Problem 1: Recall that binary search trees enjoy O(Ig(n)) search time complexity when the treeis fairly balanced, i.e., there are no nodes where the tree grows much deeper on the left sidethan the right size (and vice versa). This is well depicted by a picture:56BALANCEDb bo0-00We can then define the balance of the tree asUN BALANCEDIn this problem, we try to come up with a formula/algorithm to measure how balanced a tree is.Given a tree node, we define its height as the maximum number of generations beneath it. Forexample, a leaf node has height 0; a node with only left and/or right children and nograndchildren has height 1; a node with at least one grandchild and no great grandchildren hasheight 2; etc. Let's write the height of a node n as h(n).We can define the balance of a node n as b(n) = |h(n.left)-h(n.right)| where we defineh(NIL) = -1, i.e. the height of "NIL" is -1 to make the function work.B(T) = max b(n)n node in TWrite an algorithm that, given a binary tree T, calculates the balance B(T). Your algorithm mustrun in time 0(m) or better where m is the number of nodes in the tree.

Answer: We have written the algorithm for the Balance or Unbalance Binary Search tree

blem 1: Recall that binary search trees enjoy O(ig(n)) search time complexity when the tree s fairly balanced, i.e., there are no nodes where the tree grows much deeper on the left side han the right size (and vice versa). This is well depicted by a picture: BALANCED b be 0-00 UN BALANCED n this problem, we try to come up with a formula/algorithm to measure how balanced a tree is.

blem 1: Recall that binary search trees enjoy O(ig(n)) search time complexity when the tree s fairly balanced, i.e., there are no nodes where the tree grows much deeper on the left side han the right size (and vice versa). This is well depicted by a picture: BALANCED b be 0-00 UN BALANCED n this problem, we try to come up with a formula/algorithm to measure how balanced a tree is.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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