In Java, as in other programming languages, array sizes are fixed at some N$.$ However, in Java when an overflow occurs for an array A of size N$,$ a method is called.$$ This method performs the following three steps:

$$Allocate a new array B of capacity $2$N

Copy A$[$i$]$ to B$[$i$],$ for i$=0,1,2,...,$ N$-1$

Let A$=$B

This array replacement strategy is known as an extendable array.

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Let S be a vector implemented by means of an extendable array A$.$ Show that the total time to perform a series of n push operations in S$,$starting from S being empty and A having size N$=1$is $($n$).$ Use the accounting method.