The number of leaf nodes in a rooted tree of n nodes, with each node having 0…

2002

1. A.

   n/2

2. B.

   (n−1)/3

3. C.

   (n−1)/2

4. D.

   Let I be the number of internal nodes and L be the number of leaves. Since every internal node has exactly 3 children, the number of edges is 3I. A tree with n nodes has n - 1 edges, so 3I = n - 1 and I = (n - 1)/3. Therefore L = n - I = n - (n - 1)/3 = (2n + 1)/3.

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