GATE CS 2007 Q42 — Recursion

To find the value of $f(5)$, we trace the recursive calls while keeping track of the static variable $r$. Since $r$ is static, it retains its value across function calls and is initialized to $0$ only once.

1. Call $f(5)$: Since $5 > 3$, the static variable is updated to $r = 5$. The function returns $f(3) + 2$.
2. Call $f(3)$: Since $3 \le 3$, it executes the last statement and returns $f(2) + r = f(2) + 5$.
3. Call $f(2)$: Similarly, returns $f(1) + r = f(1) + 5$.
4. Call $f(1)$: Returns $f(0) + r = f(0) + 5$.
5. Call $f(0)$: Since $0 \le 0$, it returns $1$.

Now, substituting the values back:

• $f(1) = f(0) + 5 = 1 + 5 = 6$
• $f(2) = f(1) + 5 = 6 + 5 = 11$
• $f(3) = f(2) + 5 = 11 + 5 = 16$
• $f(5) = f(3) + 2 = 16 + 2 = 18$

Thus, the value of $f(5)$ is 18.