$$ Explain what the above Mystery algorithm outputs and simulate its operation on a valid

input instance $($e$.$g$.,$ an array of n elements $-$ you can choose n to be $10)$

$$ What is the approximate time complexity $($running time$)$ of the above algorithm $($you can

use Big$-$Oh notation$)$

$$ How does the following algorithm improve the time complexity of the algorithm $($what is

its strategy$)?$ What is its time complexity?