Hash Tables

1. Definition of Data Structure:

Fact: A data structure is a way of organizing and storing data to perform operations efficiently. Details: Data structures provide a systematic way to manage and organize data elements, facilitating optimal access, modification, and storage....

2. Types of Data Structures:

Fact: Data structures can be categorized into two types: Primitive and Non-primitive. Arrays and Linked Lists are examples of non-primitive data structures. Details: Primitive data structures consist of basic data types, while non-primitive structures include more complex arrangements of data, allowing for flexibility and scalability....

3. Importance of Algorithms:

Fact: Algorithms are step-by-step procedures or formulas for solving problems. They form the heart of any computational solution. Example: Binary Search Algorithm: An efficient search algorithm that divides the search interval in half, significantly reducing the search space....

4. Dynamic Arrays:

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5. Linked Lists:

Fact: Dynamic arrays resize themselves during runtime, providing more flexibility than static arrays. Example: ArrayList in Java: A dynamic array implementation in Java that automatically adjusts its size as elements are added or removed....

6. Time Complexity:

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7. Space Complexity:

Fact: Linked lists consist of nodes where each node points to the next node in the sequence. Example: Singly Linked List in Python: A linked list where each node contains data and a reference to the next node, forming a linear sequence....

8. Tree Structures:

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9. Hash Tables:

Fact: Time complexity measures the amount of time an algorithm takes concerning the input size. Example: Binary Search Time Complexity: O(log n) indicates logarithmic growth, showcasing its efficiency in large datasets....

10. Graphs:

Fact: Space complexity evaluates the memory space an algorithm requires concerning the input size. Example: QuickSort Space Complexity: O(log n) on average, demonstrating efficient use of memory in sorting algorithms....

11. Searching Algorithms:

Fact: Trees are hierarchical data structures with a root node and child nodes. Example: Binary Tree in Java: A tree structure where each node has at most two children, forming a hierarchical relationship....

12. Sorting Algorithms:

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13. Dynamic Programming:

Fact: Hash tables enable efficient data retrieval by using a hash function to map keys to indices. Example: Hash Table in Python (using a dictionary): A Python dictionary, leveraging a hash function for rapid key-based data access....

14. Divide and Conquer:

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15. NP-Completeness:

Fact: Graphs consist of vertices and edges, modeling relationships between different entities. Example: Graph Representation in Java: Using an adjacency list to represent a graph, with nodes and edges forming connections....

16. Heaps:

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17. Trie Data Structure:

Fact: Searching algorithms like Linear Search and Binary Search are essential for finding elements in a collection. Example: Linear Search in Python: A simple search algorithm that iterates through each element until the target is found....

18. B-Trees:

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19. AVL Trees:

Fact: Sorting algorithms arrange elements in a specific order. Examples include Bubble Sort, Merge Sort, and QuickSort. Example: Bubble Sort in Java: A simple sorting algorithm that repeatedly steps through the list, compares adjacent elements, and swaps them if they are in the wrong order....

20. In-Place Algorithms:

Fact: Dynamic programming is an optimization technique used to solve problems by breaking them down into overlapping subproblems. Example: Fibonacci Sequence with Dynamic Programming: A more efficient implementation of the Fibonacci sequence using dynamic programming....

21. Bellman-Ford Algorithm:

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22. Floyd-Warshall Algorithm:

Fact: Divide and Conquer is a problem-solving paradigm where a problem is broken into subproblems that are solved independently. Example: Merge Sort in Python: An algorithm that divides the unsorted list into n sublists, each containing one element, and then repeatedly merges sublists to produce new sorted sublists....

23. Dijkstra’s Algorithm:

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24. Big-O Notation:

Fact: NP-completeness is a class of problems for which no known polynomial-time solution exists. Details: NP-complete problems have the property that if a polynomial-time solution exists for any one of them, a solution exists for all NP-complete problems....

25. NP-Hard Problems:

Fact: A heap is a specialized tree-based data structure that satisfies the heap property. Details: Heaps are often used to implement priority queues, where elements with higher priority are served before elements with lower priority....