What are the characteristics of dynamic programming
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1According to some representations, this is even informal science marketing: https://www.youtube.com/watch?v=OQ5jsbhAv_M(3:24–4:47)
2Thomas H. Cormen et al .: Introduction to Algorithms (Third Edition), MIT Press, 2009, p. 359ff.
3Since the approach was discovered several times, the table is also called Tartaglia triangle (after Niccolò Tartaglia), Yang-Hui triangle (after 楊輝), or Chayyām triangle (after عمر خیام).
4The data structure in which the solutions are stored is also called in the context of dynamic programming State spaceand the entries as conditionsdesignated.
5This is particularly interesting if recursion is not directly supported in the programming language used or the use of an explicit stack is not possible.
6Robert Sedgewick: Algorithmen, Addison-Wesley, 1991, 674-677; Jon Kleinberg & Éva Tardos: Algorithm Design, Addison-Wesley, Pearson, 2005, Chapter 6 (in which the backpack problem is developed from the partial sum problem) and p. 271ff.
7In the implementations, no explicit representation of the “values with an infinite amount” is used, which would have made it necessary to distinguish between cases during the calculation or to use an adapted type. Instead, instance-dependent barriers are used.
8Klaus Jansen & Marian Margraf: Approximate Algorithms and Non-approximability, de Gruyter, 2008.
9In our implementation, however, we use an upper bound that tends to be smaller, obtained through relaxation.
10The implementation (not immediately executable without the mentioned instance library) is available as a solution for Visual Studio at https://github.com/DbRRaU6m/Knapsack
11Eugene Lawler: Fast Approximation Algorithms for Knapsack Problems, Mathematics of Operations Research 4 (4), 1979.
12Joseph Albahari: Linq - in a nutshell, O‘Reilly, 2016.
14The tests were implemented as component tests with MSTest.
16Such term limits are called pseudopolynomialdesignated.
17Robert Sedgewick: Algorithmen, Addison-Wesley, 674-677, 1991.
18Hans Werner Lang: Algorithms in Java, Oldenbourg Wissenschaftsverlag, chap. 11, 2006.
19Oscar H. Ibarra & Chul E. Kim: Fast Approximation Algorithms for the Knapsack and Sum Of Subset Problems, Journal of the ACM 22 (4): 463-468, 1975.
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