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The bitonic sorting network needed log n number of stages for performing the task of sorting the list. The first n-1 stages of the circuit are able to sort two n/2 numbers and the last stage uses a +BM (n) comparator having the depth of log n. As running time of the sorting is dependent upon the entire depth of the circuit, thus it can be depicted as:
D (n) = D (n/2) + log n
Answering the above mentioned recurrence relation
D (n)= (log2 n + log n)/2 = O(log2 n)
Thus, the complexity of solving a sorting algorithm using a combinational circuit is
O (log2 n).
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