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2.2.2
| Question | Answer |
|---|---|
| Computable problems | Have an algorithm to solve them Are practically possible (e.g. memory and hardware wise) Have features that enable computational methods - Enumeration - Theoretical approach - Abstraction - Decomposition |
| Algorithms are useful to programmers if they can | Solve problems... In a reasonable time frame Using a reasonable amount of memory |
| Enumeration | designing an algorithm that attempts all possible solutions until the correct one is found |
| Theoretical approach | representing a problem in mathematical equations with a logical method to find the answer |
| Abstraction (computable problems) | simplifies a problem, making it easier to solve, by using different methods Simulation Automation |
| Simulation | the process of designing a model of a real system to understand its behaviour |
| Automation | building problem-solving models and putting them into action |
| Problem Recognition | the ability to recognise and acknowledge that an issue exists and define the problem and determine exactly what it is |
| To recognise the problem/solutions | Is there a problem to be solved? What is the nature of the problem? What is it? What data do you need? What variables could alter state of problem? What processes and techniques could solve the problem? To what extent is the problem solvable? |
| Problem Decomposition | The process of breaking down a problem into sub-problems until the lowest level of subproblem is recognisably solvable, possibly by using a diagram |
| Divide and Conquer | Technique that reduces problem size with each successive iteration e.g. binary search and decomposition. Divide and conquer can be used to identify tasks that can be carried out simultaneously (so can use concurrent methods), such as merge sort |
| Divide and Conquer steps | Generally, the steps are: 1. Take a problem, or a data set 2. Apply some rules 3. Based on the outcome, discard any data that doesn't match 4. Repeat the process with the data that is left |
| Use of Abstraction (to solve a problem) | It is important to only include important aspects when you solve a problem/write code |
| Computational Methods | - Backtracking - Data mining - Heuristics - Performance modelling - Pipelining - Visualizations |
| Backtracking (Computational Methods) | good for logic problems w/ paths/route-finding Problem solved by following actions until no longer works then return to last working stage + try again (depth first search) Coding: test section at a time + save backtrack to last version in case of error |
| Data mining (Computational Methods) | the concept of analysing vast amounts of data from a variety of sources to discover new information and trends Big data: extremely large data sets Can be used to increase profits, weather forecast, or to predict what videos a user likes |
| Heuristics (Computational Methods) | an approach to solving problems that encourages finding a ‘good enough’ solution to a problem that may not be solvable otherwise They do not guarantee the best/optimal solution |
| Performance modelling (Computational Methods) | Process of approximating how well models perform using maths, reducing costly, detailed testing Not always possible to test full performance, as a real-life simulation cannot be provided More controlled, beta testing |
| Pipelining (Computational Methods) | Splitting a task into manageable, equal sized chunks and overlapping these smaller processes to speed up the overall process |
| Visualizations (Computational Methods) | allow an image of what a program will do or how it will work to be created A problem is represented visually to aid understanding |
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