Segment 6.9 noted that an array-based push method is normally O(1), but when a stack needs to be doubled in size, push is O(n). This observation is not as bad as it seems, however. Suppose that you double the size of a stack from n elements to 2n elements.
a. How many calls to push can you make before the stack must double in size again?
b. Remembering that each of these calls to push is O(1), what is the average cost of all the push operations? (The average cost is the total cost of all calls to push divided by the number of calls to push.)
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