Searching Algorithms

Learning Objectives Explain the limitations of linear search for large datasets. Identify the key prerequisite for using binary search. Describe the step-by-step process of the binary search algorithm. Trace the execution of a binary search on a given sorted list. Compare the efficiency of linear search versus binary search. Determine when binary search is the more appropriate algorithm to use. Ever tried finding a specific word in a dictionary without going page by page? 📚 There's a smarter, much faster way than just flipping one page at a time! In this lesson, we'll explore advanced searching algorithms that are incredibly efficient, especially for large amounts of data. You'll learn how to find information much quicker than with basic methods, understandi...

TermDefinitionExample Sorted DataData arranged in a specific order, either ascending (smallest to largest) or descending (largest to smallest). This is a crucial requirement for many advanced search algorithms.A list of numbers like [5, 12, 23, 30, 45] is sorted in ascending order. A list of names like ['Alice', 'Bob', 'Charlie'] is sorted alphabetically. Binary SearchAn efficient search algorithm that works on sorted data. It repeatedly divides the search interval in half, eliminating half of the remaining elements with each step.Imagine searching for 'apple' in a dictionary. You open to the middle. If 'apple' is before that page, you ignore the second half. If it's after, you ignore the first half. You repeat this until you find it....

Binary Search Prerequisite Rule Binary search can ONLY be applied to data that is already sorted (in ascending or descending order). Before attempting a binary search, always ensure your list or array is sorted. If it's not, you must sort it first, or binary search will not work correctly and might miss the target value. Midpoint Calculation Rule The midpoint index is calculated as `mid = (low + high) // 2` (using integer division). In each step, `low` is the starting index and `high` is the ending index of your current search space. This formula finds the exact middle index, rounding down if the total number of elements is even. Search Space Adjustment Rule If the target is less than the midpoint value, set `high = mid - 1`. If the target is greater than the midp...