added backtracking problem

Backtracking/FlightItinerary.java

@@ -0,0 +1,102 @@
+package backtracking;
+
+import java.util.HashSet;
+import java.util.Stack;
+
+/**
+ * given a few flights and a starting point - print if you can connect them all together into a journey
+ * <p>
+ * a Flight is just an object that has a Starting point and an Ending point
+ */
+
+/**
+ * Dynamic programming tips:
+ *
+ * Can I construct a mini problem with a solution
+ * can I verify if that solution is valid or not
+ * Can I say when the full problem is solved
+ */
+
+//  in this case:
+//  mini problem is just using less flights
+//  is_valid would check if I am at an airport that I can't fly off from and there are more flights I have yet to board
+//  full problem is solved when I have used all flights
+public class FlightItinerary {
+
+
+    public static void addFlights(String startPoint, HashSet<Flight> flights, Stack<Flight> itinerary) {
+        if (flights.isEmpty()) {
+            //yey we have made a journey with everything
+            return;
+        }
+
+        HashSet<Flight> expensiveSolution = new HashSet<>(flights);
+
+        for (Flight i : flights) {
+            if (startPoint.equals(i.start)) {
+                itinerary.push(i);
+                expensiveSolution.remove(i);
+
+                //if valid so far try adding the next flight
+                if (isValid(i.end, expensiveSolution)) {
+                    addFlights(i.end, expensiveSolution, itinerary);
+                } else {
+
+                    itinerary.pop();
+                    expensiveSolution.add(i);
+                }
+            }
+        }
+    }
+
+    public static boolean isValid(String startPoint, HashSet<Flight> flights) {
+        if (flights.isEmpty())
+            return true;
+        for (Flight i : flights) {
+            if (startPoint.equals(i.start)) {
+                return true;
+            }
+        }
+        return false;
+    }
+
+    public static void main(String[] args) {
+
+        Flight f1 = new Flight("HNL", "AKL");
+        Flight f2 = new Flight("YUL", "ORD");
+        Flight f3 = new Flight("ORD", "SFO");
+        Flight f4 = new Flight("SFO", "HNL");
+
+
+        Flight f5 = new Flight("AKL", "ORD");
+        Flight f6 = new Flight("ORD", "YUL");
+
+        String startingAirport = "YUL";
+
+        HashSet<Flight> flights = new HashSet<>();
+        Stack<Flight> itinerary = new Stack<>();
+
+        flights.add(f1);
+        flights.add(f2);
+        flights.add(f3);
+        flights.add(f4);
+
+
+        flights.add(f5);
+        flights.add(f6);
+
+        addFlights("YUL", flights, itinerary);
+
+        itinerary.stream().forEach(e -> System.out.print(e.start + " -> " + e.end + " "));
+    }
+
+    private static class Flight {
+        String start;
+        String end;
+
+        public Flight(String start, String end) {
+            this.start = start;
+            this.end = end;
+        }
+    }
+}