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Consider the following naive sorting algorithm tort a sequence A in decreasing order: Sort-Array (A) for i 1 to (A.length 1) for i (i + 1) to A.length if (A[i] > A[i]) // swap A[i] and Alj] buffer A[j] Alil A[i] A[i] buffer 1) (2 points) Express the property that Sort-Array (A) must satisfy to be correct: 2) (4 points) Can you find some loop invariants for the outer for loop? List these invariants (even if they are not that helpful for our ultimate proof of correctness of Sort-Array) 3) (9 points) Propose a loop invariant for the outer loop that is the closest to our ultimate objective: Sort-Array is correct. 4) Use the three steps: a. (4 points) Initialization b. (10 points) Maintenance C. (6 points) Termination

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