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5 (10 points) In a 5 ary tree, that is a tree with at most 5 childr

5 (10 points) In a 5 ary tree, that is a tree with at most 5 childr

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5. (10 points) In a 5-ary tree, that is a tree with at most 5

children at each node, how many nodes

can a tree of height H have. Recall that the height of a

tree is a length of the longest path from

the root to the leaf nodes of the tree.

6. (10 points) In a 5-ary tree, what is the maximum height

of a tree with N nodes. Since that was

easy, let\'s try one a little harder: what is the minimum

height of a tree with N nodes?

Solution

Answer:)

5.When H = 0, #nodes = 1

When H = 1, #nodes = 5+1

When H=2, #nodes = 25 + 5 + 1

Therefore,when H = n, #nodes = 5^n + 5^(n-1) + 5^(n-2)

+...+5^1+5^0

6.

Maximum height of a tree with N nodes = N - 1

Minimum height of a tree with N nodes = floor(log5N)

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5. (10 points) In a 5-ary tree, that is a tree with at most 5 children at each node, how many nodes can a tree of height H have. Recall that the height of a tree is a length of the longest path from the root to the leaf nodes of the tree. 6. (10 points) In a 5-ary tree, what is the maximum height of a tree with N nodes. Since that was easy, let\'s try one a little harder: what is the minimum height of a tree with N nodes? Solution Answer:) 5.When H = 0, #nodes = 1 When H = 1, #nodes = 5+1 When H=2, #nodes = 25 + 5 + 1 Therefore,when H = n, #nodes = 5^n + 5^(n -1) + 5^(n-2) +...+5^1+5^0 6. Ma ...
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