Question

Consider the following ANSI C function: 

int SimpleFunction(int Y[], int n, int x) 
{ 
	int total = Y[0], loopIndex; 
	for (loopIndex = 1; loopIndex <= n - 1; loopIndex++) 
		total = x * total + Y[loopIndex]; 
	return total; 
}

Let \( Z \) be an array of 10 elements with \( Z[i] = 1 \), for all \( i \) such that \( 0 \le i \le 9 \). The value returned by SimpleFunction(\( Z, 10, 2 \)) is \(\underline{\hspace{2cm}}\).

Hint:

Such loops often form a geometric progression when the update is of the form \( \text{total} = a \times \text{total} + b \).

Answer 1

Correct Answer: 1023

Step 1: Understand initialization.
Initially, \[ \text{total} = Y[0] = 1 \]

Step 2: Understand loop behavior.
The loop runs from \( \text{loopIndex} = 1 \) to \( 9 \). In each iteration, the update rule is:
\[ \text{total} = 2 \times \text{total} + 1 \]

Step 3: Observe the recurrence relation.
Starting from \( \text{total}_0 = 1 \), the recurrence generates the sequence:
\[ 1,\; 3,\; 7,\; 15,\; 31,\; 63,\; 127,\; 255,\; 511,\; 1023 \]

Step 4: Final value after 9 iterations.
After the final iteration, the value of \text{total} becomes:
\[ 1023 \] % Final Answer

Final Answer: \[ \boxed{1023} \]