# What are the characteristics of dynamic programming

## BLOG / RESEARCH - DYNAMIC PROGRAMMING

^{1}According to some representations, this is even informal science marketing: https://www.youtube.com/watch?v=OQ5jsbhAv_M(3:24–4:47)

^{2}Thomas H. Cormen et al .: Introduction to Algorithms (Third Edition), MIT Press, 2009, p. 359ff.

^{3}Since 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).

^{4}The data structure in which the solutions are stored is also called in the context of dynamic programming

*State space*and the entries as

*conditions*designated.

^{5}This is particularly interesting if recursion is not directly supported in the programming language used or the use of an explicit stack is not possible.

^{6}Robert 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.

^{7}In 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.

^{8}Klaus Jansen & Marian Margraf: Approximate Algorithms and Non-approximability, de Gruyter, 2008.

^{9}In our implementation, however, we use an upper bound that tends to be smaller, obtained through relaxation.

^{10}The implementation (not immediately executable without the mentioned instance library) is available as a solution for Visual Studio at https://github.com/DbRRaU6m/Knapsack

^{11}Eugene Lawler: Fast Approximation Algorithms for Knapsack Problems, Mathematics of Operations Research 4 (4), 1979.

^{12}Joseph Albahari: Linq - in a nutshell, O‘Reilly, 2016.

^{13}http://hjemmesider.diku.dk/~pisinger/codes.html

^{14}The tests were implemented as component tests with MSTest.

^{15}http://www.diku.dk/~pisinger/smallcoeff_pisinger.tgz

^{16}Such term limits are called

*pseudopolynomial*designated.

^{17}Robert Sedgewick: Algorithmen, Addison-Wesley, 674-677, 1991.

^{18}Hans Werner Lang: Algorithms in Java, Oldenbourg Wissenschaftsverlag, chap. 11, 2006.

^{19}Oscar 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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