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    <p>For a breadth-first search you need to store at least two things. One is the set of already visited nodes and the other is the set of nodes that are directly reachable from the visited nodes but are not visited themselves. Then you keep moving states from the latter set to the former, adding newly reachable states to the latter. If you need the have a path from the root to some node(s), then you will also need to store a parent node for each node (except the root) in the aforementioned sets.</p> <p>Usually the union of the set of visited nodes and the set of not-visited child nodes (i.e. the set of seen nodes) is stored in a hash table. This is to be able to quickly determine whether or not a "new" state has been seen before and ignore it if this is the case. If you have really big number of states you might indeed need a bit array (as mentioned by Joseph Bui (<a href="https://stackoverflow.com/questions/57471/c-graph-traversal-tracking-path-between-any-two-nodes#57509">57509</a>), but unless your states can be used (directly or indirectly) as indices to that array, you will need to use a hash function to map states to indices. In the latter case you might completely ignore certain states because they are mapped to the same index as a different (and seen) node, so you might want to be careful with this. Also, to get a path you still need to store the parent information which pretty much negates the use of the bit-array.</p> <p>The set of unvisited but seen nodes can be stored as a queue. (Bit arrays are of no use for this set because the array will be mostly empty and finding the next set bit is relatively expensive.)</p>
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