Question: Permute-By-Sorting 1. n = A.length 2. let P [1..n] be a new array 3. for i = 1 to n 4. P[i] = Random (1,

Permute-By-Sorting 1. n = A.length 2. let P [1..n] be a new array 3. for i = 1 to n 4. P[i] = Random (1, n^3) 5. sort A, using P as sort keys

Prove that in the array P in procedure Permute-By-Sorting (CLRS Page 125), the probability that all elements are unique is at least 1-1/n. (hint: we are not looking for the exact probability, rather we are looking for a lower bound, so you can simplify your probability expression by choosing a suitable lower bound, the inequality (1 - x)^n 1 - nx can be useful)

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