A binary search tree or BST is a popular data structure which is used to keep elements in order.

The example of perfect binary tress is: Complete Binary Tree. Since we are inserting the nodes in beginning of the doubly linked list, we need to reverse the linked list so that it follows the same order of nodes as in-order traversal of the tree. This algorithm is known as inorder tree traversal.. Method 1: This solution is similar to our previous solution but unlike array accessing middle element of linked list is not O(1).. Maximum Number of Nodes in a Binary Tree Unfortunately, your Tree class is public: public class Tree and it has the method: public Node getRoot() { return root; } That method will not be able to work in a public context at all if the calling class is not in the same package as Node (ishan.trees.tree). A binary search tree is a binary tree where the value of a left child is less than or equal to the parent node and value of the right child is greater than or equal to the parent node. Approach: i. Performing a binary search on linked list is never a good idea , as usually its running time can exceed that of standard ( linear ) search. In previous problem, we discussed how to create a balanced binary search tree for a sorted array. The postorder traversal algorithm also runs in O(n) time complexity.. Inorder Tree Traversal. In an inorder tree traversal, we visit a position between the recursive traversals of its left and right subtrees. Now, we consider a Tree Traversal Algorithm specifically for binary trees. The recursive solution I propose here works fine for both implementing a binary tree and also a BST. Thus, a perfect binary tree will have the maximum number of nodes for all alternative binary trees of the same height and it will be $2^{h+1}-1$ which we are going to prove next.

Perfect Binary Tree.

Now we’ll see how to create the same from a sorted linked list. Objective: Given a Binary tree create Linked Lists of all the nodes at each depth , say if the tree has height k then create k linked lists.

Get the middle of the linked list and make the middle element as root of the tree. A binary tree is p erfect binary Tree if all internal nodes have two children and all leaves are at the same level. Using in-order traversal. I am mainly building a tree with minimal height. Perfect Binary Tree → In a perfect binary tree, each leaf is at the same level and all the interior nodes have two children.

The idea is to do a in-order traversal of the tree and for every node encountered, we insert it in the beginning of DLL. There is no reason to ever expose the Node class to the public.