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Algorithms and Data Structures Overview
course content

Course Content

Algorithms and Data Structures Overview

Algorithms and Data Structures Overview

1. Introduction to ADS
Why Do We Need Algorithms and Data StructuresWhy Do We Need Data Structures?Algorithm AnalysisBig-O NotationChallenge: How to Determine Algorithm Complexity
2. List and Array
Array Data StructureBasic Array Operations Time ComplexityChallenge: Inserting Elements into the ArrayLinked List Data StructureBasic List Operations Time ComplexityChallenge: Inversing the Order of Elements in the ListDoubly Linked List
3. Advanced Data Structures
StacksQueuesChallenge: Using Stack to Find PalindromeHash TableChallenge: Creating Hash Table with String Keys
4. Graphs
What is GraphGraph ImplementationChallenge: Graph Traversal AlgorithmsBSTBST TraversalChallenge: Balanced Trees

bookChallenge: Balanced Trees

A balanced tree, specifically a balanced Binary Search Tree (BST), is a tree data structure in which the heights of any node's left and right subtrees differ by at most one. This balance ensures efficient searching, insertion, and deletion operations, maintaining a logarithmic time complexity for these operations. In a balanced BST, the tree's height is minimized, leading to optimal performance.
Let's look at the example of unbalanced tree:

In the provided BST, the left subtree of the root node has a height of 4, while the right subtree has a height of only 2. This significant difference in heights indicates that the tree is unbalanced, leading to inefficient search, insertion, and deletion operations compared to a balanced BST.

Task

You are provided with a Binary Search Tree (BST) implemented in Python. Your task is to write a function to determine whether the BST is balanced or not.
You have to perform the following steps:

  • calculate the height of a subtree rooted at a given node recursively. It returns the maximum height between the left and right subtrees plus one (to account for the current node). This logic is implemented in calculate_height() function.
  • Recursively check if the subtree rooted at a given node is balanced. It is implemented using the is_balanced_recursive() function. It compares the heights of the left and right subtrees and returns False if the difference in heights is greater than 1, indicating an imbalance.
  • To check if the tree is balanced, you must call the is_balanced_recursive() with the tree root as an argument.

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Section 4. Chapter 6
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bookChallenge: Balanced Trees

A balanced tree, specifically a balanced Binary Search Tree (BST), is a tree data structure in which the heights of any node's left and right subtrees differ by at most one. This balance ensures efficient searching, insertion, and deletion operations, maintaining a logarithmic time complexity for these operations. In a balanced BST, the tree's height is minimized, leading to optimal performance.
Let's look at the example of unbalanced tree:

In the provided BST, the left subtree of the root node has a height of 4, while the right subtree has a height of only 2. This significant difference in heights indicates that the tree is unbalanced, leading to inefficient search, insertion, and deletion operations compared to a balanced BST.

Task

You are provided with a Binary Search Tree (BST) implemented in Python. Your task is to write a function to determine whether the BST is balanced or not.
You have to perform the following steps:

  • calculate the height of a subtree rooted at a given node recursively. It returns the maximum height between the left and right subtrees plus one (to account for the current node). This logic is implemented in calculate_height() function.
  • Recursively check if the subtree rooted at a given node is balanced. It is implemented using the is_balanced_recursive() function. It compares the heights of the left and right subtrees and returns False if the difference in heights is greater than 1, indicating an imbalance.
  • To check if the tree is balanced, you must call the is_balanced_recursive() with the tree root as an argument.

Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
Everything was clear?

How can we improve it?

Thanks for your feedback!

Section 4. Chapter 6
toggle bottom row

bookChallenge: Balanced Trees

A balanced tree, specifically a balanced Binary Search Tree (BST), is a tree data structure in which the heights of any node's left and right subtrees differ by at most one. This balance ensures efficient searching, insertion, and deletion operations, maintaining a logarithmic time complexity for these operations. In a balanced BST, the tree's height is minimized, leading to optimal performance.
Let's look at the example of unbalanced tree:

In the provided BST, the left subtree of the root node has a height of 4, while the right subtree has a height of only 2. This significant difference in heights indicates that the tree is unbalanced, leading to inefficient search, insertion, and deletion operations compared to a balanced BST.

Task

You are provided with a Binary Search Tree (BST) implemented in Python. Your task is to write a function to determine whether the BST is balanced or not.
You have to perform the following steps:

  • calculate the height of a subtree rooted at a given node recursively. It returns the maximum height between the left and right subtrees plus one (to account for the current node). This logic is implemented in calculate_height() function.
  • Recursively check if the subtree rooted at a given node is balanced. It is implemented using the is_balanced_recursive() function. It compares the heights of the left and right subtrees and returns False if the difference in heights is greater than 1, indicating an imbalance.
  • To check if the tree is balanced, you must call the is_balanced_recursive() with the tree root as an argument.

Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
Everything was clear?

How can we improve it?

Thanks for your feedback!

A balanced tree, specifically a balanced Binary Search Tree (BST), is a tree data structure in which the heights of any node's left and right subtrees differ by at most one. This balance ensures efficient searching, insertion, and deletion operations, maintaining a logarithmic time complexity for these operations. In a balanced BST, the tree's height is minimized, leading to optimal performance.
Let's look at the example of unbalanced tree:

In the provided BST, the left subtree of the root node has a height of 4, while the right subtree has a height of only 2. This significant difference in heights indicates that the tree is unbalanced, leading to inefficient search, insertion, and deletion operations compared to a balanced BST.

Task

You are provided with a Binary Search Tree (BST) implemented in Python. Your task is to write a function to determine whether the BST is balanced or not.
You have to perform the following steps:

  • calculate the height of a subtree rooted at a given node recursively. It returns the maximum height between the left and right subtrees plus one (to account for the current node). This logic is implemented in calculate_height() function.
  • Recursively check if the subtree rooted at a given node is balanced. It is implemented using the is_balanced_recursive() function. It compares the heights of the left and right subtrees and returns False if the difference in heights is greater than 1, indicating an imbalance.
  • To check if the tree is balanced, you must call the is_balanced_recursive() with the tree root as an argument.

Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
Section 4. Chapter 6
Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
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