(a) Use induction to prove that for all integers h 0, h == 2k 2h+11. k=0...

 

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(a) Use induction to prove that for all integers h 0, h == 2k 2h+11. k=0 (b) Use part (a) to prove that the complete binary tree of height h has exactly 2h+1-1 vertices. Note: there is an alternate proof of this in the textbook. No credit will be given for using that proof. (c) Use part (b) to give an explicit formula for the minimum height of an n-vertex binary tree. (a) Use induction to prove that for all integers h 0, h == 2k 2h+11. k=0 (b) Use part (a) to prove that the complete binary tree of height h has exactly 2h+1-1 vertices. Note: there is an alternate proof of this in the textbook. No credit will be given for using that proof. (c) Use part (b) to give an explicit formula for the minimum height of an n-vertex binary tree.