Each node in a binary tree can be mapped to a binary string encoding its position in the tree. For each level below the root, the string should consist of a 0 if the node requires a left traversal or 1 if a right. This is important because a bit string s and its inverse ~s will represent symmetric paths down the tree. A solution to this symmetry problem would perform a tree traversal and, at each node in the traversal, encode the path as described above. Then, negate the path to generate ~path and fetch that node. If it exists and is identical to the original node, continue the traversal - otherwise, we stop (not symmetric).