The array$-$based Queue throws an exception, when the array$$s capacity has been reached. Consider one of the following alternatives in which we use a resize method to expand the size of the array, each time we run out of array space. The cost of a resize that makes the array larger is proportional to the new size.

i$.$ Suppose, we expand the array$$s capacity by one element. Give an analysis of the running time $($Big$-$Oh notation$)$ in the worst$-$case, for a sequence of N insertions?

ii$.$ Suppose, we double the array$$s capacity $($assume the capacity is not zero$).$ Give an analysis of the running time $($Big$-$Oh notation$)$ in the worst$-$case, for a sequence of N insertions?