### Graph Adjacency List Representation Example Source: https://github.com/thealgorithms/java/blob/master/src/main/java/com/thealgorithms/datastructures/graphs/README.md Illustrates a graph using an adjacency list, where each vertex is an entry and its connected edges are represented as a list of neighboring vertices. This example shows a simple directed graph. ```Text 0: 1-->2-->3 1: 0-->2 2: 0-->1 3: 0-->4 4: 3 ``` -------------------------------- ### Min Heap Construction Example: Adding 15 Source: https://github.com/thealgorithms/java/blob/master/src/main/java/com/thealgorithms/datastructures/heaps/Readme.md Illustrates the process of adding the value 15 to an existing Min-Heap, showing the intermediate steps of node placement and subsequent swaps to restore the heap property. ```Diagram (Algorithm Illustration) Add 15 10 10 10 / \ / \ / \ 20 30 ------> 20 30 ------> 20 15 / \ / \ / / \ / 40 50 40 50 15 40 50 30 ``` -------------------------------- ### Graph Adjacency Matrix Representation Example Source: https://github.com/thealgorithms/java/blob/master/src/main/java/com/thealgorithms/datastructures/graphs/README.md Shows a graph represented as an adjacency matrix, a |V| x |V| matrix where an entry of 1 at (i, j) indicates an edge from vertex i to vertex j, and 0 indicates no edge. This matrix corresponds to the graph shown in the adjacency list example. ```Text 0 1 2 3 4 0 0 1 1 1 0 1 1 0 1 0 0 2 1 1 0 0 0 3 1 0 0 0 1 4 0 0 0 1 0 ``` -------------------------------- ### Min Heap Deletion Example: Deleting 10 Source: https://github.com/thealgorithms/java/blob/master/src/main/java/com/thealgorithms/datastructures/heaps/Readme.md Illustrates the process of deleting the root value (10) from a Min-Heap, showing the intermediate steps of replacing the root with the last element and subsequent sifting down to restore the heap property. ```Diagram (Algorithm Illustration) Delete 10 10 50 20 20 / \ / \ / \ / \ 20 30 ------> 20 30 ------> 50 30 ------> 40 30 / \ / / / 40 50 40 40 50 ``` -------------------------------- ### Java Queue Declaration with PriorityQueue Source: https://github.com/thealgorithms/java/blob/master/src/main/java/com/thealgorithms/datastructures/queues/README.md Illustrates how to declare a Queue instance in Java, specifically using `PriorityQueue` as the concrete implementation. This snippet demonstrates the basic syntax for initializing a Queue object, typically used for managing elements based on their natural ordering or a custom comparator. ```Java Queue queue = new PriorityQueue(); ``` -------------------------------- ### Linked List Implementations and Variations Source: https://github.com/thealgorithms/java/blob/master/src/main/java/com/thealgorithms/datastructures/lists/README.md Overview of various linked list implementations and their specific functionalities within the project, detailing different file-level modules. ```APIDOC CircleLinkedList.java: A circular linked list where next pointer of last node points to first node of linked list. SinglyLinkedList.java: The classic case of single links. CountSinglyLinkedListRecursion.java: Recursively counts the size of a list. CreateAndDetectLoop.java: Create and detect a loop in a linked list. DoublyLinkedList.java: A modification of singly linked list which has a prev pointer to point to the previous node. MergeKSortedLinkedlist.java: Merges K sorted linked list with mergesort (mergesort is also the most efficient sorting algorithm for linked list). RandomNode.java: Selects a random node from given linked list and diplays it. SkipList.java: Data Structure used for storing a sorted list of elements with help of a Linked list hierarchy that connects to subsequences of elements. ``` -------------------------------- ### Min Heap Construction Algorithm Steps Source: https://github.com/thealgorithms/java/blob/master/src/main/java/com/thealgorithms/datastructures/heaps/Readme.md Step-by-step algorithm for constructing a Min-Heap by adding a new node and maintaining the heap property through comparisons and swaps with its parent. ```Algorithm (Steps) Step 1 − Create a new node at the end of heap. Step 2 − Assign new value to the node. Step 3 − Compare the value of this child node with its parent. Step 4 − If value of parent is more than child, then swap them. Step 5 − Repeat step 3 & 4 until Heap property holds. ``` -------------------------------- ### Complete Binary Tree Diagram Source: https://github.com/thealgorithms/java/blob/master/src/main/java/com/thealgorithms/datastructures/heaps/Readme.md Illustrates the structure of a complete binary tree where all levels except the last are completely filled, and nodes are left-justified. ```Diagram (ASCII) 10 / \ 20 30 / \ 40 50 COMPLETE BINARY TREE ``` -------------------------------- ### Stack Method: push(element) Source: https://github.com/thealgorithms/java/blob/master/src/main/java/com/thealgorithms/datastructures/stacks/README.md Describes the `push` operation, which adds a new element to the top of the stack, adhering to the LIFO principle. ```APIDOC push(element) element: The item to be added to the stack. Returns: void Example: If stack is [1, 3, 5], push(9) results in [1, 3, 5, 9]. ``` -------------------------------- ### Declare a Stack in Java Source: https://github.com/thealgorithms/java/blob/master/src/main/java/com/thealgorithms/datastructures/stacks/README.md Illustrates the standard syntax for declaring and initializing a new Stack object in Java, specifying the generic type for its elements. ```Java Stack stack=new Stack(); ``` -------------------------------- ### Core Queue Operations and Characteristics Source: https://github.com/thealgorithms/java/blob/master/src/main/java/com/thealgorithms/datastructures/queues/README.md Documents the fundamental operations available for Queue data structures, including adding (Enqueue), removing (Dequeue), and peeking at elements (Front, Rear). It also specifies the time complexity for each operation, highlighting the FIFO principle and the O(n) complexity for accessing the rear element in some implementations. ```APIDOC Operations: Enqueue: Description: Adds an item to the rear of the queue. Time Complexity: O(1) Example: If queue is 1, 2, 3, 4, 5 and Enqueue(8) is called, queue becomes 1, 2, 3, 4, 5, 8. Dequeue: Description: Removes an item from the front of the queue. Time Complexity: O(1) Example: If queue is 1, 2, 3, 4, 5 and Dequeue() is called, 1 is removed and returned, queue becomes 2, 3, 4, 5. Front: Description: Gets the front item from the queue without removing it. Time Complexity: O(1) Example: If queue is 1, 2, 3, 5 and Front() is called, 1 is returned. Rear: Description: Gets the last item from the queue without removing it. Time Complexity: O(n) Example: If queue is 1, 2, 3, 5 and Rear() is called, 5 is returned. ``` -------------------------------- ### Stack Method: peek() / top() Source: https://github.com/thealgorithms/java/blob/master/src/main/java/com/thealgorithms/datastructures/stacks/README.md Explains the `peek` operation, which retrieves the element at the top of the stack without removing it, allowing for inspection. ```APIDOC peek() / top() Returns: The element at the top of the stack. Example: If stack is [1, 3, 5], peek() returns 5. ``` -------------------------------- ### Min Heap Deletion Algorithm Steps Source: https://github.com/thealgorithms/java/blob/master/src/main/java/com/thealgorithms/datastructures/heaps/Readme.md Step-by-step algorithm for deleting the root node from a Min-Heap, involving moving the last element to the root and then sifting it down to maintain the heap property. ```Algorithm (Steps) Step 1 − Remove root node. Step 2 − Move the last element of last level to root. Step 3 − Compare the value of this child node with its parent. Step 4 − If value of parent is more than child, then swap them. Step 5 − Repeat step 3 & 4 until Heap property holds. ``` -------------------------------- ### Min Heap Diagram Source: https://github.com/thealgorithms/java/blob/master/src/main/java/com/thealgorithms/datastructures/heaps/Readme.md Visual representation of a Min-Heap, where the value of each parent node is less than or equal to the values of its children, recursively true for all sub-trees. ```Diagram (ASCII) 10 / \ 20 30 / \ / \ 40 50 60 70 MIN HEAP ``` -------------------------------- ### Stack Method: pop() Source: https://github.com/thealgorithms/java/blob/master/src/main/java/com/thealgorithms/datastructures/stacks/README.md Details the `pop` operation, which removes and returns the element from the top of the stack, following the LIFO principle. ```APIDOC pop() Returns: The element removed from the top of the stack. Example: If stack is [1, 3, 5, 9], pop() returns 9 and stack becomes [1, 3, 5]. ``` -------------------------------- ### Max Heap Diagram Source: https://github.com/thealgorithms/java/blob/master/src/main/java/com/thealgorithms/datastructures/heaps/Readme.md Visual representation of a Max-Heap, where the value of each parent node is greater than or equal to the values of its children, recursively true for all sub-trees. ```Diagram (ASCII) 70 / \ 50 60 / \ / \ 40 30 10 20 MAX HEAP ``` -------------------------------- ### Basic Java Binary Tree Structure Source: https://github.com/thealgorithms/java/blob/master/src/main/java/com/thealgorithms/datastructures/trees/README.md This Java code snippet defines the fundamental structure for a binary tree. It includes a generic type `E` for the node's value and references to `left` and `right` child nodes, which are themselves `Tree` objects. This structure is foundational for implementing binary tree algorithms. ```java class Tree{ E value; Tree left; Tree right; } ``` -------------------------------- ### LinkedList Node Structure Source: https://github.com/thealgorithms/java/blob/master/src/main/java/com/thealgorithms/datastructures/lists/README.md Defines the basic structure of a node in a generic linked list, including its value and a reference to the next node. The 'next' variable points to the subsequent node, and 'value' stores the data. ```Java class LinkedList{ E value; LinkedList next; } ``` === COMPLETE CONTENT === This response contains all available snippets from this library. No additional content exists. Do not make further requests.