In Class: Week 8
Search

Topics

• Searching using the in and not in operators
• Linear search
• Complexity of linear search
• Big-O notation
• Binary search
• Complexity of binary search

In-class work

Linear Search

1. We have used Python functions for searching (e.g., in, list.find()). How do these methods actually work? We will discuss the algorithm for searching a collection of items.
2. Open up the file searchCards.py. This program creates a list of random ints and asks the user for a value to search the list for. We will write a function findCard() that takes in a deck of cards (a list of ints) and an int value to search for. Our function can return a boolean value for whether the value was found, or the actual position of the value in the list.

Complexity of Search

3. How do we analyze how long it takes for search to finish? We will count steps to analyze a programs complexity. What counts as a step? What happens in the best case? Worst case? How many steps does linear search take in the worst case?

Binary Search

4. Using playing cards, we will consider how we can make searching go faster if the list of items is in sorted order. Binary search works by using divide and conquer. Each step of the algorithm divides the number of items to search in half until it finds the value or has no items left to search.
5. In testsearches.py, we will implement the binary search algorithm to search a list for some random value.
6. Why is it called binary search? How many steps does it take for binary search to run? We will see that binary search is O(log N). What does this mean relative to linear search? Run testsearches.py with different values of N to see how the run time of binary search grows with increasing list sizes. How does this compare to linear search's growth?