divide the input array into thirds (rather than halves), recursively sort each third, and finally combine the results using a three-way Merge subroutine. What is the running time of this algorithm as a function of the length n of the input array, ignoring constant factors and lower-order terms

The answer is "nlogn".

Explanation:

The time complexity can only shift to 3 with the last instance.  For the 2nd case, they need one parallel. However, 2 parallels are needed to sort with splitting into 3-way frames. It decreases the number of passes even after breaking the collection in 3 by increasing contrast. So, the time complexity remains the same but the log is divided into 3 bits.  The complexity of time is:  

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