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When have you ever directly applied the concepts of dynamic programming to solve a problem in the field? It's sometimes not evident how it can be applied when using it to solve a made-up instance of the knapsack problem.
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Dynamic programming is used where we have problems, which can be divided into similar sub-problems, so that their results can be re-used. Mostly, these algorithms are used for optimization. Before solving the in-hand sub-problem, dynamic algorithm will try to examine the results of the previously solved sub-problems.
Dynamic programming is heavily used in computer networks, routing, graph problems, computer vision, artificial intelligence, machine learning, etc.
Dynamic Programming ExampleA fibonacci series is the sequence of numbers in which each number is the sum of the two preceding ones. For example, 0,1,1, 2, 3 . Here, each number is the sum of the two preceding numbers. Let n be the number of terms.
The term dynamic programming was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another.
It's probably a lot more common to use memoization to solve problems in the field, since it's applicable to a wider set of problems. DP is really only called for when you have a lot of overlapping sub-problems, like in calculating fibonacci numbers (the hard way), or prime numbers (the efficient way).
Incidentally, the page you linked to has a list of algorithms that use DP.
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