How did my textbook  get  2(n − 1) + 1 = 2n − 1 comparisons are used whenever this algorithm is applied:  (textbook solves the time complexity of finding the maximum element in a finite set using the following algorithm)  Algorithm below: procedure max(a1, a2,…, an: integers) max := a1 for i := 2 to n     if max < ai then max := ai return max{max is the largest element}

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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.