1. Introduction to Sorting
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