examples: add another graph example for bread first search with backtracking (#19463)

Author: KeitoTobi1

examples/graphs/bfs3.v

@@ -0,0 +1,57 @@
+// Author: CCS & KeitoTobi1
+// Backtracking Supported.
+import datatypes
+
+fn find_pattern(adj map[string][]string, start string, target string) [][]string {
+	mut visited := visited_init(adj)
+	mut queue := datatypes.Queue[[]string]{}
+	mut res := [][]string{}
+	queue.push([start])
+	for !queue.is_empty() {
+		mut v := queue.pop() or { panic(err) }
+		node := v.last()
+		if node == target {
+			res << v
+		}
+		print('Expansion of node ${node} (true/false): ${adj[node]}')
+		for next in adj[node] {
+			if visited[next] == false {
+				mut copy := v.clone()
+				copy << next
+				queue.push(copy)
+				visited[node] = true
+			}
+		}
+		print('Expansion of node ${queue} (true/false): ${visited}\n')
+	}
+	return res
+}
+
+fn print_pattern(pat [][]string) {
+	for p in pat {
+		println(p)
+	}
+}
+
+fn visited_init(adj map[string][]string) map[string]bool {
+	mut temp := map[string]bool{}
+	for i, _ in adj {
+		temp[i] = false
+	}
+	return temp
+}
+
+fn main() {
+	adj := {
+		'A': ['B', 'C']
+		'B': ['A', 'D', 'E']
+		'C': ['A', 'F']
+		'D': ['B']
+		'E': ['B', 'F']
+		'F': ['C', 'E']
+	}
+
+	path := find_pattern(adj, 'A', 'F')
+	println('The all pattern path from node A to node F is:')
+	print_pattern(path)
+}