The LNR/LRN New-type Threaded Binary Tree (LNR/LRN NTBT for short) is first proposed in this paper. It is shown that n, the number of nodes of the binary tree, is the time complexity * of the LNR-NTBT traversal algorithm, if there is a special pointer pointing to the first node in LNR order. But under the same condition, the time complexity of ordinary traversal algorithms for traditional LNR threaded binary trees is approximate to 2n. So the LNR-NTBT and its traversal algorithm are the best. The LRN-NTBT and its traversal algorithm are also very efficient.
International Journal of Computer Mathematics