[solved] – Question 80327

In an experiment, the Merge Sort algorithm will be modified into a 3-MergeSort algorithm in the hope of getting a new algorithm that is more efficient. Basically, the modification made is that the input array of length n is no longer split into 2, but into 3, so that each new array created will have a length of n/3. Answer the following questions:

To accommodate the above modification, the Merge function will be changed to a Merge3 function which no longer accepts input in the form of 2 arrays, but 3 arrays (which have been ordered). Consider the implementation of the Merge3 function in the following pseudocode:
function Merge3(array A, array B, array C):
AB = Merge(A, B)
return Merge(AB, C)

* The Merge function called in the Merge3 function above is the same Merge function as the standard Merge Sort algorithm, which accepts 2 sorted arrays as input.

Calculate the time complexity of the Merge3 function! Use Big O notation with m as input, where m is the total sum of the lengths of the arrays A, B, and C!

Calculate the time complexity of the 3-MergeSort algorithm as a whole! Use Big O notation with n as input, where n is the length of the initial input array!

When compared to the time complexity of the standard Merge Sort algorithm, can the 3-MergeSort algorithm be said to be significantly more efficient?

Suppose the 3-MergeSort algorithm created above is run on the following array: [4, 8, 2, 9, 1, 7, 5, 3, 6]. What will the contents of the array look like when the three outermost recursion function calls have finished, but just before the most recent Merge3 function executed?

Expert Answer

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Answer to In an experiment, the Merge Sort algorithm will be modified into a 3-MergeSort algorithm in the hope of getting a new algorithm……