Recall that the algorithm for computing the strongly connected components of a directed graph uses two passes of DFS, first in the reverse graph and then in the original graph (always starting at nodes with maximal DFS number). For each of the following statements, decide whether the statement is true of false. If the statement is true, argue why. If the statement is false, give a counterexample.

(i) The algorithm would remain correct if it used BFS instead of DFS in the first pass (and the BFS numbers instead of the DFS numbers in the second pass).

(ii) The algorithm would remain correct if it used BFS instead of DFS in the second pass (always starting at nodes with maximal DFS number).

(iii) The algorithm would remain correct if it used the original graph in its first pass and the reversed graph in its second pass. (iv) The algorithm would remain correct if it used the original graph in both passes, provided in the second pass it always starts at nodes with minimal DFS number.