a tree is binary, if every node has at most two children nodes. prove that the...

a tree is binary, if every node has at most two children nodes. prove that the maximum of nodes in a binary tree of height h is 2^(h+1)-1

Expert Solution

We want to show that maximum of nodes in a binary tree of height h is 2^(h+1)-1.

We want to find the maximum number of nodes of binary tree,which means that the binary tree is completed.

For level 1 of complete binary tree,number of nodes=1=2⁰

for level 2,number of nodes=2=2¹

for level 3,number of nodes =4=2²

for level 4,number of nodes=8=2³

^.

for level h,number of nodes=2^h

Total number of nodes in a complete binary tree will be,

=2⁰+2¹+2²+2⁴+.....+2^h

= from the equation of sum of geometrical progression= ,where a is the first term,r is the common ratio and n is the number of terms.

= 2^(h+1)-1

Hence proved.

venereology answered 3 months ago

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