examples: 2 new examples for graph algorithms (topological sorting) (#14303)

examples/graphs/topological_sorting_dfs.v

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+// https://en.wikipedia.org/wiki/Topological_sorting
+// A DFS RECURSIVE ALGORITHM ....
+// An alternative algorithm for topological sorting is based on depth-first search. The algorithm loops through each node of the graph, in an arbitrary order, initiating a depth-first search that terminates when it hits any node that has already been visited since the beginning
+// of the topological sort or the node has no outgoing edges (i.e. a leaf node)
+// Discussion: https://www.gatevidyalay.com/topological-sort-topological-sorting/
+// $ v run dfs_topological_ordering.v
+// Author: CCS
+
+// THE DFS RECURSIVE .... classical searchig for leaves nodes
+// the arguments are used in the function to avoid global variables....
+fn dfs_recursive(u string, mut visited map[string]bool, graph map[string][]string, mut top_sorting []string) {
+	print(' Visiting: $u -> ')
+	visited[u] = true
+
+	for v in graph[u] {
+		if visited[v] == false {
+			dfs_recursive(v, mut visited, graph, mut top_sorting)
+		}
+	}
+	top_sorting << u
+}
+
+// Creating aa map to initialize with of visited nodes .... all with false in the init
+// so these nodes are NOT VISITED YET
+fn visited_init(a_graph map[string][]string) map[string]bool {
+	mut array_of_keys := a_graph.keys() // get all keys of this map
+	mut temp := map[string]bool{} // attention in these initializations with maps
+	for i in array_of_keys {
+		temp[i] = false
+	}
+	return temp
+}
+
+// attention here a map STRING ---> ONE BOOLEAN ... not a string
+
+fn main() {
+	// A map illustration to use in a graph
+	// the graph: adjacency matrix
+	graph_01 := {
+		'A': ['C', 'B']
+		'B': ['D']
+		'C': ['D']
+		'D': []
+	}
+
+	graph_02 := {
+		'A': ['B', 'C', 'D']
+		'B': ['E']
+		'C': ['F']
+		'D': ['G']
+		'E': ['H']
+		'F': ['H']
+		'G': ['H']
+		'H': [] // no cycles
+	}
+	// from: https://en.wikipedia.org/wiki/Topological_sorting
+	graph_03 := {
+		'5':  ['11']
+		'7':  ['11', '8']
+		'3':  ['8', '10']
+		'11': ['2', '9', '10']
+		'8':  ['9']
+		'2':  []
+		'9':  []
+		'10': []
+	}
+
+	mut graph := map[string][]string{} // the graph: adjacency matrix
+	for index, g_value in [graph_01, graph_02, graph_03] {
+		println('Topological sorting for the graph $index using a DFS recursive')
+		graph = g_value.clone() // graphs_sample[g].clone() // choice your SAMPLE
+
+		// mut n_nodes := graph.len
+		mut visited := visited_init(graph) // a map with nodes not visited
+
+		// mut start := (graph.keys()).first() // arbitrary, any node if you wish
+		mut top_sorting := []string{}
+		// advantages of map ... getting all nodes
+		for i in graph.keys() {
+			if visited[i] != true {
+				dfs_recursive(i, mut visited, graph, mut top_sorting)
+			}
+		}
+
+		print('\n A topological sorting of graph $index : ')
+		// println(g_value)
+		println(top_sorting.reverse())
+		println('')
+	} // End of for
+}