Question: Consider the following algorithm to generate a random permutation. PERMUTE(n) 1 fori 1 to n 2 3 for i 1 to n 4 used(i) =

Consider the following algorithm to generate a random permutation. PERMUTE(n) 1

Consider the following algorithm to generate a random permutation. PERMUTE(n) 1 fori 1 to n 2 3 for i 1 to n 4 used(i) = FALSE repeat rRANDINT(1,n) until used(r) = FALSE perm(i) = r used(r) = TRUE 9 return perm (a) Prove that the algorithm is correct in the sense that all permutations are equally likely to be chosen. (Hint: what should be the probability for each permutation?) (b) let X denote the number of times that RANDINT is called in line 5. What is ET]

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