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: ;*-?A[j] ++. A[j] 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] SA[i+k] for all i in the range 15 is n-k. d. Describe an algorithm that k-sorts an n-element array in time (n logn)