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Understanding Linear and Binary Search Algorithms

This guide explores two fundamental search algorithms: Linear Search and Binary Search. Linear Search is ideal for unsorted or small datasets, operating with a time complexity of O(n). In contrast, Binary Search is optimized for sorted datasets, boasting a time complexity of O(logn). We discuss when to choose each method, including scenarios where data sets are frequently updated or require high performance. Additionally, you'll learn the step-by-step implementation of both algorithms, with emphasis on their respective search keys and handling of exceptions.

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Understanding Linear and Binary Search Algorithms

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Presentation Transcript

  1. Search and Recursion CS221 – 2/23/09

  2. List Search Algorithms • Linear Search: Simple search through unsorted data. Time complexity = O(n) • Binary Search: Fast search through sorted data. Time complexity = O(logn)

  3. How to Choose? • Linear search is optimal for • Unsorted data • Small data sets • Data sets that will change often between searches • Binary search is optimal for • Sorted data • Large data sets where performance is important • Data sets that are relatively stable

  4. How to Implement Linear Search • Take a data-set to search and a key to search for • Iterate through the data set • Test each item to see if it equals your key • If it does, return true • If you exit the iteration without the item, return false

  5. Integer Linear Search

  6. Search Keys • Generally, search key and search result are not the same • Consider: • Search for a business by address • Search for a passenger by last name • Search for a bank account by social security #

  7. Search Keys • How would the search change if the key is not the result?

  8. Generic Linear Search

  9. How to Implement Binary Search • Take a sorted data-set to search and a key to search for • Start at the mid-point and see if that’s the key • If not, see if you need to search above or below the mid-point • Pick halfway point above or below and test again • Repeat until you can no longer cut the remaining set in half

  10. Binary Search

  11. Binary Search

  12. How to Implement Binary Search • Given a sorted array and a key • First = start of list • Mid = middle of list • Last = end of list • if array[mid] == key • Return key • If mid > key • Last = mid - 1 • If mid < key • First = mid + 1 • Mid = (first + last)/2 • Continue until first > last • If the key isn’t found, throw an exception

  13. Integer Binary Search

  14. Generic Binary Search

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