SortingInteger.md

Integer Sorting Algorithms

Topics

• Contrast comparison sorting with integer sorting
• Integer sorting algorithms: pigeonhole sort, counting sort, bucket sort, radix sort

Slides

You can find the slides here

Resources

• Play with VisuAlgo's interactive sorting visualizations including counting sort and radix sort
• Play with USF's interactive sorting animations including counting sort, bucket sort, and radix sort
• Read Interview Cake's counting sort article (spoiler alert: contains solution code)
• Read Vaidehi Joshi's articles on counting sort and radix sort with beautiful drawings and excellent analysis
• Watch Barack Obama's answer to a Google interview question on how to sort one million 32-bit integers

Challenges

• Implement integer sorting algorithms using sorting starter code:
  • counting_sort(numbers) - sort numbers (integers) by counting occurrences of each number, then looping over counts and copying that many numbers into output list.
  • bucket_sort(numbers, num_buckets) - sort numbers by distributing into buckets representing subranges, then sorting each bucket and concatenating all buckets in sorted order
• Annotate functions with complexity analysis of running time (operations) and space (memory usage)
• Run python sorting.py to test sorting algorithms on a small random sample:

  $ python sorting.py counting_sort 15 5
  Initial items: [2, 3, 1, 5, 5, 2, 5, 5, 1, 4, 1, 5, 2, 3, 1]
  Sorting items with counting_sort(items)
  Sorted items:  [1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 5, 5, 5]
  
  $ python sorting.py counting_sort 20 10
  Initial items: [1, 6, 2, 2, 5, 8, 9, 7, 8, 9, 10, 10, 8, 10, 3, 3, 8, 2, 5, 7]
  Sorting items with counting_sort(items)
  Sorted items:  [1, 2, 2, 2, 3, 3, 5, 5, 6, 7, 7, 8, 8, 8, 8, 9, 9, 10, 10, 10]
  

  • Experiment with different list sizes, orderings, integer ranges, and distributions to find when integer sorting algorithms are faster than other sorting algorithms
• Expand the sorting unit tests to ensure your integer sorting algorithms are robust
  • Write tests in a way that lets you add new sorting functions without needing to write more tests
  • Include a variety of test cases that cover several integer distributions, orderings, and edge cases
• Run pytest sorting_test.py::IntegerSortTest to run only the integer sorting unit tests and fix any failures

Stretch Challenges

• Extend counting sort algorithm to handle sorting floating-point numbers, characters, or strings
• Implement radix sort for 32-bit integers (most or least significant digit or bit)
• Extend bucket sort or radix sort algorithm to handle sorting strings in lexicographical order
• Annotate functions with complexity analysis of running time (operations) and space (memory usage)