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Questions and Answers
What is the top-most node in a tree called?
What is the top-most node in a tree called?
What is the maximum depth of any node in a tree called?
What is the maximum depth of any node in a tree called?
What is the path from the root to any node called?
What is the path from the root to any node called?
In a binary search tree, what ensures the ordering of its nodes?
In a binary search tree, what ensures the ordering of its nodes?
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What action takes place when inserting a new value into a binary search tree (BST)?
What action takes place when inserting a new value into a binary search tree (BST)?
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What happens if a duplicate node is encountered during insertion in a binary search tree?
What happens if a duplicate node is encountered during insertion in a binary search tree?
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Which algorithm divides the input into two sub-arrays: the sorted sub-array and the unsorted sub-array?
Which algorithm divides the input into two sub-arrays: the sorted sub-array and the unsorted sub-array?
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What is the key characteristic of Bubble Sort?
What is the key characteristic of Bubble Sort?
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Which traversal algorithm explores the graph depth by depth?
Which traversal algorithm explores the graph depth by depth?
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In Tree Sort, what is the purpose of performing an in-order traversal on the binary search tree?
In Tree Sort, what is the purpose of performing an in-order traversal on the binary search tree?
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What makes Quick Sort generally faster than Merge Sort?
What makes Quick Sort generally faster than Merge Sort?
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What does Insertion Sort do to build the final sorted array?
What does Insertion Sort do to build the final sorted array?
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Study Notes
Trees
A tree is a hierarchical data structure composed of nodes that have at most two children. The top-most node is called the root, and every non-empty tree has one. Each node can have zero or more children, except the root, which has no parent. The path from the root to any node is called the depth of the node. The maximum depth of any node in the tree is called the height of the tree. Trees are often used in computing in data compression, file storage, game trees, and more.
Binary Search Trees (BST)
A binary search tree (BST) is a binary tree with no duplicate nodes that imposes an ordering on its nodes. In a BST, the value of any node is greater than or equal to the values of all nodes in its left subtree and less than or equal to the values of all nodes in its right subtree. This ordering invariant ensures that inserting a new value into the BST involves traversing the tree to find the appropriate position for the new node.
Insertion in a BST
To insert a node into a binary search tree, you traverse the tree to find the appropriate position for the new node. If the tree is empty, create a new leaf node with the value of the node to be inserted. If the node is already in the tree, throw an exception, as duplicates are not allowed in a BST. If the value is less than the root value, traverse the left subtree; otherwise, traverse the right subtree. This process continues until you reach an empty tree, at which point you create a new leaf node with the value of the node to be inserted.
Sorting
Sorting is the process of arranging data in a specific order. There are several sorting algorithms, including:
Bubble Sort
Bubble sort is an in-place comparison sorting algorithm that repeatedly steps through the list, compares adjacent elements and swaps them if they are in the wrong order. The pass continues until no more swaps are needed, which indicates that the list is sorted.
Selection Sort
Selection sort is a simple sorting algorithm that divides the input into two sub-arrays: the sorted sub-array and the unsorted sub-array. The algorithm repeatedly selects the smallest element from the unsorted sub-array and swaps it with the rightmost element of the sorted sub-array.
Insertion Sort
Insertion sort is a simple sorting algorithm that builds the final sorted array (or list) one item at a time. It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge sort.
Merge Sort
Merge sort is a divide-and-conquer algorithm that works by recursively breaking down the input list into smaller and smaller sub-lists until each sub-list consists of a single element, which is considered sorted. It then merges these sub-lists together in a sorted manner.
Quick Sort
Quick sort is a divide-and-conquer algorithm that uses a pivot strategy to partition the input list into smaller sub-lists, which are then sorted recursively. It is generally faster than merge sort and is often used in practice.
Tree Sort
Tree sort is a sorting algorithm that uses a binary search tree to sort the elements of an array. It first creates a binary search tree from the elements of the input list or array and then performs an in-order traversal on the tree to get the elements in sorted order.
Graphs
A graph is a data structure that contains a set of vertices and a set of edges that connect pairs of the vertices. Vertices can represent entities, such as people, places, or things, while edges represent relationships between those entities. Graphs are used to model a wide variety of real-world systems, such as social networks, transportation networks, and computer networks.
Graph Traversal
There are two common graph traversal algorithms: Breadth-First Search (BFS) and Depth-First Search (DFS). BFS is generally faster than DFS on sparse graphs, as it explores the graph level by level, while DFS explores the graph depth by depth.
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Description
Explore the concepts of Binary Search Trees (BST) and various sorting algorithms such as Bubble Sort, Selection Sort, Insertion Sort, Merge Sort, Quick Sort, and Tree Sort. Learn how to perform insertion in a BST and understand the process of sorting data efficiently using different algorithms.
