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6. (This is a slight re-wording of problem 8-5 on page 207 of CLRS 3rd edition.) Suppose that, instead of sorting an array, we just require that the elements increase on average. More precisely, we call an n-element array A[1 ... n] k-sorted if for all i in the range 1 sisn - k, the following holds: jk-1 A[i] &j=k+1 A[j] k a. What does it mean for an array to be 1-sorted? b. Give a permutation of the numbers {1, 2, 3, ..., 10} that is 2-sorted, but not sorted. c. Prove that an n-element array is k-sorted if and only if A[i] = A[i + k] for all i in the range 1 s i