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tynan74
tynan74
06.10.2019 • 
Mathematics

Let q ≥ 2 be a given integer. a full q-ary tree is a rooted tree (t, r) such that every vertex has either 0 or q children. a. show that if (t, r) is a full q-ary tree with p parents, then there must be exactly (q − 1)p + 1 non-parents. b. if (t, r) is a full q-ary tree, let vk be the set of vertices of t that are at level k. use the fact (do not reprove ) that |v0 | = 1 and for any k ≥ 0, |vk+1 | ≤ q |vk |, to show that |vk | ≤ q k. c. find the minimum possible height of a full 5-ary tree with 109 total vertices.

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