# 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 spaceand the entries as conditionsdesignated.

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.

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http://www.diku.dk/~pisinger/smallcoeff_pisinger.tgz

16

Such term limits are called pseudopolynomialdesignated.

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.