Question: Let A[1 n] be an array of n distinct numbers. If i < j and A[i] > A[j], then the pair (i, j) is

Let A[1 ¬ n] be an array of n distinct numbers. If i < j and A[i] > A[j], then the pair (i, j) is called an inversion of A.
a. List the five inversions of the array ¬2, 3, 8, 6, 1¬.
b. What array with elements from the set {1, 2, . . . , n} has the most inversions? How many does it have?
c. What is the relationship between the running time of insertion sort and the number of inversions in the input array? Justify your answer.
d. Give an algorithm that determines the number of inversions in any permutation on n elements in Θ (n lg n) worst-case time. (Hint: Modify merge sort.)

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a The inversions are 1 5 2 5 3 4 3 5 4 5 Remember that inversions are specified by indices rather than by the values in the array b The array with ele... View full answer

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