Problem-solving and Thinking Methodology
Yanqing Zhang
In order to help students enhance their ability and intelligence for tackling complex real world problems, we’d like to describe commonly used powerful and useful problem-solving and thinking methodologies which will be updated weekly after new methodologies are introduced. These methodologies are very useful for not only the current class but also other classes and even real jobs and new problems after graduation. Best wishes and great luck!
1. Methodology One: Explicit, Logical and Complete Work
To create explicit, logical and complete solutions such as an assignment solution, a class research report, and a software system, an effective method is to use a logical algorithm to finish any work step by step, and then write a solution in an elegant and professional manner. In other words, a solution is not only correct but also explicit, logical and complete.
2. Methodology Two: Creative, Original, Imaginary Thinking Skills
Creation, originality and imagination are three basic skills of a scientist and an engineer. Every one should keep creating new ideas, novel techniques, original theories, and imaginary works, and then apply for patents.
3. Methodology Tree: Hybrid Thinking Methods
We may merge two or more different and relevant techniques to build a hybrid system (method) that is more powerful that each individual one in most cases.
4. Methodology Four: Divide-and-Conquer Strategy
To solve a complex big problem, the clever way is Divide-and-Conquer methodology which can divide the original complex big problem into simple smaller sub-problems that are easy to be solved. So if you can solve these small simple sub-problems, then you’ll be able to solve the original complex big problem.
5. Methodology Five: Binary Thinking Method
To get a complete solution to a difficult problem, sometimes we have to consider the problem from two totally different extreme ways such as (1) top-down and down-top, (2) best-case and worst-case, (3) left-side and right-side, ……, and so on.
6. Methodology Six: Simple-Case-to-Final-Solution Thinking Method
To solve a general-case problem, we may first test some basic simple cases to discover useful information, then consider more general cases to get the final solution.
7. Methodology Seven: Similarity-oriented Thinking Method
A lot of algorithms, methods, techniques and theories come from simple daily life events, problems and ideas by finding similarity between a computer science problem and a simple daily life problem. So if you can find the similarity, you’ll be able to create a new technique!
8. Methodology Eight: Calmness-Meditation-oriented Thinking Method
To solve a challenging problem, a person should be calm after a hard effort. In other words, the person should meditate (don’t think anything on the brain, empty (nothing) in the brain like a sleep but much better than the sleep) for few minutes or more, then comes back to the original problem. This method is useful for assignments, tests, research, …, etc.