a$.$ Recall the dynamic array : You start with an array of size $1.$ When the array is full, you allocate a new one with the size being doubled, then copy all the items to it$.$ We have shown that the amortized cost for each add$/$push is $3.$

Consider now that allocating memory for $\backslash (\backslash$boldsymbol$\{$k$\}\backslash )$ positions costs $\backslash (\backslash$boldsymbol$\{$k$\}\backslash )($instead of $0).$ This means allocating a new array of size $2$ n and copying n items to it would now cost $3$ n $.$ Does the amortized cost for each add$/$push still hold? What would be the new value for the amortized cost? Justify your answer.

b$.$ Consider a stack implemented on an "infinite array", with no need to grow and shrink, and with push and pop operations, each one costing $1.$ Now we need to add another operation multipush $(\backslash ($ k $\backslash )),$ that pushes kelements to the stack. Would the amortized cost per operation still be constant? Justify your answer.