Question 56

Notice that fun1 and fun2 each declare their own distinct static variable named i, both initialized to 0 once at the start of execution:

• Let $i_1$ denote the static variable in fun1.
• Let $i_2$ denote the static variable in fun2.

Behavior of fun1(k):

• When fun1(k) is invoked with argument $k$, if $k > 0$ it increments $i_1$ by 1 and recursively calls fun1(k-1).
• Thus, a call fun1(k) executes the ++i statement exactly $k$ times, increasing $i_1$ by $k$, and returns the updated value of $i_1$.

Trace of fun2(5) step by step:

• Initially: $i_1 = 0$, $i_2 = 0$.
• Step 1 ($n = 5$):
  • Calls fun1(5): increments $i_1$ by 5 $\implies i_1 = 5$, returns 5.
  • Updates $i_2$: $i_2 = i_2 + 5 = 0 + 5 = 5$.
  • Recursive call fun2(4).
• Step 2 ($n = 4$):
  • Calls fun1(4): increments $i_1$ by 4 $\implies i_1 = 5 + 4 = 9$, returns 9.
  • Updates $i_2$: $i_2 = i_2 + 9 = 5 + 9 = 14$.
  • Recursive call fun2(3).
• Step 3 ($n = 3$):
  • Calls fun1(3): increments $i_1$ by 3 $\implies i_1 = 9 + 3 = 12$, returns 12.
  • Updates $i_2$: $i_2 = i_2 + 12 = 14 + 12 = 26$.
  • Recursive call fun2(2).
• Step 4 ($n = 2$):
  • Calls fun1(2): increments $i_1$ by 2 $\implies i_1 = 12 + 2 = 14$, returns 14.
  • Updates $i_2$: $i_2 = i_2 + 14 = 26 + 14 = 40$.
  • Recursive call fun2(1).
• Step 5 ($n = 1$):
  • Calls fun1(1): increments $i_1$ by 1 $\implies i_1 = 14 + 1 = 15$, returns 15.
  • Updates $i_2$: $i_2 = i_2 + 15 = 40 + 15 = 55$.
  • Recursive call fun2(0).
• Step 6 ($n = 0$):
  • Condition $n > 0$ is false; returns $i_2 = 55$.

All recursive returns pass back $i_2 = 55$. Thus, fun2(5) returns 55.