binary-search-tree

Given a set of values, it's possible for there to be many different possible binary search trees that can be formed from those values. For example, for the values 1, 2, and 3, there are five BSTs we can make from those values: 1 1 2 3 3 \ \ / \ / / 2 3 1 3 1 2 \ / \ / 3 2 2 1 Many data structures that are based on balanced binary search trees use tree rotations as a primitive for reshaping a BST without breaking the required binary search tree invariants. Tree rotations can be used to pull a node up above its parent, as shown here: rotate u right v / \ -----> / \ v C A u / \ <----- / \ A B

For a given binary tree, find the largest subtree which is also binary search tree? Example: Input: 10 / \ 50 150 / \ / \ 25 75 200 20 / \ / \ / \ / \ 15 35 65 30 120 135 155 250 Output: 50 / \ 25 75 / \ / 15 35 65 This answer previously contained an O(n log n) algorithm based on link/cut trees. Here is a simpler O(n) solution. The core is a procedure that accepts a node, the unique maximum BSST rooted at its left child, the unique maximum BSST rooted at its right child, and pointers to the left-most and right-most elements of these BSSTs. It destroys its inputs (avoidable with persistent data

Is there a formula to calculate what the maximum and minimum height for an AVL tree, given a certain number of nodes? For example: Textbook question: What is the maximum/minimum height for an AVL tree of 3 nodes, 5 nodes, and 7 nodes? Textbook answer: The maximum/minimum height for an AVL tree of 3 nodes is 2/2, for 5 nodes is 3/3, for 7 nodes is 4/3 I don't know if they figured it out by some magic formula, or if they draw out the AVL tree for each of the given heights and determined it that way. The solution below is appropriate for working things out by hand and gaining an intuition, please

How to convert a binary tree to binary search tree in-place, i.e., we cannot use any extra space. You don't give much to go on, but if the requirement is what I think it is, you have a binary tree already created and sitting in memory, but not sorted (the way you want it to be sorted, anyway). I'm assuming that the tree nodes look like struct tree_node { struct tree_node * left; struct tree_node * right; data_t data; }; I'm also assuming that you can read C While we could just sit around wondering why this tree was ever created without having been created in sorted order that doesn't do us any

I am learning algorithms and data structures and to train I am trying to design and implement a binary tree using objective-c. So far I have the following Classes: main - for testing Node - node of tree BinaryTree - for all methods related to the tree One of the first methods in BinaryTree class I implemented is insertNode:forRoot: . - (void)insertNodeByRef:(Node **)node forRoot:(Node **)root{ if (head == NULL) { head = *node; } // Case 2 root is null so can assign the value of the node to it if (root == NULL) { root = node; } else { if (node.data > root.data) { // to the right [self