traverse an array in c#

There are two ways to traverse each element of an array, one use a foreach loop, in this case you dont have to bother the depth of each dimension, or how many dimensions you have.

but in 2nd case you, you must know the dimensions of your array, using those dimension you get the lower and upper bound index of the array. (upper and lower bound of array is required when you are using an array which start index is not zero, c# allows to use such arrays. for zero based arrays you can simply use .Length() )

 string[,] str = {{"a","b"},{"a","c"},{"b","b1"},{"b","b2"},{"b","b3"},
                {"b3","b31"},{"b3","b32"},{"b31","b311"},{"b32","b321"}};
foreach(string s in str)
{
    Console.WriteLine(s);
}
Console.WriteLine("");
for (int i = str.GetLowerBound(0); i <= str.GetUpperBound(0); i += 1)
{
    for (int j = str.GetLowerBound(1); j <= str.GetUpperBound(1); j += 1)
        Console.Write(str[i, j] + " , ");
    Console.WriteLine("");
}
Console.ReadKey();

Personally I'd probably map the data representation to something closer to what you are actually representing.

Dictionary<string, List<string>> Tree;
public void BuildTree(string[,] a)
{
  if (a == null)
    throw new ArgumentNullException("a");
  Tree = new Dictionary<string, List<string>>();
  int rows = a.GetLength(0);
  for (int r = 0; r < rows; r++)
  {
    string key = a[r, 0];
    List<string> subTree;
    if (!Tree.TryGetValue(key, out subTree))
    {
      subTree = new List<string>();
      Tree.Add(key, subTree);
    }
    subTree.Add(a[r, 1]);
  }
}

public IEnumerable<string> TraverseTree(string startNode)
{
  if (startNode == null)
    throw new ArgumentNullException("startNode");
  yield return startNode;
  List<string> subTree;
  if (Tree.TryGetValue(startNode, out subTree))
  {
    foreach (var node in subTree.SelectMany(n => TraverseTree(n)))
    {
      yield return node;
    }
  }
}

TraverseTree("b") will return "b" and all of the nodes under it:

// Starting with:
string[,] str = {{"a","b"},
                 {"a","c"},
                 {"b","b1"},
                 {"b","b2"},
                 {"b","b3"},
                 {"b3","b31"},
                 {"b3","b32"},
                 {"b31","b311"},
                 {"b32","b321"}};

BuildTree(str); // Constructs the Tree
TraverseTree("b");  // will produce the sequence:
"b", "b1", "b2", "b3", "b31", "b311", "b32", "b321"