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    <p>This is a job for <a href="http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm" rel="nofollow">Djikstra's Algorithm</a>. Once you build a representation of your graph it should be easy enough to produce the lowest cost traversal ... since in your case it seems that all paths have an equal cost (1).</p> <p>You can <a href="http://www.codeproject.com/KB/recipes/Shortest_Path_Problem.aspx" rel="nofollow">look here on CodeProject</a> for a reasonably decent implementation of Djikstra in C#.</p> <blockquote> <p>could you present me with a pseudo code of your version of the graph representation for this case?</p> </blockquote> <p>There are multiple ways to represent a graph in such a problem. If the number of vertices in your graph are likely to be small - it would be sufficient to use an <a href="http://en.wikipedia.org/wiki/Adjacency_matrix" rel="nofollow">adjacency matrix</a> for the representation of edges. In which case, you could just use a .NET <a href="http://msdn.microsoft.com/en-us/library/2yd9wwz4%28VS.71%29.aspx" rel="nofollow">multidimensional array</a>. The trick here is that you need to convert vertices labelled with characters to ordinal values. One approach would be to write a wrapper class that maps character codes to indices into the adjacency matrix:</p> <pre><code>class AdjacencyMatrix { // representation of the adjacency matrix (AM) private readonly int[,] m_Matrix; // mapping of character codes to indices in the AM private readonly Dictionary&lt;char,int&gt; m_Mapping; public AdjacencyMatrix( string edgeVector ) { // using LINQ we can identify and order the distinct characters char[] distinctChars = edgeVector.Distinct().OrderBy(x =&gt; x); m_Mapping = distinctChars.Select((c,i)=&gt;new { Vertex = c, Index = i }) .ToDictionary(x=&gt;x.Vertex, x=&gt;x.Index); // build the adjacency cost matrix here... // TODO: I leave this up to the reader to complete ... :-D } // retrieves an entry from within the adjacency matrix given two characters public int this[char v1, char v2] { get { return m_Matrix[m_Mapping[v1], m_Mapping[v2]]; private set { m_Matrix[m_Mapping[v1], m_Mapping[v2]] = value; } } } </code></pre>
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    1. COcould you present me with a pseudo code of your version of the graph representation for this case?
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    2. COadjacency matrix is what i needed.. thanks!
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