A Practical Introduction to Data Structures and Algorithm Analysis

Sec. 4.2 Stacks 129Currptr β 1CurrptrnCurrptrβ 23β 1CurrptrnCurrptrnCurrptrβ 32β 23β 1Currptr β 2n 4 n 4n 4Currptr β Currptr β Currptr β Currptr βCall fact(4) Call fact(3) Call fact(2) Call fact(1)nCurrptrnCurrptr3β 14βReturn 1CurrptrnCurrptrβ 14βReturn 2CurrptrβReturn 6Return 24Figure 4.21 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 (from Section 2.5), both the return addressand the current value of n must be saved. Each return from fact pops thetop activation record off the stack.Consider what happens when we call fact with the value 4. We use β toindicate the address of the program instruction where the call to fact is made.Thus, the stack must first store the address β, and the value 4 is passed to fact.Next, a recursive call to fact is made, this time with value 3. We will name theprogram address from which the call is made β 1 . The address β 1 , along with thecurrent 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 parame-