Question
Suppose that we implement the following wrapper algorithm: RepeatedRandomizedApproximateMiddle(A,p) // p is a probability value { K = ...... // K is calculated based on
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.
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