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Question

Suppose that you have *n* values to put into an empty binary search tree.

- In how many different orders can you add the
*n*values to the tree? This is not the same as the number of possible binary search trees for*n*values. Explain why. - What is the probability that a randomly constructed binary search tree has worst-case performance?
*Hint:*Compute the fraction of the total number of possible orders that results in the worst case.

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 5a. The number of different orders $n$ values can be added to a tree is the number of permutations of $n$ values, $n!$. The number of possible binary search trees for $n$ values is given by this formula:

$\frac{(2n)!}{(n + 1)! \cdot n!}$

These numbers are called Catalan numbers.

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