Question: Algorithms Input: n: positive integer Output: phi(n) Algorithm: EulerPhi for a = 2 to Squareroot do if a divides n then b = n/a g

Algorithms Input: n: positive integer Output: phi(n) Algorithm: EulerPhi for a

Algorithms

Input: n: positive integer Output: phi(n) Algorithm: EulerPhi for a = 2 to Squareroot do if a divides n then b = n/a g = gcd(a, b) return EulerPhi(a) middot EulerPhi(b) middot g/EulerPhi(g) end end return n - 1 Describe a small example for why this algorithm is a good candidate for dynamic programming. You may use Wolfram Alpha (or some other calculator) to compute god's. What data structure would you use in order to store the solutions to subproblems? What is a reasonable sentinel value to indicate that the algorithm has not yet computed phi(n)? Give pseudocode for a memorized implementation of this algorithm. You may assume that someone has implemented a function gcd(m, n) that computes the god off two integers

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