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Algorithms and Data Structures Overview
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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.

Tarefa

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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Seção 4. Capítulo 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.

Tarefa

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 desktopMude para o desktop para praticar no mundo realContinue de onde você está usando uma das opções abaixo
Tudo estava claro?

Como podemos melhorá-lo?

Obrigado pelo seu feedback!

Seção 4. Capítulo 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.

Tarefa

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 desktopMude para o desktop para praticar no mundo realContinue de onde você está usando uma das opções abaixo
Tudo estava claro?

Como podemos melhorá-lo?

Obrigado pelo seu 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.

Tarefa

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 desktopMude para o desktop para praticar no mundo realContinue de onde você está usando uma das opções abaixo
Seção 4. Capítulo 6
Switch to desktopMude para o desktop para praticar no mundo realContinue de onde você está usando uma das opções abaixo
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