# Need help in understanding a python code

Discussion in 'Python' started by silverburgh.meryl@gmail.com, Nov 16, 2008.

1. ### Guest

Hi,

I am trying to understand the following line:
# a is an integer array

max([(sum(a[j:i]), (j,i))

Can you please tell me what that means,
I think sum(a[j:i] means find the some from a[j] to a
But what is the meaning of the part (j,i)?

, Nov 16, 2008

2. ### Chris RebertGuest

On Sat, Nov 15, 2008 at 8:41 PM,
<> wrote:
> Hi,
>
> I am trying to understand the following line:
> # a is an integer array
>
> max([(sum(a[j:i]), (j,i))

This code isn't valid. You have a [ with no closing ].

Cheers,
Chris
--
Follow the path of the Iguana...
http://rebertia.com

>
> Can you please tell me what that means,
> I think sum(a[j:i] means find the some from a[j] to a
> But what is the meaning of the part (j,i)?
>
> --
> http://mail.python.org/mailman/listinfo/python-list
>

Chris Rebert, Nov 16, 2008

3. ### John MachinGuest

On Nov 16, 3:41 pm, ""
<> wrote:
> Hi,
>
> I am trying to understand the following line:
> # a is an integer array
>
> max([(sum(a[j:i]), (j,i))
>
> Can you please tell me what that means,
> I think sum(a[j:i] means find the some from a[j] to a
> But what is the meaning of the part (j,i)?

0. "integer array" is a very loose term in Python. Fortunately the
1. Sorry, the max... line is not syntactically correct; there are two
[s and only one ]; there are 4 (s and only 3 )s. Try copying the line
and pasting, not re-typing.
2. I'm not going to try to guess how to fix the bracket mismatches.
3. Note that you have left off a ) from your question about "sum" ...
it probably should be sum([j:i]).
4. That is the sum (not "some"!!) of a[j] to a[i-1] both inclusive.
It's a standard idiom in Python for the end of a range to be expressed
as the first unused element.
5. Even after fixing the bracket mismatches, it looks like you will
have an expression whose value is thrown away. Perhaps you might like
to give us a few lines of context before and after the line of
interest.

John Machin, Nov 16, 2008
4. ### Meryl SilverburghGuest

This is the full source code:
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)
if w[i-1] <= j: return max(A(w,v, i-1, j), v[i-1] + A(w,v, i-1, j - w[i-1]))

http://20bits.com/articles/introduction-to-dynamic-programming/

On Sat, Nov 15, 2008 at 10:54 PM, Chris Rebert <> wrote:
> On Sat, Nov 15, 2008 at 8:41 PM,
> <> wrote:
>> Hi,
>>
>> I am trying to understand the following line:
>> # a is an integer array
>>
>> max([(sum(a[j:i]), (j,i))

>
> This code isn't valid. You have a [ with no closing ].
>
> Cheers,
> Chris
> --
> Follow the path of the Iguana...
> http://rebertia.com
>
>>
>> Can you please tell me what that means,
>> I think sum(a[j:i] means find the some from a[j] to a
>> But what is the meaning of the part (j,i)?
>>
>> --
>> http://mail.python.org/mailman/listinfo/python-list
>>

>

Meryl Silverburgh, Nov 16, 2008

See below.

On Nov 15, 11:15 pm, "Meryl Silverburgh" <>
wrote:
> This is the full source code:
> 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)
>     if w[i-1] <= j: return max(A(w,v, i-1, j), v[i-1] + A(w,v, i-1, j - w[i-1]))
>
> I am reading this blog
>
> http://20bits.com/articles/introduction-to-dynamic-programming/
>
> On Sat, Nov 15, 2008 at 10:54 PM, Chris Rebert <> wrote:
> > On Sat, Nov 15, 2008 at 8:41 PM,
> > <> wrote:
> >> Hi,

>
> >> I am trying to understand the following line:
> >> # a is an integer array

>
> >> max([(sum(a[j:i]), (j,i))

>
> > This code isn't valid. You have a [ with no closing ].

>
> > Cheers,
> > Chris
> > --
> > Follow the path of the Iguana...
> >http://rebertia.com

>
> >> Can you please tell me what that means,
> >> I think sum(a[j:i] means find the some from a[j] to a
> >> But what is the meaning of the part (j,i)?

>
>
>

> if w[i-1] <= j: return max(A(w,v, i-1, j), v[i-1] + A(w,v, i-1, j - w[i-1]))

This means:

Calculate 'A(w,v, i-1, j)', calculate 'v[i-1] + A(w,v, i-1, j - w
[i-1])', and return whichever is larger.

6. ### Guest

silverburgh:
> max([(sum(a[j:i]), (j,i))

today the max() function has a key optional attribute, so that code
can also be written as:

max(((j, i) for ...), key=lambda (j, i): sum(a[j : i]))

I think you have copied that part from code that runs in O(n^2);
remember that you can find the max subarray with a well known O(n)
algorithm too.

Bye,
bearophile

, Nov 16, 2008
7. ### John MachinGuest

On Nov 16, 4:15 pm, "Meryl Silverburgh" <>
wrote:
> This is the full source code:
> 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)
>     if w[i-1] <= j: return max(A(w,v, i-1, j), v[i-1] + A(w,v, i-1, j - w[i-1]))

Huh??? There is only a very slight resemblance to the code that you
posted previously ... both contain 'max, 'i', and 'j'

> I am reading this blog
>
> http://20bits.com/articles/introduction-to-dynamic-programming/

I suggest that you don't bother reading a blog written by somebody who
(presumably consciously) keyed in that "if w[i-1] <= j: " above.

Oh, very interesting, it contains:
def msum(a):
return max([(sum(a[j:i]), (j,i)) for i in range(1,len(a)+1) for j
in range(i)])

Would you care to tell us which part of which function you are now
trying to understand?

John Machin, Nov 16, 2008
8. ### Steven D'ApranoGuest

On Sun, 16 Nov 2008 01:50:16 -0800, John Machin wrote:

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

>> I am reading this blog
>>
>> http://20bits.com/articles/introduction-to-dynamic-programming/

>
> I suggest that you don't bother reading a blog written by somebody who
> (presumably consciously) keyed in that "if w[i-1] <= j: " above.

That is a translation of standard terminology for a hybrid function.
Mathematics doesn't have an "else", so you write hybrid functions by
enumerating each branch as an if.

While it's not especially good Python technique, it's a perfectly
idiomatic mathematical expression, and shouldn't be the basis for
dismissing an entire blog.

--
Steven

Steven D'Aprano, Nov 16, 2008
9. ### John MachinGuest

On Nov 16, 9:31 pm, Steven D'Aprano <st...@REMOVE-THIS-
cybersource.com.au> wrote:
> On Sun, 16 Nov 2008 01:50:16 -0800, John Machin wrote:
> > > 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)
> > >     if w[i-1] <= j: return max(A(w,v, i-1, j), v[i-1] +
> > >       A(w,v, i-1, j - w[i-1]))
> >> I am reading this blog

>
>
> > I suggest that you don't bother reading a blog written by somebody who
> > (presumably consciously) keyed in that "if w[i-1] <= j: " above.

>
> That is a translation of standard terminology for a hybrid function.
> Mathematics doesn't have an "else", so you write hybrid functions by
> enumerating each branch as an if.

An else is not required.
if w[i-1] > j:
return A(w, v, i-1, j)
return max(A(w,v, i-1, j), v[i-1] + A(w,v, i-1, j - w[i-1]))

> While it's not especially good Python technique, it's a perfectly
> idiomatic mathematical expression, and shouldn't be the basis for
> dismissing an entire blog.

He's meant to be writing Python code, not mathematical expressions.

John Machin, Nov 16, 2008
10. ### Steven D'ApranoGuest

On Sun, 16 Nov 2008 02:41:03 -0800, John Machin wrote:

> On Nov 16, 9:31Â pm, Steven D'Aprano <st...@REMOVE-THIS-
> cybersource.com.au> wrote:
>> On Sun, 16 Nov 2008 01:50:16 -0800, John Machin wrote:
>> > > def A(w, v, i,j):
>> > > Â  Â  if i == 0 or j == 0: return 0
>> > > Â  Â  if w[i-1] > j: Â return A(w, v, i-1, j) if w[i-1] <= j: return
>> > > Â  Â  max(A(w,v, i-1, j), v[i-1] +
>> > > Â  Â  Â  A(w,v, i-1, j - w[i-1]))
>> >> I am reading this blog

>>
>>
>> > I suggest that you don't bother reading a blog written by somebody
>> > who (presumably consciously) keyed in that "if w[i-1] <= j: " above.

>>
>> That is a translation of standard terminology for a hybrid function.
>> Mathematics doesn't have an "else", so you write hybrid functions by
>> enumerating each branch as an if.

>
> An else is not required.
> if w[i-1] > j:
> return A(w, v, i-1, j)
> return max(A(w,v, i-1, j), v[i-1] + A(w,v, i-1, j - w[i-1]))

Which is also not valid terminology for hybrid functions.

>> While it's not especially good Python technique, it's a perfectly
>> idiomatic mathematical expression, and shouldn't be the basis for
>> dismissing an entire blog.

>
> He's meant to be writing Python code, not mathematical expressions.

And he's written Python code. Perfectly valid Python code. Just because
it is not what you consider to be idiomatic Python code isn't a good
reason to dismiss his entire blog.

What you've done is rather like me saying that because you failed to use
a colon after "required", and therefore haven't written what *I* consider
good English style, not only is your specific post best avoided, but
*all* your posts should be avoided. I trust you understand the logical

http://en.wikipedia.org/wiki/Style_over_substance_fallacy

--
Steven
and now begins the arguments as to whether it is a fallacy, and if so, if
it is the fallacy I have said it is...

Steven D'Aprano, Nov 16, 2008
11. ### John MachinGuest

On Nov 16, 11:04 pm, Steven D'Aprano <st...@REMOVE-THIS-
cybersource.com.au> wrote:
> On Sun, 16 Nov 2008 02:41:03 -0800, John Machin wrote:
> > On Nov 16, 9:31 pm, Steven D'Aprano <st...@REMOVE-THIS-
> > cybersource.com.au> wrote:
> >> On Sun, 16 Nov 2008 01:50:16 -0800, John Machin wrote:
> >> > > 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) if w[i-1] <= j: return
> >> > >     max(A(w,v, i-1, j), v[i-1] +
> >> > >       A(w,v, i-1, j - w[i-1]))
> >> >> I am reading this blog

>
>
> >> > I suggest that you don't bother reading a blog written by somebody
> >> > who (presumably consciously) keyed in that "if w[i-1] <= j: " above.

>
> >> That is a translation of standard terminology for a hybrid function.
> >> Mathematics doesn't have an "else", so you write hybrid functions by
> >> enumerating each branch as an if.

>
> > An else is not required.
> >     if w[i-1] > j:
> >        return A(w, v, i-1, j)
> >     return max(A(w,v, i-1, j), v[i-1] + A(w,v, i-1, j - w[i-1]))

>
> Which is also not valid terminology for hybrid functions.

I couldn't care less. It's valid and efficient (compared to the
original) Python.

> >> While it's not especially good Python technique, it's a perfectly
> >> idiomatic mathematical expression, and shouldn't be the basis for
> >> dismissing an entire blog.

>
> > He's meant to be writing Python code, not mathematical expressions.

>
> And he's written Python code. Perfectly valid Python code. Just because
> it is not what you consider to be idiomatic Python code isn't a good
> reason to dismiss his entire blog.
>
> What you've done is rather like me saying that because you failed to use
> a colon after "required", and therefore haven't written what *I* consider
> good English style, not only is your specific post best avoided, but
> *all* your posts should be avoided. I trust you understand the logical

Nothing to do with style. It was the screaming inefficiency of:
if non_trivial_condition: return x
if not non_trivial_condition: return y
that fired me up.

Quoted Wikipedia -> instant disqualification -> you lose. Good night.

John Machin, Nov 16, 2008
12. ### George SakkisGuest

On Nov 16, 7:34 am, John Machin <> wrote:
> On Nov 16, 11:04 pm, Steven D'Aprano <st...@REMOVE-THIS-
>
>
> Quoted Wikipedia -> instant disqualification -> you lose. Good night.

When quoting wikipedia became the new Godwin's law ??

George

George Sakkis, Nov 16, 2008
13. ### alex23Guest

On Nov 17, 5:26 am, George Sakkis <> wrote:
> When quoting wikipedia became the new Godwin's law ??

Probably at the point the editors started becoming revisionists and
culling anything they didn't consider notable enough.

alex23, Nov 17, 2008
14. ### Matt NordhoffGuest

Benjamin Kaplan wrote:
> If you really believe that, you haven't been following this list long
> enough. Every terminology dispute always includes at least 1 Wikipedia
>
> Also, you might want to look at this study:
> http://news.cnet.com/2100-1038_3-5997332.html

That study has been disputed; see the links at the top of
<http://en.wikipedia.org/wiki/Reliability_of_Wikipedia>.

/me ducks
--

Matt Nordhoff, Nov 17, 2008
15. ### alex23Guest

On Nov 17, 11:40 am, Matt Nordhoff <> wrote:
> That study has been disputed; see the links at the top of
> <http://en.wikipedia.org/wiki/Reliability_of_Wikipedia>.

Now, if there was any independent refutation of the original study
that isn't based on Britannica's - not that I'm outright accusing them
of any bias here - that might make a reasonable disputation...

alex23, Nov 17, 2008
16. ### Steven D'ApranoGuest

On Sun, 16 Nov 2008 04:34:40 -0800, John Machin wrote:

> Nothing to do with style. It was the screaming inefficiency of:
> if non_trivial_condition: return x
> if not non_trivial_condition: return y
> that fired me up.

"Screaming inefficiency"?

Try "micro-optimization". The difference in execution time between "if
x... if not x..." versus "if x... else..." on my slow, underpowered
inefficiency" I can't understand why you're programming in Python in the
first place.

Of course, if x is an expensive function call (say, a network lookup or
database query rather than a relatively cheap list indexing operation)
then the more readable, Pythonic solution will also be significantly
faster. There's no doubt that it should be preferred -- I'm not defending
it, as such, just pointing out the over-reaction of dismissing what is a
generally well-written and thought-out article on the basis of a
triviality.

>
> Quoted Wikipedia -> instant disqualification -> you lose. Good night.

Oh gosh, well, you've certainly proven your case, how could I be so
stupid? My apology for thinking that you were acting like an arrogant,
bad-tempered dick. I don't know *what* I was thinking.

--
Steven
who would link to Wikipedia for the definition of sarcasm except I've