Nonrecursive algorithms for reconstructing a binary tree from its traversals

The authors propose two nonrecursive algorithms for reconstructing the original binary tree from its inorder and preorder traversals. The proposed algorithms proceed in two stages: the first stage establishes the i-p sequence while the second stage reconstructs the binary tree from the i-p sequence. One algorithm, which requires O(N) time, is time-optimal but space-inefficient, while the other requires O(N log N) time and O(N) space. If sorting and binary search are used, then the space required is optimal within a constant factor. If, instead, hashing is used, the computation time required is optimal within a constant factor. Simple modifications of the proposed algorithm can be used to reconstruct the original binary tree from its inorder and postorder traversals.<>