Question

Let’s work together to develop a call tree for the execution of the following recursive method. (The method allows us to recursively generate the nth integer in the Fibonacci sequence, although you don’t need to be familiar with that sequence to understand this problem.)

public static int fib(int n) {
    if (n == 0 || n == 1) {
        return 1;
    } else {
        int prev1 = fib(n - 2);
        int prev2 = fib(n - 1);
        return prev1 + prev2;
    }
}

Assume that we begin with the following initial call to this method:

fib(4)

1. Let’s draw a call tree for the sequence of calls that are involved in computing the result of fib(4). As we do so, we’ll number each call of the method in the order in which they are made.

2. The order in which the calls are made is not the same as the order in which the calls return. A given invocation of the method can’t return until both of the calls that it makes (fib(n - 2) and fib(n - 1)) return.

   Underneath your call tree, list the order in which the calls return, as well as their return values. When you refer to a given call in this part of the problem, use its number from the call tree.

   For example, the initial call always returns last, so the last line in this part of the problem should look like this:

   call 1 (fib(4)) returns ...
   

   where you replace the ... with its return value.

3. Re-write the fibonacci recursive method to not use multiple return statements. Does it work the same way?

Answer 1

Please find the solution below.

call Tree for fibcu) (1) fib(4) y return value of children 6) fible) + føb(3)63 fibco) + fibca) call Number fiblo) + fib( 1) (ix) from "Tep to botton The calls are executed Left to right: call 3 fiblo) returns I. call 4 fibcis returns a call a fib(2) returns 2 call 6 fible) returis I call 8 fibco) returns I call a filci) returns 1 call 7 fils (2) returns 2 calls fib(3) returns 3 call I fibcus returns 5

Trying to write a Program without multiple returns :- public static int fibcn). if (n=1) return filo CN-2) + fibcn-1); ) return an ? Base Case l Recursive lase. else correctly computes the Here, the above program oth Fibonacci number: atleast a But, we need returns 9 Base case : where there is no recursive call. 2) Recursive case : Here we call the same function again.

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