GATE 2024 DA Q.41: solution and answer

Official answer: CSource: Official answer key, GATE 2024 DA (IISc Bengaluru)

1. The function is:

   def fun(D, s1, s2):
           if s1 < s2:
               D[s1], D[s2] = D[s2], D[s1]
               fun(D, s1+1, s2-1)

   Both the swap and the recursive call sit inside the if, so when s1 < s2 is false the function does nothing and returns. This is the base case, reached when the indices meet (s1 == s2) or cross (s1 > s2).

2. When s1 < s2, the tuple assignment D[s1], D[s2] = D[s2], D[s1] evaluates the right-hand side first and then assigns, so it exchanges the two end elements of the window with no temporary variable needed.

3. The call fun(D, s1+1, s2-1) moves both indices one step inward. It shrinks the window by two and swaps the next pair counted from the outside. The list D is mutable and passed by reference, so every swap changes the caller's list.

4. Trace with D = [a, b, c, d, e], s1 = 0, s2 = 4. The pair (0, 4) gives [e, b, c, d, a]. The pair (1, 3) gives [e, d, c, b, a]. At (2, 2) the test 2 < 2 fails, so the call stops. The result is the reverse of the list.

5. Even length, D = [a, b, c, d] with s1 = 0, s2 = 3. The pair (0, 3) gives [d, b, c, a]. The pair (1, 2) gives [d, c, b, a]. At (2, 1) the test 2 < 1 fails and the call stops. This is again the full reverse.

6. General argument by induction on the window length $n=s2-s1+1$. For $n\le 1$ nothing happens, and a window of length 0 or 1 is its own reverse. For $n\ge 2$ the first swap puts the old last element at index s1 and the old first element at index s2. The recursion then reverses the inner window s1+1 .. s2-1, which has length $n-2$, by the induction hypothesis. Together this gives the reverse of the whole window s1 .. s2. Elements outside the window are never touched.

7. Nothing in the code compares elements, so it cannot find a minimum (A) or sort (B). It performs about $(n)/2$ swaps rather than a single swap, so (D) is wrong, since (D) would leave the interior unchanged. Only option (C) matches. The answer is C.