2.2.2 Computational methods
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What are the features that make a problem solvable?
-abstraction and decomposition -enumeration -theoretical approach -simulation and automation
How do abstraction and decomposition make a problem solvable?
Simplify the complexity of a problem and break it down makes it far easier to write an algorithm to solve a problem
How does enumeration make a problem solvable?
involves designing an algorithm that performs an exhaustive search and attempts all possible solutions until the correct one is found
How does a theoretical approach make a problem solvable?
If a problem can be boiled down to pure theory, I becomes easy to represent using mathematical equations
How do simulation and automation make a problem solvable?
-Simulation is the process of designing a model of a real system in an attempt to understand its behaviour. -Automation is about building problem solving models and putting them into action -they both make heavy use of abstraction to turn complex problems into more easily solved problems
What are the key principles of computational methods?
-decomposition -pattern recognition -abstraction -algorithms -calculations and storage
What is problem recognition?
The ability to: “Recognise and acknowledge that an issue exists or that a situation needs attention in an existing process or program”. “Define the problem and determine exactly what it is.”
What is problem decomposition?
“The process of taking a large problem and breaking it down into several smaller problems.” -not all problems are easily broken down by a top-down approach
What is a good way of tackling problem decomposition?
step wise refinement to produce a top-down modular design
What is the aim of problem decomposition?
To end up with small independent modules, which can then be written by a single person or a small team
What is the divide and conquer technique?
A technique that reduces the size of a problem with each successive iteration -can also refer to the concept of splitting a task down into smaller tasks, which are then tackled separately (similar to decomposition)
What is backtracking?
-The process of incrementally building towards a solution, abandoning partial success when the solution can’t be completed and going back to a previously successful match -Logic problems, especially those that involve paths or route-finding, can particularly benefit from using backtracking as an approach
What is data mining?
-the concept of analysing vast amounts of data gathered from a variety of sources to discover new information and trends -It is often associated with the concept of Big Data which refers to extremely large data sets
Who is data mining used by?
-Used by companies to help them maximise their profits
Practical application of data mining:
-Weather modelling -Science and engineering -Medical research -Law enforcement
What is heuristics?
-an approach to solving problems that allows or even encourages us to make use of our experience and find a solution that can be considered “good enough”. -do not guarantee the best solution
What is a heuristic approach to solving a problem?
-We take previous experiences into account, apply them to the problem and make an educated guess
What is performance modelling?
-the process of approximating how well models perform using mathematics -can then be used to calculate how the servers would perform under more stress
What is pipelining?
-splitting a large task into manageable chunks and overlapping these smaller processes to speed up the overall process
What is visualisation?
-allows us to create a mental image of what a program will do or how it will work -it makes it easier to understand -this is why we often use flow diagrams to illustrate the logic of an algorithm
Advantages of visualisation:
-Visualisations present the information in a simpler form to understand -Visualisations can best explain complex situations