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Topic: the base case and step for induction proof (Read 1251 times) |
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transgalactic
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Posts: 11
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the base case and step for induction proof
« on: Jan 15th, 2012, 1:31pm » |
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there is a binary tree which has
l1..lm leaves
and their depth are d1,..,dm
prove that
[TEX]\sum ^m_{i=1} 2^{-d_i}\leq1[/TEX]
there is a link to the foto of expression
http://i39.tinypic.com/1o3ep5.jpg
??
i have to prove it by induction
i found out that each node must have only 0 or 2 sons.
i dont know why??
i cant see what is the base cae here?
what is the inductive step here
?
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| « Last Edit: Jan 15th, 2012, 1:33pm by transgalactic » |
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towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
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Posts: 13730
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Re: the base case and step for induction pro
« Reply #1 on: Jan 15th, 2012, 10:05pm » |
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on Jan 15th, 2012, 1:31pm, transgalactic wrote:
i found out that each node must have only 0 or 2 sons.
i dont know why?? |
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Because it's a binary tree.
Quote:| i cant see what is the base cae here? |
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Base case is a tree composed of a single leaf.
Quote:| what is the inductive step here |
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Given the formula holds for all binary trees of depth D-1, prove it holds for a binary tree of depth D
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Wikipedia, Google, Mathworld, Integer sequence DB
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