Merge pull request #48 from hmdsefi/dev

update tarjan comments

connectivity/tarjan.go

@@ -2,11 +2,17 @@ package connectivity
 
 import "github.com/hmdsefi/gograph"
 
+// Tarjan's algorithm is based on depth-first search and is widely used for
+// finding strongly connected components in a graph. The algorithm is efficient
+// and has a time complexity of O(V+E), where V is the number of vertices and E
+// is the number of edges in the graph.
+
+// tarjanVertex wraps the gograph.Vertex struct to add new fields to it.
 type tarjanVertex[T comparable] struct {
-	*gograph.Vertex[T]
-	index   int
-	lowLink int
-	onStack bool
+	*gograph.Vertex[T]      // the vertex that being wrapped.
+	index              int  // represents the order in which a vertex is visited during the DFS search.
+	lowLink            int  // the minimum index of any vertex reachable from the vertex during the search.
+	onStack            bool // a boolean flag that shows if the vertex is in the stack or not.
 }
 
 func newTarjanVertex[T comparable](vertex *gograph.Vertex[T]) *tarjanVertex[T] {
@@ -24,6 +30,10 @@ func newTarjanSCCS[T comparable](vertices map[T]*tarjanVertex[T]) *tarjanSCCS[T]
 	return &tarjanSCCS[T]{vertices: vertices}
 }
 
+// tarjan  is the entry point to the algorithm. It initializes the index,
+// stack, and sccs variables and then loops through all the vertices in
+// the graph. It returns a slice of vertices' slice, where each inner
+// slice represents a strongly connected component of the graph.
 func tarjan[T comparable](g gograph.Graph[T]) [][]*gograph.Vertex[T] {
 	var (
 		index     int
@@ -57,6 +67,11 @@ func tarjan[T comparable](g gograph.Graph[T]) [][]*gograph.Vertex[T] {
 	return result
 }
 
+// visit updates the index and lowLink values of the vertex, adds it to
+// the stack, and recursively calls itself on each of its neighbors. If
+// a neighbor has not been visited before, its index and lowLink values
+// are updated, and the recursion continues. If a neighbor has already
+// been visited and is still on the stack, its lowLink value is updated.
 func (t *tarjanSCCS[T]) visit(
 	v *tarjanVertex[T],
 	index *int,
@@ -95,6 +110,7 @@ func (t *tarjanSCCS[T]) visit(
 	}
 }
 
+// min is a helper function that returns the minimum of two integers.
 func min(x, y int) int {
 	if x < y {
 		return x