1. Introduction to Searching

1.1 What is Searching? 
 Searching is the process of finding a particular element or checking if an element exists in a data structure (array, linked list, tree, etc.). 
 Real-World Analogies: 
 
 Finding a book in a library 
 Searching for a contact in your phone 
 Looking up a word in a dictionary 
 Finding a file on your computer 
 
 Types of Searching: 
 
 Linear Search - Sequential search through elements 
 Binary Search - Divide and conquer approach (requires sorted data) 
 Jump Search - Jumping ahead by fixed steps 
 Interpolation Search - Improved binary search for uniformly distributed data 
 Exponential Search - Finding range then binary search 
 
 Note: There's actually a lot more searching algorithms, but we'll focus on the most common ones. 
 1.2 Why Study Searching Algorithms? 
 Importance: 
 
 One of the most common operations in programming 
 Critical for database queries 
 Essential for data retrieval systems 
 Foundation for more complex algorithms 
 Performance impact on large datasets 
 
 Performance Metrics: 
 
 Best Case: Minimum number of comparisons 
 Average Case: Expected number of comparisons 
 Worst Case: Maximum number of comparisons 
 Space Complexity: Extra memory required