This Java program prints the distance between two cities if there is a
flight between them otherwise, prints 0. The depth-first search algorithm
is used to find the result.

Java Code:
import java.util.*;
import java.io.*;

//Flight information.
class FlightInfo {
  String from;

  String to;

  int distance;

  boolean skip; // used in backtracking

  FlightInfo(String f, String t, int d) {
    from = f;
    to = t;
    distance = d;
    skip = false;
  }
}

public class Depth {
  final int MAX = 100; // maximum number of connections

  // This array holds the flight information.
  FlightInfo flights[] = new FlightInfo[MAX];

  int numFlights = 0; // number of entries in flight array

  Stack btStack = new Stack(); // backtrack stack

  public static void main(String args[]) {
    String to, from;
    Depth ob = new Depth();
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

    ob.setup();

    try {
      System.out.print("From? ");
      from = br.readLine();
      System.out.print("To? ");
      to = br.readLine();

      ob.isflight(from, to);

      if (ob.btStack.size() != 0)
        ob.route(to);
    } catch (IOException exc) {
      System.out.println("Error on input.");
    }
  }

  //Initialize the flight database.
  void setup() {
    addFlight("New York", "Chicago", 900);
    addFlight("Chicago", "Denver", 1000);
    addFlight("New York", "Toronto", 500);
    addFlight("New York", "Denver", 1800);
    addFlight("Toronto", "Calgary", 1700);
    addFlight("Toronto", "Los Angeles", 2500);
    addFlight("Toronto", "Chicago", 500);
    addFlight("Denver", "Urbana", 1000);
    addFlight("Denver", "Houston", 1000);
    addFlight("Houston", "Los Angeles", 1500);
    addFlight("Denver", "Los Angeles", 1000);
  }

  //Put flights into the database.
  void addFlight(String from, String to, int dist) {
    if (numFlights < MAX) {
      flights[numFlights] = new FlightInfo(from, to, dist);

      numFlights++;
    } else
      System.out.println("Flight database full.\n");
  }

  // Show the route and total distance.
  void route(String to) {
    Stack rev = new Stack();
    int dist = 0;
    FlightInfo f;
    int num = btStack.size();

    // Reverse the stack to display route.
    for (int i = 0; i < num; i++)
      rev.push(btStack.pop());

    for (int i = 0; i < num; i++) {
      f = (FlightInfo) rev.pop();
      System.out.print(f.from + " to ");
      dist += f.distance;
    }

    System.out.println(to);
    System.out.println("Distance is " + dist);
  }

  /*
   * If there is a flight between from and to, return the distance of flight;
   * otherwise, return 0.
   */
  int match(String from, String to) {
    for (int i = numFlights - 1; i > -1; i--) {
      if (flights[i].from.equals(from) && flights[i].to.equals(to)
          && !flights[i].skip) {
        flights[i].skip = true; // prevent reuse
        return flights[i].distance;
      }
    }

    return 0; // not found
  }

  // Given from, find any connection.
  FlightInfo find(String from) {
    for (int i = 0; i < numFlights; i++) {
      if (flights[i].from.equals(from) && !flights[i].skip) {
        FlightInfo f = new FlightInfo(flights[i].from, flights[i].to,
            flights[i].distance);
        flights[i].skip = true; // prevent reuse

        return f;
      }
    }

    return null;
  }

  // Determine if there is a route between from and to.
  void isflight(String from, String to) {
    int dist;
    FlightInfo f;

    // See if at destination.
    dist = match(from, to);
    if (dist != 0) {
      btStack.push(new FlightInfo(from, to, dist));
      return;
    }

    // Try another connection.
    f = find(from);
    if (f != null) {
      btStack.push(new FlightInfo(from, to, f.distance));
      isflight(f.to, to);
    } else if (btStack.size() > 0) {
      // Backtrack and try another connection.
      f = (FlightInfo) btStack.pop();
      isflight(f.from, f.to);
    }
  }
}