We are interested in measuring the time complexity of executing a sequence of n invocations of the following function with the array A initially containing all 0's. Function increment (A) Input: A[0..m-1] is an array of 0-1 bits representing a binary counter Output: A after its value incremented by 1 modulo 2m i 0 while i < m and A[i] = 1 do A[i] +0 i + i +1 end if i < m then | A[i] + 1 end (a) Note the time complexity of the function is proportional to number of itera- tions of the while loop and can be 0(m) in the worst case. Thus concluding that the sequence of n invocations takes O(mn) time is incorrect as it is a loose bound. We can use amortized complexity analysis to improve the bound. Using accounting method show that the amortized complexity of a single invocation in a sequence of n invocations is 0(1). [Hint: Assume cost of a function is measured by number of bit flips(0 to 1 and 1 to 0) required. Argue that the amortized cost is 2 units per invocation] (b) What potential function will you use for the amortized analysis ? Derive the amortized time complexity using this potential function.