Lecture 22 — Problem Solving and Design

Overview

This is the last “official” set of lecture notes. Material from these notes will be on the final.

• Design:
  • Choice of container/data structure; choice of algorithm
  • 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, but there are many things in this chapter we will skip:
  • Discussion of functions, default parameters, variable numbers of arguments
  • Exceptions
  • Specific design patterns
• We will start with a completely blank slate so that the whole process unfolds from scratch. This includes looking for other code to adapt.

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 three.
• 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:
  • Theoretical
  • 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%

Practice Problems

• These will be generated after class based on how the discussion progresses.

Summary of Problem Solving Steps

1. Understand the problem: play with examples, ask (yourself) questions, consider variations.
2. Think about the core approach, algorithm(s) and data structure(s.
   • Several choices are often possible
   • The choice dictates the details of what follows.
3. Narrow choices based on considerations of efficiency, clarity and ease of implementation.
4. Gradually progress from a sketch of your ideas, to a detailed algorithm, to an implementation.
5. Generate test cases
6. Test and debug