It too will detect all occurrences of the two most frequently appearing types of transcription errors, namely altering one single digit, and transposing two adjacent digits (including the transposition of the trailing check digit and the preceding digit). But the Damm algorithm has the benefit that it makes do without the dedicatedly constructed permutations and its position specific powers being inherent in the Verhoeff scheme. For clustering to make sense for an application, you first need to think about the specifications. Most algorithms have some more or less explicit specifications, and people care much too little about them. It has the key assumptions that A) the mean is a sensible representative of the cluster and that B) variance must be minimized. Hence,it is essential to be reasonably sure about the effectiveness of the algorithm beforeit is coded. This process, at the algorithm level,is called"validation". Essentially, it's a check to see if a binary tree is a binary search tree. Here the invariant is  any two sequential elements of the BST in the inorder traversal must be in strictly increasing order of their appearance (can't be equal, always increasing in inorder traversal). This page allows you to draw a binary tree and The best solution I found is O(n) and it uses no extra space. So solution can be just a simple inorder traversal with remembering the last visited node and comparison the current node against the last visited one to ' should prevent that.
