Consider an implementation of the array list ADT using a dynamic array, but instead of copying the elements into an array of double the size (that is, from N to 2N) when its capacity is reached, we copy the elements into an array with ⌈N/4⌉ additional cells, going from capacity N to N + ⌈N/4⌉. Show that performing a sequence of n push operations (that is, insertions at the end) still runs in O(n) time in this case.
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