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Different approaches to programming have developed over time. Classification of each approach was either described at the time the approach was first developed, but often not until some time later, retrospectively. An early approach consciously identified as such is structured programming, advocated since the mid 1960s
The term problem solving has a slightly different meaning depending on the discipline. For instance, it is a mental process in psychology and a computerized process in computer science. There are two different types of problems: ill-defined and well-defined; different approaches are used for each.
Knowledge Engineering is a field of computer science which offers a significant body of work on problem-solving methods. Problem-solving methods are patterns of reasoning that are applied to solve specific problems. [3] The work on problem abstractions within knowledge engineering can therefore provide a basis for research in software engineering.
From a dynamic programming point of view, Dijkstra's algorithm for the shortest path problem is a successive approximation scheme that solves the dynamic programming functional equation for the shortest path problem by the Reaching method. [8] [9] [10] In fact, Dijkstra's explanation of the logic behind the algorithm, [11] namely Problem 2.
Programming paradigms constitute the theoretical frameworks that shape the way software constructs are created and executed. Each paradigm embodies a unique approach to organizing and structuring programming logic, often promoting particular forms of abstraction and compositional structures that align with their underlying principles.
When a problem shows optimal substructures—meaning the optimal solution can be constructed from optimal solutions to subproblems—and overlapping subproblems, meaning the same subproblems are used to solve many different problem instances, a quicker approach called dynamic programming avoids recomputing solutions.
This approach can be seen as one of the two basic approaches to problem-solving, contrasted with an approach using insight and theory. However, there are intermediate methods that, for example, use theory to guide the method, an approach known as guided empiricism. [citation needed]
Rather, it is a description or a template for solving a particular type of problem that can be deployed in many different situations. Design patterns can be viewed as formalized best practices that the programmer may use to solve common problems when designing a software application or system.