20bits - Latest Comments in Introduction to Dynamic Programming

Re: Introduction to Dynamic Programming

Jeremy Wilson — Wed, 08 Jun 2011 12:58:05 -0000

> What if all the numbers in the array are negative?

Then the "largest subarray with the maximum sum" will be an array containing just the single "largest" number (i.e. closest to zero). e.g. in the array [-5,-6,-2,-3] the result would be [-2], because it is the largest, and adding anything more to it would make it smaller (more negative). I think his python code works correctly for this case.

Re: Introduction to Dynamic Programming

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Re: Introduction to Dynamic Programming

Rajranimehra — Tue, 08 Feb 2011 19:57:43 -0000

its good but explain it with some example

Re: Introduction to Dynamic Programming

Hugo A M Torres — Tue, 08 Feb 2011 01:37:43 -0000

Hi. How could I retrieve the combination of items used to produce the optimal solution to the knapsack problem?

Re: Introduction to Dynamic Programming

chad salvador — Tue, 30 Nov 2010 03:43:30 -0000

is there a ydynamic member in variable if there please give me one

Re: Introduction to Dynamic Programming

Amdkfgi — Sun, 28 Nov 2010 14:33:35 -0000

its the tree between my legs, consist of a big banana and two eggs

Re: Introduction to Dynamic Programming

Sarthakgovind — Wed, 27 Oct 2010 08:51:13 -0000

what is definition of optimal binary search tree and its algorithm described?

Re: Introduction to Dynamic Programming

vivek — Wed, 12 May 2010 11:10:26 -0000

thanks..it helped a lot

Re: Introduction to Dynamic Programming

Nelson — Sun, 04 Apr 2010 00:02:47 -0000

Again thanks, just thought I might add though that my only feedback would be perhaps writing the example code in a more readable rather than compact way could help. e.g.
for i in range(len(a)):
t = t + a[i]
if t > s:
bounds = (j, i+1)
s = t
if t < 0:
t = 0
j = i+1
return (s, bounds)

Re: Introduction to Dynamic Programming

Nelson — Sat, 03 Apr 2010 23:33:06 -0000

Buddy quit whining over free lollies. This guy's giving helpful information out for free, if you don't like it then tough. Eat a dick or something.
By the way thanks for the info jesse, I'm trying to get my head around dynamic programming and I appreciate the help.

Re: Introduction to Dynamic Programming

swapneelpatil — Fri, 05 Mar 2010 14:15:25 -0000

I always tend to go for recursive functions, as they are easy to debug

# s: new number in the seq
# s_1: the prev number in the sequence
# i : iterator, which can be eliminated
# if implemented as a local function (like Scheme)
def fibo(n, i=1, s=1, s_1=0):
if n <= i: return s
else: return fibo(n, i+1, s+s_1, s)

print (fibo(10))

Re: Introduction to Dynamic Programming

Jesse Farmer — Fri, 05 Feb 2010 22:03:08 -0000

Dynamic Programming is a type of D&C algorithm, but it relies on the existence of overlapping subproblems.

Re: Introduction to Dynamic Programming

disqus_NfQ8E9Byln — Fri, 05 Feb 2010 07:30:45 -0000

What is the basic difference between Divide-and-Conquer Technique and Dynamic Programming??

Re: Introduction to Dynamic Programming

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

great post,

Re: Introduction to Dynamic Programming

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

Nice work. Keep it up.....

Re: Introduction to Dynamic Programming

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

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

Re: Introduction to Dynamic Programming

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

Excellent..

Re: Introduction to Dynamic Programming

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

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

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

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

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

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

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

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

Jack,

I'm using a Ruby graphing library called Gruff.