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.

  • There is no direct connect to a chapter in the text.

  • 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 temperature, 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 learn 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%