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    <p>Code would help. What data structure are you using to store the partial or candidate solutions? You say your using a queue to store nodes to be examined, but really the objects stored in the queue should wrap some structure (e.g. <code>List</code>) that indicates the nodes traversed to get to the node to be examined. So, instead of simple <code>Node</code>s being stored in the queue, some more complex object would be needed to make available the information necessary to know the complete path taken to that point. A simple node would only have information about itself, and it's children. But if you're examining node X, you also need to know how you arrived to node X. Just knowing node X isn't enough, and the only way (I know of) to know the path taken to node X is to store the path in the object that represents a "partial solution" or "candidate solution". If this is done, then finding the length of the path is trivial, because it's just the length of this list (or whichever data structure chosen). Hope I'm making some sense here. If not, post code and I'll take a look.</p> <p><strong>EDIT</strong><br/></p> <p>These bits of code help show what I mean (they're by no means complete):</p> <pre><code>public class Solution { List&lt;Node&gt; path; } Queue&lt;Solution&gt; q; </code></pre> <p>NOT</p> <pre><code>Queue&lt;Node&gt; q; </code></pre> <p><strong>EDIT 2</strong><br/></p> <p>If all you need is the length of the path, and not the path, per se, then try something like this:</p> <pre><code>public class Solution { Node node; // whatever represents a node in you algorithm. int len; // the length of the path to this node. } // Your queue: LinkedList&lt;Solution&gt; q; </code></pre> <p>With this, before enqueuing a candidate solution (node), you do something like:</p> <pre><code>Solution sol = new Solution(); sol.node = childNodeToEnqueue; sol.len = parentNode.len + 1; q.add(sol); </code></pre>
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    1. COI think I understand, I need to create linked lists that store the path...but how do I do that? I need to iteratively create a potentially infinite amount of linked lits? How do I name and instantiate them iteratively? Or would this be more like an array the size of my graph that is composed of linked lists?
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    2. COSay you have a graph, root node A with children B and C (a[b,c]), and B and C have children, and so forth. With each partial solution, you store an array or list or whatever. To start the algorithm, this list would contain A. When examining B the list would contain A,B. If be had a child D, then at D, the list would contain A,B,D, etc. You add an additional node to the path of nodes just before enqueuing a node.
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    3. COBut, the number of list needed is not infinite. I could be quite large, but it's a function of the number of nodes in the graph. In essence, you don't enqueue nodes, you enqueue paths taken to get to the nodes. And these paths aren't all created together, they're created with each child node that you want to enqueue.
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