Write a recursive function using python for the problem: A palindrome is a sequence of characters which is the same when the sequence is reversed. Given an array A indexed from p to q containing characters, determine if the sequence of characters in A[p..q] forms a palindrome. Return True is a palindrome is formed and return False if it does not.

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A: The complete python code is below:

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A: Below i have answered:

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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.