6. Consider the following idea for sorting a list of size n: Split the list into...

 

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6. Consider the following idea for sorting a list of size n: Split the list into n1/3 lists of size n2/3 each, sort each of the smaller list individually and then merge the sorted lists to get a single sorted list. (a) Let T(n) denote the worst case running time of an algorithm based on this idea. Derive a recurrence relation for T(n). Provide a clear explanation of how you arrived at this recurrence. (b) Solve the recurrence relation to determine a function g(n) such that T(n) is (g(n)). 6. Consider the following idea for sorting a list of size n: Split the list into n1/3 lists of size n2/3 each, sort each of the smaller list individually and then merge the sorted lists to get a single sorted list. (a) Let T(n) denote the worst case running time of an algorithm based on this idea. Derive a recurrence relation for T(n). Provide a clear explanation of how you arrived at this recurrence. (b) Solve the recurrence relation to determine a function g(n) such that T(n) is (g(n)).