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    <p>You cannot use only one list, because you'll get no sense of the depth of the tree. Thus, you definitely require two or more lists.</p> <p>Here's my attempt at a solution:</p> <p>Use your preorder traversal as a means of knowing the ordering of the data. This makes sense because you know the first node is the top, and you know that data further to the left of the traversal belongs to the left of the tree, etc.</p> <p>Your post order traversal can determine the depth of the tree. For example, let's say I have a structure like this:</p> <pre><code> 1 2 5 6 3 4 7 Where 2 is the parent of 3 and 4, and 5 is the parent of 7. Preorder: 1 2 3 4 5 7 6 Postorder: 3 4 2 7 5 6 1 </code></pre> <p>We know we start with 1, because it is the first node in the preorder traversal. Then we look at the next number, 2. In the post order, because the number 2 comes BEFORE node 1, we know that 2 has to be a child of 1. Next we look at 3. 3 comes before 2, and thus 3 is a child of 2. 4 is before 2 but after 3, so we know 4 is a child of 2 but NOT a child of 3. Etc.</p> <p>Now, this may not work if the nodes are not unique, but at the very least its a start to a solution.</p> <p><strong>Edit:</strong> The order of the children is preserved with this solution, simply due to knowing the ordering of the nodes via the preorder traversal, and then knowing the structure via the postorder traversal.</p> <p><strong>Edit2:</strong> The proof may lie here: <a href="http://ieeexplore.ieee.org/Xplore/login.jsp?url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel2%2F215%2F626%2F00017225.pdf%3Farnumber%3D17225&amp;authDecision=-203" rel="noreferrer">http://ieeexplore.ieee.org/Xplore/login.jsp?url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel2%2F215%2F626%2F00017225.pdf%3Farnumber%3D17225&amp;authDecision=-203</a></p> <p>I think you need to purchase the document, however...</p> <p>Here is a written proof presented to be a solution:</p> <p><a href="http://www14.informatik.tu-muenchen.de/lehre/2007WS/fa-cse/tutorials/tutorial09-solutions.pdf" rel="noreferrer">http://www14.informatik.tu-muenchen.de/lehre/2007WS/fa-cse/tutorials/tutorial09-solutions.pdf</a></p>
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    1. POreconstructing a tree from its preorder and postorder lists
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    1. COMy solution is very similar, however I am looking for a proven algorithm. If there is none, I might try to prove my algorithm by SO. If even the whole SO community can not prove it wrong it must be right...right?
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    2. COIf the whole SO community can not prove it wrong then it MIGHT be right :P
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    3. COI say code this one, and try it with as many trees as you can, however I believe it to be mathematically sound, I'm just no good at starting off proofs from scratch.
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