Question

I am given a string of characters, in which every consequent pair of characters comprises an edge. What I mean by that is this is the string: ABBCAD. Edges of the string are:

A->B
B->C
A->D

Shortest path distance is A->D

The task at hand is to build up a Directed Acyclic Graph in memory from the string using the above rule and find the shortest path staring at the root node(in the example given it’s A label) ending at terminal node.

NJKUUGHBNNJHYAPOYJHNRMNIKAIILFGJSNAICZQRNM

I gather one of the approaches that suites the task is to use the Depth First Search algo.

This is not homework…

Answer 1

This is a job for Djikstra’s Algorithm. 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).

You can look here on CodeProject for a reasonably decent implementation of Djikstra in C#.

could you present me with a pseudo code of your version of the graph representation for this case?

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 adjacency matrix for the representation of edges. In which case, you could just use a .NET multidimensional array. 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:

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<char,int> m_Mapping;

    public AdjacencyMatrix( string edgeVector )
    {
        // using LINQ we can identify and order the distinct characters
        char[] distinctChars = edgeVector.Distinct().OrderBy(x => x);

        m_Mapping = distinctChars.Select((c,i)=>new { Vertex = c, Index = i })
                                 .ToDictionary(x=>x.Vertex, x=>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; }
    }
}