Suppose that we implement the following wrapper algorithm:

RepeatedRandomizedApproximateMiddle(A,p) // p is a probability value { 

 K = ...... // K is calculated based on p // Below, RandomizedApproximateMiddle is called K times in total min = RandomizedApproximateMiddle(A); // It is called here for the first time 

 for (i = 1; i < K; i++) { 

 newOne = RandomizedApproximateMiddle(A); // It is called K-1 times here if (newOne < min) 

newOne = min;

}

return min; }

RepeatedRandomizedApproximateMiddle calls RandomizedApproximateMiddle exactly K times. It does this to make sure that the probability that RepeatedRandomizedApproximateMiddle returns an element with rank less than n/10 is at least p, where p is an input to the algorithm.

The value K is computed in the beginning of RepeatedRandomizedApproximateMiddle. The place the computation is performed for K is left as blank (......) above in the code. Please fill in the blanks above such that the probability that RepeatedRandomizedApproximateMiddle returns an element with rank less than n/10 is at least p.

YOU MUST SHOW ALL THE STEPS OF YOUR CALCULATION TO GET FULL GRADE. JUST WRITING THE RESULT WILL NOT GET YOU ANY POINT.