You might want to look into the Day-Stout-Warren algorithm, which is an O(n)-time, O(1)-space algorithm for reshaping an arbitrary binary search tree into a complete binary tree. Intuitively, the algorithm works as follows: Using tree rotations, convert the tree into a degenerate linked list. By applying selective rotations to the linked list, convert the list … Read more
Here is a quick example of a binary insert: class Node: def __init__(self, val): self.l_child = None self.r_child = None self.data = val def binary_insert(root, node): if root is None: root = node else: if root.data > node.data: if root.l_child is None: root.l_child = node else: binary_insert(root.l_child, node) else: if root.r_child is None: root.r_child = … Read more
To answer your questions: What is the difference between AVL trees and splay trees? Both splay trees and AVL trees are binary search trees with excellent performance guarantees, but they differ in how they achieve those guarantee that performance. In an AVL tree, the shape of the tree is constrained at all times such that … Read more
Actually that is the mistake everybody does in an interview. Leftchild must be checked against (minLimitof node,node.value) Rightchild must be checked against (node.value,MaxLimit of node) IsValidBST(root,-infinity,infinity); bool IsValidBST(BinaryNode node, int MIN, int MAX) { if(node == null) return true; if(node.element > MIN && node.element < MAX && IsValidBST(node.left,MIN,node.element) && IsValidBST(node.right,node.element,MAX)) return true; else return false; … Read more
The problem lies in your base case. “The height of a tree is the length of the path from the root to the deepest node in the tree. A (rooted) tree with only a node (the root) has a height of zero.” – Wikipedia If there is no node, you want to return -1 not … Read more
One advantage that no one else has pointed out is that binary search tree allows you to do range searches efficiently. In order to illustrate my idea, I want to make an extreme case. Say you want to get all the elements whose keys are between 0 to 5000. And actually there is only one … Read more
Summary Type BST (*) Heap Insert average log(n) 1 Insert worst log(n) log(n) or n (***) Find any worst log(n) n Find max worst 1 (**) 1 Create worst n log(n) n Delete worst log(n) log(n) All average times on this table are the same as their worst times except for Insert. *: everywhere in … Read more
Probably the two most common self balancing tree algorithms are Red-Black trees and AVL trees. To balance the tree after an insertion/update both algorithms use the notion of rotations where the nodes of the tree are rotated to perform the re-balancing. While in both algorithms the insert/delete operations are O(log n), in the case of … Read more
Binary tree: Tree where each node has up to two leaves 1 / \ 2 3 Binary search tree: Used for searching. A binary tree where the left child contains only nodes with values less than the parent node, and where the right child only contains nodes with values greater than or equal to the … Read more