3. Consider the following algorithm Algorithm Mystery(A[0..n - 1, 0..n - 1]) //Input: A matrix A[0..n-1, 0..n - 1] of real numbers for i 0 to n - 2 do for ji+ 1 to n - 1 do if A[i, j] # A[j,i] return true return false a. What does this algorithm compute? If the square matric is symmetric or not. If it is symmetric it will return true. b. What is its input size? i=number of rows j= number of columns Input size: (ix j) c. What is its basic operation? The basic operation of the algorithm is to check if the elements A[ i, j ] and are equal or not. d. How many times is the basic operation executed? e. What is the efficiency class of this algorithm? f. Suggest an improvement, or a better algorithm altogether, and indicate its effici class. If you cannot do it, try to prove that, in fact, it cannot be done.

Topological sort is a sorting technique that sets up a hierarchy in a process. In this technique, when a directed network has nodes connected by arrows, the root node is placed before the successor node.