# Lecture 24 — 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¶

- Understand the problem: play with examples, ask (yourself) questions, consider variations.
- Think about the core approach, algorithm(s) and data structure(s.
- Several choices are often possible
- The choice dictates the details of what follows.

- Narrow choices based on considerations of efficiency, clarity and ease of implementation.
- Gradually progress from a sketch of your ideas, to a detailed algorithm, to an implementation.
- Generate test cases
- Test and debug