GATE CS 2020 Q46 — Recursion

To find the return value of fun2(5), we trace the execution step-by-step. Both functions use static variables, which retain their values across multiple function calls.

• Let $i_1$ be the static variable inside fun1 (initially $0$). Calling fun1(k) increments $i_1$ by $k$ and returns the updated value of $i_1$.
• Let $i_2$ be the static variable inside fun2 (initially $0$).

Tracing the recursive calls of fun2(5):

1. fun2(5): Calls fun1(5). $i_1$ becomes $0 + 5 = 5$. fun1(5) returns $5$. $i_2 = i_2 + 5 = 0 + 5 = 5$.
2. fun2(4): Calls fun1(4). $i_1$ becomes $5 + 4 = 9$. fun1(4) returns $9$. $i_2 = i_2 + 9 = 5 + 9 = 14$.
3. fun2(3): Calls fun1(3). $i_1$ becomes $9 + 3 = 12$. fun1(3) returns $12$. $i_2 = i_2 + 12 = 14 + 12 = 26$.
4. fun2(2): Calls fun1(2). $i_1$ becomes $12 + 2 = 14$. fun1(2) returns $14$. $i_2 = i_2 + 14 = 26 + 14 = 40$.
5. fun2(1): Calls fun1(1). $i_1$ becomes $14 + 1 = 15$. fun1(1) returns $15$. $i_2 = i_2 + 15 = 40 + 15 = 55$.
6. fun2(0): Base case ($n \le 0$). Returns $i_2 = 55$.

Thus, the final return value of fun2(5) is 55.