Problem $2$ Topological Ordering and Cycles

$5$ pts$.$

Most software projects consists of multiple modules that are interdependent on each other. For example. Module A may depend on Module B$,$ Module B may depend on Module C$,$ and Module C may depend on Module A$.$ This forms a cycle in the dependency graph, which can cause issues during the build process. Given the dependency graph on the various software modules, develop a single algorithm called TopoSortCycles $(G)$ on a dependency $($directed$)$ graph $G$ that does both of the following:

$($a$)$ Return the topological ordering of modules using DFS$\_$Topo $(G,s)$ subroutine $($given below$)$ to build the software.

$(2$ pts$)$

DFS$\_$Topo$(G,s,$ CurrentLabel$)$

$,$for each vertex vinG.$V$

$,,v.$ explored $=0$

$,$s$.$ explored $=1$

$,$for each vertex vinG.V

$,,$if $v.$ cxplond $=1$

$,,,$DFS$\_$TOPO $(G,v)$

$,$s$.$onder $=$ Current Label $//$ Assign position of $s$ in the topological ordering

$,$Current Label $=$ CurrentLabel $-1.$

$,$return Current Label

$($b$)$ Detect any cycle in the dependency graph, in which case, it should throw an error and print the cycle.

$(3$ pts$)$