Data Structures and Algorithm Analysis - Computer Science at ...

122 Chap. 4 Lists, Stacks, and QueuesCurrptrβCall fact(4)Currptrβ1CurrptrCurrptrββ 1n 4 n 4Currptr β Currptr βCall fact(3) Call fact(2)CurrptrCurrptrββ2 2n 3 n 3CurrptrnCurrptrβ3n 214βCall fact(1)CurrptrCurrptrnCurrptrββ2n 3Currptrβ1 14 n 4β Currptr βReturn 1 Return 2CurrptrβReturn 6Return 24Figure 4.22 Implementing recursion with a stack. β values indicate the addressof the program instruction to return to after completing the current function call.On each recursive function call to fact (as implemented in Section 2.5), both thereturn address and the current value of n must be saved. Each return from factpops the top activation record off the stack.current value for n (which is 4), is saved on the stack. Function fact is invokedwith input parameter 3.In similar manner, another recursive call is made with input parameter 2, requiringthat the address from which the call is made (say β 2 ) and the current valuefor n (which is 3) are stored on the stack. A final recursive call with input parameter1 is made, requiring that the stack store the calling address (say β 3 ) and currentvalue (which is 2).At this point, we have reached the base case for fact, and so the recursionbegins to unwind. Each return from fact involves popping the stored value forn from the stack, along with the return address from the function call. The returnvalue for fact is multiplied by the restored value for n, and the result is returned.Because an activation record must be created and placed onto the stack foreach subroutine call, making subroutine calls is a relatively expensive operation.While recursion is often used to make implementation easy and clear, sometimes