Talk:Dynamic programming

1. REDIRECT Template:Archives

Confusion

The first paragraph of the second part and the article on algorithms states that dynamic programming is a bottom-up approach, but later this article says dynamic programming may use bottom-up or top-down approaches. --zeno 11:46, 9 Feb 2004 (UTC)

I've revised that section. It was very vague and somewhat incorrect. I hope there's less confusion now. Derrick Coetzee 20:18, 5 Oct 2004 (UTC)

Weirdness

The page says "i dont know" in those terms, which is not only weirdly misplaced, but also improperly formatted. Someone check.

Misplaced section

The part following "The steps for using dynamic program goes as follows:" is out of place. Out of nowhere the article starts using terms like 'gap penalties' and 'sequence alignment.' Seems like this was copied from some article on a specific application, such as protien sequencing. Anon, Wed Jul 11 14:11:43 EDT 2007

Too many examples

This is not a textbook. One good example would suffice. Even worse, many of them are just too long (and boring). Put them in wikibooks. Unfortunately, any attempt to fix this article would be blocked as "vandalism". Way to go, Wikipedia!

Why ALGOL

Hello , in

function fib(n)

   if n <= 1 return n
   return fib(n − 1) + fib(n − 2)

I doubt that the return function would return a false if, so maybe you make a if n larger or equal to 1 out of it ? That also has the nice side effect that the Fibonacci numbers would become larger than -1, like the original series is larger than +1, I guess that is what you intended ...

Call-by-need is not memoization

This is technically correct but quite misleadingly worded. In call-by-need, the value at a particular call site may be (but need not be) memoized. If I call the same function with the same arguments but from a different call site, the result will be computed again. That is, rather than a memo table, call-by-need at most provides a cached value for a particular function call.

For example, in Haskell, a "lazy" language with call-by-need, we can define factorial recursively as

fact n = if n == 0 then 1 else n * fact (n -1)

If we then call it from a single call site

sum (map (\_ -> fact 5) [1..3])

the call to fact 5 and its child calls will each be evaluated but once, even though the lambda appears to be evaluated three times.

However, in

fact 5 + fact 5 + fact 5

each call to fact 5 and children will be evaluated separately: no memoization will occur.

This distinction makes call-by-need useless for memoization when decomposing a typical recursion: the subproblems are all called from separate call sites, and thus no memoization will occur.

Citations needed, at the least. Futures / promises are not a memoization mechanism, but a manual implementation of the call-by-need caching described above. In general Scheme and Perl, at least, are strict languages as far as I am aware. Bart Massey (talk) 20:03, 19 February 2025 (UTC)

A type of balanced 0–1 matrix

This section describes a dynamic programming approach, in which the state of a partially-filled matrix specifies, for each column, the number of 0's and 1's to be placed in that column. This simplifies the problem, but not nearly enough to compute all of the terms included in the OEIS. In the case of an 18 by 18 matrix, this approach requires 44,926,130,009,521,017 different states. For example, after filling one row there are 48,620 different states. Each of these states has (9, 8) nine times and (8, 9) nine times, and there is one way to reach each of these states.

A better approach is to realize that these states are essentially all the same. We can count matrices without knowing which columns are (9, 8) and which columns are (8, 9). I would describe all of these as a single state (9, 9, 0, 0, 0, 0, 0, 0, 0, 0), indicating 9 columns with 0 ones, 9 columns with 1 one, and 0 columns with 2, 3, 4, 5, 6, 7, 8, or 9 ones. There are 48,620 ways to reach this state.

After filling the second row, there are 10 different states: (0, 18, 0, 0, 0, 0, 0, 0, 0, 0), (1, 16, 1, 0, 0, 0, 0, 0, 0, 0), (2, 14, 2, 0, 0, 0, 0, 0, 0, 0), ..., (9, 0, 9, 0, 0, 0, 0, 0, 0, 0). This approach uses a total of 194,182 states to count about 2.2*10⁷² matrices. David.wasserman (talk) 01:06, 19 May 2025 (UTC)

External links

Some things just grow during incremental edits and sometimes get out of hand. The "External links" section, one of the optional appendices, has grown to 12 entries. Three seems to be an acceptable number, and of course, everyone has their favorite to try to add for a fourth. Consensus needs to determine this. A tag indicates concerns.

However, none is needed for article promotion.

Some links may be included in WP:ELNO, various points in What Wikipedia is not like WP:NOTREPOSITORY or WP:NOTGUIDE, WP:ELDEAD, Others, listed below:

• ELpoints #3) states: Template:Tq
• LINKFARM states: Template:Tq
• ELMIN: Template:Tq. --
• ELCITE: Template:Tq

External links This page in a nutshell: Template:Tq

Second paragraph, Template:Tq

• • Please also note:
• WP:ELBURDEN: Template:Tq. Please do not add back more links without consensus. Simple solution to facilitate career maintenance tag. Move links here for discussion.

Moved links:

• A Tutorial on Dynamic programming
• MIT course on algorithms - Includes 4 video lectures on DP, lectures 15–18
• Applied Mathematical Programming by Bradley, Hax, and Magnanti, Chapter 11
• More DP Notes
• Dynamic Programming: from novice to advanced A TopCoder.com article by Dumitru on Dynamic Programming
• Algebraic Dynamic Programming – a formalized framework for dynamic programming, including an entry-level course to DP, University of Bielefeld
• Dreyfus, Stuart, "Richard Bellman on the birth of Dynamic Programming. Template:Webarchive"
• Dynamic programming tutorial
• A Gentle Introduction to Dynamic Programming and the Viterbi Algorithm
• Tabled Prolog BProlog, XSB, SWI-Prolog
• IFORS online interactive dynamic programming modules including, shortest path, traveling salesman, knapsack, false coin, egg dropping, bridge and torch, replacement, chained matrix products, and critical path problem. -- Otr500 (talk) 15:41, 12 June 2025 (UTC)