Question

2. To calculate the computational complerity a measure for the maximal possible number of steps needed in a computation of the mergesort' algorithm (an algorithm for sorting natural numbers in non-decreasing order) one can proceed by solving the following recurrence relation an 2 an-1 2 -1 with ao0 (a) Use the method of generating functions to solve this recurrence relation. (b) The relation between the number tm of computations needed to sort m numbers, and the solution am of the recurrence relation, is given bymam. Use this to find an expression for t where n 2rn (or log2 n = m), explicitly as a function of n , and conclude that tn ~ n log2 n for large n . 0 1R2 OL5 1ORO 1R1 2 1R4 1R5 3 OR1 1L3 4 1L3 1L5

Answer 1

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