# Tagged Questions

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### Use strong induction to prove number of vertices on complete tree is $2l-1$

Can someone help me construct this proof using strong induction? Use strong induction on $l$ to show that for all $l \geq 1$, a full binary tree with $l$ leaves has $2l-1$ vertices total.
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### Search L leaves smaller than node N

So in my binary $kd$-tree I have a node $N$. Now I search for the number of leafs $L$ "on the left" side of $N$ (this includes the left child branch of $N$ and all parents where the node is a right ...
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### Inserting values left to right in a binary search tree

What does it mean to build a binary search tree by inserting values from left to right starting from an empty tree? The "left to right" part confuses me..I know how to build one by normally inserting ...
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### creating a Binary tree based on a prefix expression

I want to find the value of a the prefix expression -/+8,10,2*3,2 and build its binary tree I am trying to learn this for a math course, but have absolutely no clue ...
I have a binary tree, with {a,b,c} nodes and {p,q} edges. When $p + q = 1$. the first tree a - p - b - q - c this generate the expresion $bq + cq$ ...
### Explanation of why the height of a binary tree $\theta({lg}(n))$.
From Heap Sort chapter of Introduction to algorithms : Since a heap of n elements is based on a complete binary tree , its height is $\theta({lg}(n))$. I know this is correct but how can this ...