Minimal Height Binary Search Tree

Introduction

In computer science, a binary search tree (BST) is a binary tree data structure in which each node has at most two children, which are referred to as the left child and the right child. A binary search tree is a binary tree where the value of each node is greater than or equal to the values in its left subtree and less than or equal to the values in its right subtree. The height of a binary search tree is the number of edges between the tree's root and its furthest leaf. In this challenge, we will create a binary search tree with minimal height from a sorted array.

Skills Graph

%%%%{init: {'theme':'neutral'}}%%%% flowchart RL algorithm(("`Algorithm`")) -.-> algorithm/BasicAlgorithmsGroup(["`Basic Algorithms`"]) python(("`Python`")) -.-> python/BasicConceptsGroup(["`Basic Concepts`"]) python(("`Python`")) -.-> python/ControlFlowGroup(["`Control Flow`"]) python(("`Python`")) -.-> python/DataStructuresGroup(["`Data Structures`"]) python(("`Python`")) -.-> python/FunctionsGroup(["`Functions`"]) python(("`Python`")) -.-> python/ObjectOrientedProgrammingGroup(["`Object-Oriented Programming`"]) python(("`Python`")) -.-> python/ErrorandExceptionHandlingGroup(["`Error and Exception Handling`"]) algorithm/BasicAlgorithmsGroup -.-> algorithm/graphs_trees("`Graphs Trees`") algorithm/BasicAlgorithmsGroup -.-> algorithm/recursion_dynamic("`Recursion Dynamic`") python/BasicConceptsGroup -.-> python/variables_data_types("`Variables and Data Types`") python/BasicConceptsGroup -.-> python/strings("`Strings`") python/BasicConceptsGroup -.-> python/type_conversion("`Type Conversion`") python/ControlFlowGroup -.-> python/conditional_statements("`Conditional Statements`") python/DataStructuresGroup -.-> python/lists("`Lists`") python/DataStructuresGroup -.-> python/tuples("`Tuples`") python/FunctionsGroup -.-> python/function_definition("`Function Definition`") python/FunctionsGroup -.-> python/default_arguments("`Default Arguments`") python/ObjectOrientedProgrammingGroup -.-> python/classes_objects("`Classes and Objects`") python/ObjectOrientedProgrammingGroup -.-> python/constructor("`Constructor`") python/ObjectOrientedProgrammingGroup -.-> python/polymorphism("`Polymorphism`") python/ObjectOrientedProgrammingGroup -.-> python/encapsulation("`Encapsulation`") python/ErrorandExceptionHandlingGroup -.-> python/raising_exceptions("`Raising Exceptions`") python/FunctionsGroup -.-> python/build_in_functions("`Build-in Functions`") subgraph Lab Skills algorithm/graphs_trees -.-> lab-268819{{"`Minimal Height Binary Search Tree`"}} algorithm/recursion_dynamic -.-> lab-268819{{"`Minimal Height Binary Search Tree`"}} python/variables_data_types -.-> lab-268819{{"`Minimal Height Binary Search Tree`"}} python/strings -.-> lab-268819{{"`Minimal Height Binary Search Tree`"}} python/type_conversion -.-> lab-268819{{"`Minimal Height Binary Search Tree`"}} python/conditional_statements -.-> lab-268819{{"`Minimal Height Binary Search Tree`"}} python/lists -.-> lab-268819{{"`Minimal Height Binary Search Tree`"}} python/tuples -.-> lab-268819{{"`Minimal Height Binary Search Tree`"}} python/function_definition -.-> lab-268819{{"`Minimal Height Binary Search Tree`"}} python/default_arguments -.-> lab-268819{{"`Minimal Height Binary Search Tree`"}} python/classes_objects -.-> lab-268819{{"`Minimal Height Binary Search Tree`"}} python/constructor -.-> lab-268819{{"`Minimal Height Binary Search Tree`"}} python/polymorphism -.-> lab-268819{{"`Minimal Height Binary Search Tree`"}} python/encapsulation -.-> lab-268819{{"`Minimal Height Binary Search Tree`"}} python/raising_exceptions -.-> lab-268819{{"`Minimal Height Binary Search Tree`"}} python/build_in_functions -.-> lab-268819{{"`Minimal Height Binary Search Tree`"}} end

Bst Min

Problem

Given a sorted array, we need to create a binary search tree with minimal height. The height of a binary search tree is the number of edges between the tree's root and its furthest leaf. The goal is to create a binary search tree with the minimum possible height.

Requirements

To solve this problem, we need to meet the following requirements:

The array must be in increasing order.
The array elements must be unique.
We must assume that we already have a Node class with an insert method.
We must assume that this fits memory.

Example Usage

Here are some examples of how to use the function:

Input: [0, 1, 2, 3, 4, 5, 6]
Output: A binary search tree with height 3
Input: [0, 1, 2, 3, 4, 5, 6, 7]
Output: A binary search tree with height 4

Summary

In this challenge, we learned how to create a binary search tree with minimal height from a sorted array. We also learned about the requirements that need to be met to solve this problem. By following these requirements, we can create an efficient solution to this problem.