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Dijkstra:Shortest Route Calculation - Object Oriented

, 3 Jan 2008
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Calculation of the shortest path between x points
All points are locations. The connections between the points have a specific weight. Not all connections are bidirectional (a dot marks a start travel point). When Calculate is pressed, all routes from the selected location are calculated. When a route is selected in the listbox, the shortest route is visually shown by coloring the start dots red.
In this example, the shortest route from 0 to 4 is going through location 2, 1 and then 4.

Introduction

Dijkstra was a Dutch computer scientist who invented a fast and simple way to calculate the shortest path between two points. Many examples I have found on the Internet implement that algorithm but none of them have done it in an Object Oriented way. So I thought of making my own.

Background

Information about Dijkstra can be found here.

Using the Code

The code contains two Project classes:

  1. GUI: Shows the information visually
    • To add locations, click on the 'Add Location' button and then click on the map where you want to add locations.
    • To add routes, click on the 'Add Location' button to deactivate the add location, then click on a start location, then click on a end location. The weight of the route can be configured on top.
  2. RouteEngine: Calculates the route

I will only go into details about the RouteEngine. How the UI is handled is not so important for this article but if you need information about it, you can always ask.

Project RouteEngine

  1. Connection: This class holds the information about the connection between two dots. This is a one directional connection from A (the startpoint is visually shown with a dot) to B with a specific weight attached.
  2. Location: Just a location (for example 1).
  3. RouteEngine: This class will calculate all routes from one given startPoint.
  4. Route: This class holds the information about a route between two points (generated with the RouteEngine class).

Location

The most simple class. It only holds a name to display.

Connection

This class contains two Location objects and a weight.

public Connection(Location a, Location b, int weight)
{
    this._a = a;
    this._b = b;
    this._weight = weight;
}

Route

This class contains a route. It has only a list of connections and the total weight. This class is generated by the route engine.

Route Engine

This is the class that drives the component. The algorithm is as follows:

  1. Set the startPosition as active
  2. Set the total weight to all routes to infinite
  3. Iterate through all connections of the active position and store their weight if their weight is smaller than their current weight
  4. Set the active position as used
  5. Set the nearest point (on whatever location) that isn't used as active
  6. Repeat 3, 4, 5 until all positions are used

The following method will perform all these steps (and some extra checking and thinking). The Dictionary returned is a list of destination locations and the corresponding route to each destination location.

/// <summary />
/// Calculates the shortest route to all the other locations
/// </summary />
/// <returns />List of all locations and their shortest route</returns />
public Dictionary<location, /> CalculateMinCost(Location _startLocation)
{
    //Initialise a new empty route list
    Dictionary<location, /> _shortestPaths = new Dictionary<location, />();
    //Initialise a new empty handled locations list
    List<location /> _handledLocations = new List<location />();

    //Initialise the new routes. the constructor will set the route weight to in.max
    foreach (Location location in _locations)
    {
        _shortestPaths.Add(location, new Route(location.Identifier));
    }

    //The startPosition has a weight 0.
    _shortestPaths[_startLocation].Cost = 0;

    //If all locations are handled, stop the engine and return the result
    while (_handledLocations.Count != _locations.Count)
    {
        //Order the locations
        List<location /> _shortestLocations = (List < Location > )(from s in _shortestPaths
                                orderby s.Value.Cost
                                select s.Key).ToList();

        Location _locationToProcess = null;

        //Search for the nearest location that isn't handled
        foreach (Location _location in _shortestLocations)
        {
            if (!_handledLocations.Contains(_location))
            {
                //If the cost equals int.max, there are no more possible connections 
                //to the remaining locations
                if (_shortestPaths[_location].Cost == int.MaxValue)
                    return _shortestPaths;
                _locationToProcess = _location;
                break;
            }
        }

        //Select all connections where the startposition is the location to Process
        var _selectedConnections = from c in _connections
                                   where c.A == _locationToProcess
                                   select c;

        //Iterate through all connections and search for a connection which is shorter
        foreach (Connection conn in _selectedConnections)
        {
            if (_shortestPaths[conn.B].Cost > conn.Weight + _shortestPaths[conn.A].Cost)
            {
                _shortestPaths[conn.B].Connections = 
                        _shortestPaths[conn.A].Connections.ToList();
                _shortestPaths[conn.B].Connections.Add(conn);
                _shortestPaths[conn.B].Cost = conn.Weight + _shortestPaths[conn.A].Cost;
            }
        }
        //Add the location to the list of processed locations
        _handledLocations.Add(_locationToProcess);
    }

    return _shortestPaths;
}

History

  • 24 December, 2007: First release

License

This article, along with any associated source code and files, is licensed under The Code Project Open License (CPOL)

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Comments and Discussions

 
GeneralMy vote of 5 PinmemberJocelyn62France3-Jul-12 23:49 

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