root of T. All other edges come from T and T. The set of finite trees is then defined by: o the tree on a single vertex is in T; o if T and T are in T, then Tree (T, T) is in T. A leaf of a tree is a vertex with outdegree 0. Denote by I the number of leaves in a tree . Then 7 (v+1)/2 where u is the number of vertices. = Prove this using structural induction.
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Related Book For
Introduction to Algorithms
ISBN: 9780262033848
3rd edition
Authors: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest
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