Question

Consider the following program:

int main() {
    f1();
    f2(2);
    f3();
    return(0);
}

int f1() {
    f1();
    return(1);
}

int f2(int X) {
    f3();
    if (X==1)
        return f1();
    else
        return (X * f2(X-1));
}

int f3() {
    return(5);
}

Which one of the following options represents the activation tree corresponding to the main function?

• A.
• B.
• C.
• D.

Hint:

When drawing activation trees, always expand function calls step by step, including recursive calls. Each call becomes a node, and its direct calls become its children.

Answer 1

The Correct Option is A

Step 1: Understand function calls in main().
The function main() calls:
\[ f1(); f2(2); f3(); \]
So, the activation tree root (main) has three children: \(f1\), \(f2\), and \(f3\).

Step 2: Analyze f1().
f1() calls itself recursively once and then returns 1.
So \(f1\) has a recursive self-call in the activation tree.

Step 3: Analyze f2(2).
For \(f2(2)\):
- It first calls \(f3()\).
- Since \(X = 2 \neq 1\), it returns \(2 \times f2(1)\).
- Now \(f2(1)\) calls \(f3()\) and then returns \(f1()\).

So inside \(f2(2)\), we have calls: \(f3 \to f2(1) \to (f3, f1)\).

Step 4: Analyze f3().
f3() simply returns 5 with no further calls.

Step 5: Activation Tree Construction.
- Root: main
- Child 1: \(f1\) (recursive call inside)
- Child 2: \(f2(2)\)
- \(f3\)
- \(f2(1)\)
- \(f3\)
- \(f1\)
- Child 3: \(f3\)

This exactly matches option (A).

\[ \boxed{\text{Correct Option: (A)}} \]