The transitive closure of a directed graph of n vertices can be defined as the n-by-n boolean matrix , in which the element in the ith row is 1 if there exists a nontrival directed path (i.e., a directed path of a positive length) from the ith vertex to the jth vertex; otherwise is 0. (In English can you get there from here)
a) What would be the transitive closure?
b) How might you solve this from a smaller problem to a bigger problem?
2. Use the below Warshall's algorithm to compute R(0), R(1), ... , R(n)
ALGORITHM Warshall ( A[1..n, 1..n])// Implements Warshall's algorithm for computing the transitive closure
// Input: The adjacency matrix A of a digraph with n vertices
// Output: The transitive closure of the digraph
for to n do
for to n do
for to n do
or ( and )
return R (n)