GATE | GATE-CS-2014-(Set-3) | Question 20

Let A be a square matrix of size n x n. Consider the following program. What is the expected output? 

C = 100
for i = 1 to n do
    for j = 1 to n do
    {
        Temp = A[i][j] + C
        A[i][j] = A[j][i]
        A[j][i] = Temp - C
    } 
for i = 1 to n do
    for j = 1 to n do
        Output(A[i][j]);

(A)

The matrix A itself

(B)

Transpose of matrix A

(C)

Adding 100 to the upper diagonal elements and subtracting 100 from diagonal elements of A

(D)

None of the above

Answer: (A)

Explanation:

If we take look at the inner statements of first loops, we can notice that the statements swap A[i][j] and A[j][i] for all i and j. Since the loop runs for all elements, every element A[l][m] would be swapped twice, once for i = l and j = m and then for i = m and j = l. Swapping twice means the matrix doesn’t change.

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