Consider a function tetrahedral( ) that computes the n^th tetrahedral number for a given integer n>=0: T(n)= Tri(1)+Tri(2)+Tri(3)+...+Tri(n-1)+Tri(n)    where Tri(n) is defined as Tri(n)+1+2+3+...+(n-1)+n a) Implement the function tetrahedral( ) using recursion in order to perform the repeated additions. b) Find an algebraic representation for T(n) that does not require any repeated additions. Implement the function tetrahedral( ) with a one-line definition using this formula.

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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.