Question

1. Suppose we are maintaining a data structure under a series of n operations. Let f (k) denote the actual running time of the kth operation. For each of the following functions f, determine the resulting amortized cost of a single operation. (For practice, try all of the methods described in this note.) (a) f(k) is the largest integer i such that 2' divides k.

The example shows that the actual cost of action number k is the largest integer i so that 2i goes up. For example, if k is 12, then i = 2, because 22 = 4 goes up 12 and a higher square of 2 does not.

Answer 1

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