GATE CS 1993 Q7.4 — Asymptotic Worst Case Time and Space Complexity

Let the initial values of the variables $a$ and $b$ be $a_0$ and $b_0$ respectively.

We can trace the execution of the statements step-by-step:

1. a := a + b;
   The new value of $a$ becomes:$$a = a_0 + b_0$$
2. b := a - b;
   Using the updated value of $a$:$$b = (a_0 + b_0) - b_0 = a_0$$
3. a := a - b;
   Using the updated values of $a$ and $b$:$$a = (a_0 + b_0) - a_0 = b_0$$

After the execution of these three statements, the final value of $a$ is $b_0$ and the final value of $b$ is $a_0$. Thus, the values of $a$ and $b$ are exchanged (swapped) without using a temporary variable.

Therefore, the correct option is A.