APS Test 1

Understanding Problem Solving and Computational Thinking

• Programmers think differently and must harness the computational thinking approach to problem solving, which paves the way for providing a solution that both computers and humans can understand.
• Before solving a problem, it's essential to fully understand the problem, carefully read documentation, identify uncertainties, and clarify any unclear points.

Computational Thinking Stages

• There are 4 main parts to the computational thinking approach:
  • Decomposition
  • Pattern recognition and data representation
  • Abstraction
  • Algorithms

Decomposition

• Decomposition is the process of breaking down complex problems into more manageable parts.
• It helps to identify and simplify complex problems, making them more manageable.
• Example: Breaking down a morning routine into smaller tasks like waking up, showering, brushing teeth, getting dressed, eating breakfast, and going to work/school.

Pattern Recognition and Data Representation

• This stage involves identifying common behavior and attributes, making parts reusable and eliminating redundancies.
• It simplifies solutions, makes them more efficient, and reduces repetition.
• Example: Identifying patterns in baking different types of cakes, such as requiring specific ingredients, amounts, and temperatures.

Abstraction

• Abstraction concentrates on generalizing characteristics of a problem and/or pattern, filtering out specific details to form an idea or concept.
• It declutters characteristics of a problem and solution, ensuring the solution addresses the problem.
• Example: Abstraction in baking a cake, focusing on the general process rather than specific details like baking time and temperature.

Algorithms

• The final stage of computational thinking, representing a master plan with specific step-by-step instructions.
• Algorithms can refer to other algorithms for larger problems and must include unit-testing during assembly.
• Algorithms can be represented in two ways: pseudo code (best for programmers) and flowcharts (best for non-technical people).

Abstraction

• Abstraction involves recognizing that two things differ only in small ways and moving those small differences into parameters.
• It involves retaining the fundamental problem-solving technique, focusing on the essential aspects of the problem.

Abstraction Example

• Finding the sum of 10 values and finding the product of 15 values are similar problems.
• Both involve visiting a series of values and combining them into a single value.
• The common aspect between these problems is the combination of values into a single value.
• The differences between these problems are:
  • The operation to combine the values (e.g., +, -, *, /).
  • The number of values to combine.
  • The values themselves.

Parameters in Abstraction

• Make differences between similar problems into parameters.
• Create a parameters table to organize and compare the differences between similar problems.
• Example parameters table:
  • Operator (e.g., +, -, *, /)
  • Number of values to combine (# Values)
  • Values to combine

Decomposition

• Divide a problem into smaller, more manageable sub-problems.
• Solve each sub-problem separately.
• Combine solutions to sub-problems to yield a solution to the original problem.

Example 1: Summing Several Values

• Analyze the problem: need to sum multiple values.
• Identify key requirements:
  • Need a place to store the sum.
  • Sum needs to be initialized to zero.
  • Need to access each of the values.
  • Need to add each value to the sum.
• Solution:
  • Create and initialize sum.
  • Decompose the problem:
    • Access each value in turn by having the user enter values one at a time.
    • Add each value onto the sum.

Example 2: Sorting Two Values in Ascending Order

• Analyze the problem: need to sort two values in ascending order.
• Identify key requirements:
  • Compare the first value to the second.
  • If out of order, swap them.
• Solution:
  • Swapping values:
    • Use a third variable to store the first value when overwriting with the second.
    • Copy first value to temp.
    • Copy second value to first.
    • Copy temp to second value.
• Putting it all together:
  • Compare first to second.
  • If out of order:
    • Copy first to temp.
    • Copy second to first.
    • Copy temp to second.

Pattern Recognition in Data

• Patterns in data involve looking for commonalities among several things, and factoring them out into a new piece of information that individual things can reference.
• Examples of patterns in data include:
  • A cheque with common fields such as date, amount, and account number
  • A bank deposit with common fields such as date, amount, and account number

Commonalities in Data

• Commonalities in data include:
  • Date: a combination of day, month, and year
  • Amount: a simple number
  • Account: a bank identifier, branch ID, and account number

Factorization of Complex Common Parts

• Date can be broken down into:
  • Day
  • Month
  • Year
• Account can be broken down into:
  • Bank
  • Branch
  • AcctNumber

Patterns in Functionality

• Patterns in functionality involve looking for the same operations performed in different places, and factoring out the repeating operations.
• Example: finding the maximum of a series of values in both weather and expenses data.

Commonality in Functionality

• The commonality in functionality is finding the maximum value of a series of values.
• This can be applied to:
  • Finding the hottest day from a list of temperatures
  • Finding the most expensive meal from a list of bills