We have already had a recurrence relation of an algorithm, which is T (n) = 4T (n/2) + n log n. We know T (1) ≤c. (a) express it as T (n) = O(f (n)), by using the iteration method. (b) Prove, by using mathematical induction, that the iteration rule you have observed in 4(a) is correct and you have solved the recurrence relation correctly. [Hint: You can write out the general form of T (n) at the iteration step t, and prove 3 that this form is correct for any iteration step t by using mathematical induction. Then by finding out the eventual number of t and substituting it into your general form of T (n), you get the O(·) notation of T (n).]

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Randomized Select Algorithm

A randomized algorithm is defined as one that uses a certain amount of randomization in its logic or operation. It is said to be an algorithm that depends on the random number to perform its operation. It is used for reducing the overall time complexity, space complexity in the standard algorithm. The randomized algorithm uses the concept of random numbers to find the solutions to the different kinds of problems and also to improve the problem solutions.