Lecture 14 — Problem Solving and Design, Part 1

Overview

This is the first of our lectures dedicated primarily to problem solving and design rather than on particular programming constructs and techniques

  • Design:
    • Choice of container/data structure; choice of algorithm.
      • At the moment, we don’t know too many containers, but we will think about different ways to use the one container - lists - we do know about.
    • Implementation
    • Testing
    • Debugging
  • We will discuss these in the context of several variations on one problem:
    • Finding the mode in a sequence of values — the value (or values) occuring most often.
  • Our discussion is loosely based on Chapter 12, although we are not really ready for much of the material discussed there.
  • We will start with a completely blank slate so that the whole process unfolds from scratch. This includes looking for other code to adapt.
  • Working through problems like this is a good way to review what we’ve learned thus far.

Problem: Finding the Mode

  • Given a series of values, find the one that occurs most often.
  • Variation 1: is there a limited, indexable range of values?
    • Examples that are consistent with this variation include test scores or letters of the alphabet
    • Examples not consistent include counting words and counting amino acids
  • Variation 2: do we want just the modes or do we want to know how many times each value occurs?
  • Variation 3: do we want a histogram where values are grouped?
    • Example: ocean temperature measurements, pixel intensities, income values.
    • In each of these cases, a specific value, the number of occurrences of a specific ocean, such as 2.314C, is not really of interest. More important is the number of temperature values in certain ranges.

Our Focus: A Sequence of Numbers

  • Integers, such as test scores
  • Floats, such as temperature measurements

Sequence of Discussion

  • Brainstorm ideas for the basic approach. We’ll come with at least two.
    • We will discuss an additional approach when we learn about dictionaries.
  • Algorithm / implementation
  • Testing
    • Generate test cases
    • Which test cases we generate will depend on the choice of algorithm. We will combine them.
  • Debugging:
    • If we find a failed test case, we will need to find the error and fix it.
    • Use a combination of carefully reading the code, working with a debugger, and generating print statements.
  • Evaluation
    • We can analyze using theoretical tools we will learna about later or through experimental timing

Discussion of Variations

  • Frequency of occurrence:
    • What are the ten most frequently occurring values? What are the top ten percent most frequent values?
    • Output the occurrences for each value.
  • Clusters / histograms:
    • Test scores in each range of 10
  • Quantiles: bottom 25% of scores, median, top 25%