Test by Bikram | Mock GATE | Test 4 | Question: 14

Question

The worst case running time to search for an element in binary search tree with $2^{\log_2 n}$ elements is represented as $\Theta\left(n^{x \log_2 y}\right)$ .

The value of $x$ + $y$ is _____.

Answer 1

Worst case searching time in BST for $n$ elements $=O(n).$

$2^{\log_2 n} = n$ {using $\log$ property)

Now  $n^{x\log y} = n$ for $x=1$ and $y=2.$

So, answer = $x+y = 3.$

Comments

@jatin khachane 1 x=1/4 and y=16 , x=1/16 and y=$2^{16}$ also satisfying the equation there is no unique value  

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so don't put values in the equation just find it otherwise you will get the wrong answer

$x\log_2y=1$ $\rightarrow y^x=2^1$

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How come there is unique value for x and y? xlogy=1 can have many solutions as long as nothing is being said about the values x and y can have, right?