Describe an efecient in-place algorithm called Partition-Even-Odd(A) that partitions an array A in even and odd numbers. The algorithm must terminate with A containing all its even elements preceding all its odd elements. For example, for input A = [7, 17, 74, 21, 7, 9, 26, 10], the result might be A = [74, 10, 26, 17, 7, 21, 9, 7]. Partition-Even-Odd must be an in-place algorithm. What does this mean about your algorithm? (a) Write the pseudo-code for Partition-Even-Odd. (b) Characterize the complexity of Partition-Even-Odd. Brie y justify your answer. (c) Formalize the correctness of the partition problem as stated above, and prove that Partition-Even- Odd is correct using a loop-invariant.

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