20bits - Latest Comments in Introduction to Dynamic Programming | 20bits

Re: Introduction to Dynamic Programming | 20bits

coderoger — Thu, 16 Jul 2009 16:48:28 -0000

great post,

Re: Introduction to Dynamic Programming | 20bits

pickatutorial — Thu, 25 Jun 2009 11:14:11 -0000

Nice work. Keep it up.....

Re: Introduction to Dynamic Programming | 20bits

biker — Tue, 23 Jun 2009 03:49:53 -0000

Superb tutorial..........nice one!!!!

Re: Introduction to Dynamic Programming | 20bits

Nilavalagan — Mon, 18 May 2009 00:39:21 -0000

Excellent..

Re: Introduction to Dynamic Programming | 20bits

james — Sun, 16 Nov 2008 02:55:45 -0000

you should make a function that returns the nth fibonacci number without using recursion.

Re: Introduction to Dynamic Programming | 20bits

SimonTewbi — Sat, 15 Nov 2008 17:33:00 -0000

Come to think of it, I think this might be cleaner:

def fib2(n):
n2, n1 = 0, 1
for i in range(n):
n2, n1 = n1, n1 + n2
return n2

Re: Introduction to Dynamic Programming | 20bits

SimonTewbi — Sat, 15 Nov 2008 17:10:22 -0000

Great article, thanks Jesse.

By the way, I believe your fib2 function is missing a line. It is incorrect for n=0. I think it should read:

def fib2(n):
if n == 0: return 0
n2, n1 = 0, 1
for i in range(n-2):
n2, n1 = n1, n1 + n2
return n2 + n1

Cheers
Simon

Re: Introduction to Dynamic Programming | 20bits

Jesse — Sat, 15 Nov 2008 16:53:52 -0000

offo,

Sorry for making you work so hard. Do you have any examples of good graphs?

Help me learn — don't just berate me.

Re: Introduction to Dynamic Programming | 20bits

offo foffo — Sat, 15 Nov 2008 16:25:04 -0000

Ok if I want to a view an image I don't want to see some stupid transition. Show me the goddamn image.

Second, your graphs are hard to read. Why does your graph use a gradient background? The change in contrast makes it difficult to read and gives really no benefit.

Also your graphs go against the norm, the label of the y axis is upside down. I don't care if it is your software or some designer jerk being a douchebag suggesting this is better...

IT ISN'T. I have to parse through 100s of chart a day in my day job and this kind of shit just pisses me off. I shouldn't have to fight with your eye-candy.

Re: Introduction to Dynamic Programming | 20bits

Metta — Sat, 18 Oct 2008 19:27:20 -0000

Great post - simple introduction to a complex algorithmic concept.

Regarding the knapsack problem, once the table is ready, the complexity is indeed only O(nW)
But building the table itself is of exponential cost in terms of running time, correct?
We go through every single possibility using recursion to build the table, and I think running time to build the table is n^m. It would be great if you could clarify.

Re: Introduction to Dynamic Programming | 20bits

Jesse — Sun, 12 Oct 2008 13:13:06 -0000

Horst,

Thanks. I wrote this like a year and a half ago — I'm surprised nobody has caught that yet.

Re: Introduction to Dynamic Programming | 20bits

Jesse — Sun, 12 Oct 2008 13:12:29 -0000

Jack,

I'm using a Ruby graphing library called Gruff.

Re: Introduction to Dynamic Programming | 20bits

draegtun — Sun, 12 Oct 2008 08:57:59 -0000

re: Memoization

Perl also has a module called Memoize and its been part of the core Perl library for some years now.

Here's an article about Memoization by the author of the above module.

/I3az/

PS. Nice article.

Re: Introduction to Dynamic Programming | 20bits

Jack — Sun, 12 Oct 2008 07:19:53 -0000

What tool did you used to create this figures (http://20bits.com/include/images/fib_performanc...

Re: Introduction to Dynamic Programming | 20bits

Horst — Sun, 12 Oct 2008 04:35:08 -0000

Great article, I would like to read more of these!

But it seems I'm the first one to actually try your function A(..), as it doesn't work:

>>> A([10, 20], [30, 40], 2, 10000)
Traceback (most recent call last):
File "", line 1, in
File "", line 3, in A
IndexError: list index out of range

You're mixing zero-based arrays (Python) and one-based arrays (your text), so the correct function A would look like this:

def A(w, v, i,j):
if i == 0 or j == 0: return 0
if w[i-1] > j: return A(w, v, i-1, j)
else: return max(A(w,v, i-1, j), v[i-1] + A(w,v, i-1, j - w[i-1]))

Cheers
Horst

Re: Introduction to Dynamic Programming | 20bits

John Mount — Sat, 11 Oct 2008 20:18:43 -0000

Nice introduction to dynamic programming. Some of your readers might enjoy the small article on the doing arithmetic using dynamic programming and how you can use it to bet on the world series: http://www.win-vector.com/dfiles/BestOf.pdf .

Re: Introduction to Dynamic Programming | 20bits

John — Wed, 24 Sep 2008 03:29:02 -0000

thank you, i enjoyed your article, but i do think you could clarify part of the maximal sum section. i had the same problem as EK because it's not made explicit in the description that when you change j, you don't change the bounds or s. (it's clear from the code, though).

specifically the phrase "if t+a[i] is negative set t = 0 and set the left-hand bound of the optimal subarray to i+1" should be revised, since actually the optimal subarray does not change; only the starting point of further consideration changes. (consider [1,2,-5,1,1,-2]: t goes negative but the optimal subarray remains at the front.)

Re: Introduction to Dynamic Programming | 20bits

Pratyush — Thu, 26 Jun 2008 14:48:30 -0000

Really very nicely written. So easy was this to understand. Thank you.

Re: Introduction to Dynamic Programming | 20bits

Trevor — Fri, 16 May 2008 18:44:37 -0000

Typo: overlappling

Re: Introduction to Dynamic Programming | 20bits

David — Fri, 16 May 2008 01:10:31 -0000

Nice explaination! Check out some more dynamic programming puzzles on fudge.
http://fudge.fit.edu/Problems/Archive

Re: Introduction to Dynamic Programming | 20bits

miriaim — Mon, 17 Mar 2008 10:26:13 -0000

please send me some characteristic of dynamic programming, multi stage decision process, max-min and min-max route all in dynamic programming to miriamudele4real@yahoo.co.uk

Re: Introduction to Dynamic Programming | 20bits

eatesh — Fri, 22 Feb 2008 15:04:42 -0000

good work man...[:)]
give some code implementation also...

Re: Introduction to Dynamic Programming | 20bits

Jesse — Tue, 22 Jan 2008 19:09:29 -0000

CT,

It's called Dean's Code Highlighter.

Re: Introduction to Dynamic Programming | 20bits

CT — Mon, 21 Jan 2008 15:08:42 -0000

Hey Jesse,

Great post. What wordpress plugin do you use to embed code in your posts?

Thanks

Re: Introduction to Dynamic Programming | 20bits

Mike — Sat, 23 Jun 2007 19:54:06 -0000

> If t + a[i] is negative, however, the contiguity constraint
> means that we cannot include a[j:i+1] in our subarray since
> any such subarray will have a smaller sum than a subarray without it.

What if all the numbers in the array are negative? I guess this is okay if the Maximum Subarray can be zero length.

If the subarray can't be zero length, do we have to go to a O(N^2) solution? Would it suffice to keep track of the largest single number?