[algogeeks] Re: Counting number of rectangles

2010-08-23 Thread Adam
Write here again:
I find an easier non-recursive solution to compute the rectangle
number (represented as RN) of an h x w rectangle (which has a height
of h units and a width of w units):

Situation 1:

If (h and w are coprime) or (h = 1) or (w = 1)

then RN = h + w - 1.

Situation 2:

If h and w are not relatively prime, we can find the greatest common
divisor (represented as gcd) that makes
(1) h = h' x gcd, w = w' x gcd
and
(2) (h' and w' are coprime) or (h' = 1) or (w' = 1),

then we finally get the result RN = (h' + w' - 1) x gcd.

This computation method will obviously help you find all the
rectangles with a given pair of height and width. It's pretty much
like a reverse problem.

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[algogeeks] Re: Counting number of rectangles

2010-08-23 Thread Adam
Write here again:
I find an easier non-recursive solution to compute the rectangle
number (represented as RN) of an h x w rectangle (which has a height
of h units and a width of w units):

Situation 1:

If (h and w are coprime) or (h = 1) or (w = 1)

then RN = h + w - 1.

Situation 2:

if h and w are not relatively prime, we can find the greatest common
divisor (represented as gcd) that makes
(1) h = h' x gcd, w = w' x gcd
and
(2) (h' and w' are coprime) or (h' = 1) or (w' = 1),

then we finally get the result RN = (h' + w' - 1) x gcd.

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[algogeeks] Re: Counting number of rectangles

2010-08-23 Thread Adam
I find an easier non-recursive solution to compute the rectangle
number (represented as RN) of an h x w rectangle (which has a height
of h units and a width of w units):

Situation 1. if (h and w are coprime) or (h = 1) or (w = 1), then RN =
h + w - 1

Situation 2. if h and w are not relatively prime, we can find the
greatest common divisor (represented as gcd) that makes
 (1) h = h' x gcd, w = w' x gcd.
 and
 (2) (h' and w' are coprime) or (h' = 1) or (w' = 1).
 then RN = (h' + w' - 1) x gcd



On Aug 23, 8:37 am, Nikhil Jindal  wrote:
> Here's my try:
>
> The following function returns the rectangle number given the dimensions of
> the rectangle.
>
> int FindRectangleNumber(int row, int colm)
> {
>  if (row == colm)
>   return row;
>  if (row == 1)
>   return colm;
>  if (row%2 == 0 && colm%2 == 0)
>   return 2*FindRectangleNumber(row/2, colm/2);
>  if (row%2 == 1 && colm%2 == 0)
>   return FindRectangleNumber(row - 1, colm) + 2;
>  if (row%2 == 0 && colm%2 == 1)
>   return FindRectangleNumber(row, colm - 1) + 2;
>  if (row%2 == 1 && colm%2 == 1)
>   return FindRectangleNumber(row - 1, colm-1) + 1;
>
> }
>
> This function can be used to solve the given problem.
>
> On Sun, Aug 22, 2010 at 3:29 PM, Saikat Debnath wrote:
>
>
>
> > Can anyone help in finding number of rectangles having a given
> > recatngle number. A rectangle number is defined as the number of unit
> > sided square formed inside the given rectangle having a common point
> > with a diagonal of rectangle. The sides of rectangle have integer
> > length. E.g. number of rectangle with rectangle number 4 is 4, i.e.
> > 1X4, 2X4, 2X3 and 4X4.
>
> > --
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[algogeeks] Re: linked list as tree

2010-08-23 Thread Adam
What do you exactly mean? You want to represent a linear structure by
using a tree structure?
You can imagine a linked list as a tree with all its root and inner
nodes only having one descendent/child node.

On Aug 23, 10:50 am, Raj N  wrote:
> What will be the representation. How do you define left and right pointers
> of the tree for a linked list.
>
> On Mon, Aug 23, 2010 at 10:35 PM, Yan Wang wrote:
>
> > Actually, a linear data structure like a linked list is also a
> > specific kind of tree structure.
>
> > 2010/8/23 Raj N :
> > > Hi,
> > > Could anyone help me representing linked list in the form a binary
> > > tree ?
>
> > > Thanks !!
>
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[algogeeks] Re: Sorting algorithm

2010-08-23 Thread RV
Dat's Inplace count sort

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Re: [algogeeks] linked list as tree

2010-08-23 Thread Raj N
What will be the representation. How do you define left and right pointers
of the tree for a linked list.

On Mon, Aug 23, 2010 at 10:35 PM, Yan Wang wrote:

> Actually, a linear data structure like a linked list is also a
> specific kind of tree structure.
>
> 2010/8/23 Raj N :
> > Hi,
> > Could anyone help me representing linked list in the form a binary
> > tree ?
> >
> > Thanks !!
> >
> > --
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> >
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Re: [algogeeks] Counting number of rectangles

2010-08-23 Thread Nikhil Jindal
Here's my try:

The following function returns the rectangle number given the dimensions of
the rectangle.

int FindRectangleNumber(int row, int colm)
{
 if (row == colm)
  return row;
 if (row == 1)
  return colm;
 if (row%2 == 0 && colm%2 == 0)
  return 2*FindRectangleNumber(row/2, colm/2);
 if (row%2 == 1 && colm%2 == 0)
  return FindRectangleNumber(row - 1, colm) + 2;
 if (row%2 == 0 && colm%2 == 1)
  return FindRectangleNumber(row, colm - 1) + 2;
 if (row%2 == 1 && colm%2 == 1)
  return FindRectangleNumber(row - 1, colm-1) + 1;
}

This function can be used to solve the given problem.


On Sun, Aug 22, 2010 at 3:29 PM, Saikat Debnath wrote:

> Can anyone help in finding number of rectangles having a given
> recatngle number. A rectangle number is defined as the number of unit
> sided square formed inside the given rectangle having a common point
> with a diagonal of rectangle. The sides of rectangle have integer
> length. E.g. number of rectangle with rectangle number 4 is 4, i.e.
> 1X4, 2X4, 2X3 and 4X4.
>
> --
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>
>

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Re: [algogeeks] Sorting algorithm

2010-08-23 Thread Raj N
@Tanveer: Count sort is not in place. uses extra memory

On Mon, Aug 23, 2010 at 4:32 PM, varun bhatia wrote:

> Who said count sort does not uses extra space???
>
> As faras I know, it does need extra space to need thr frequency of each and
> every element within a given range..
>
> Regards,
>
> Varun Bhatia
>
>
>
> On Mon, Aug 23, 2010 at 4:20 PM, Tanveer Asif wrote:
>
>> Count sort..
>>
>>
>> --
>> *From:* Subhranil Banerjee 
>> *To:* algogeeks@googlegroups.com
>> *Sent:* Mon, August 23, 2010 3:36:12 AM
>> *Subject:* [algogeeks] Sorting algorithm
>>
>> Can anyone suggest a sorting algorithm that sorts in linear time without
>> using extra space.
>>
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[algogeeks] Re: Sorting algorithm

2010-08-23 Thread Gene
Right.  If there is a O(n) sort that uses only constant space, I'd
love to hear about it.  Radix sort, bucket sort, counting sort all
need O(n) space.



On Aug 23, 7:02 am, varun bhatia  wrote:
> Who said count sort does not uses extra space???
>
> As faras I know, it does need extra space to need thr frequency of each and
> every element within a given range..
>
> Regards,
>
> Varun Bhatia
>
> On Mon, Aug 23, 2010 at 4:20 PM, Tanveer Asif wrote:
>
>
>
> > Count sort..
>
> > --
> > *From:* Subhranil Banerjee 
> > *To:* algogeeks@googlegroups.com
> > *Sent:* Mon, August 23, 2010 3:36:12 AM
> > *Subject:* [algogeeks] Sorting algorithm
>
> > Can anyone suggest a sorting algorithm that sorts in linear time without
> > using extra space.
>
> > --
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> >http://groups.google.com/group/algogeeks?hl=en.- Hide quoted text -
>
> - Show quoted text -

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Re: [algogeeks] linked list as tree

2010-08-23 Thread Yan Wang
Actually, a linear data structure like a linked list is also a
specific kind of tree structure.

2010/8/23 Raj N :
> Hi,
> Could anyone help me representing linked list in the form a binary
> tree ?
>
> Thanks !!
>
> --
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>
>

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[algogeeks] Re: 5 pirate problem

2010-08-23 Thread Dave
This is not a computer problem. Think about it backwards.

If there are only 2 pirates left, then the elder can claim all 100
coins, at worst the vote will be tied, and so he survives and takes
100 coins.

If there are 3 pirates left, then the oldest can claim 99 coins and
give the youngest 1 coin, with the second oldest pirate getting
nothing. Since the youngest gets more than he would if he voted no, he
will vote yes with the oldest, so the oldest survives and takes 99
coins.

If there are 4 pirates left, then the oldest can claim 99 coins and
give the third oldest 1 coin, with the second oldest and youngest
getting nothing. The third oldest vote yes because he gets more than
if he voted no, so the vote is at least tied, so the oldest survives
and takes 99 coins.

At the beginning, with all 5 pirates, the oldest can claim 98 coins
and give the third oldest and the youngest 1 coin each. They will vote
with him because they will get more than if they voted no, so the
oldest pirate survives and takes 98 coins.

Dave

On Aug 22, 10:36 pm, hari  wrote:
> Five  pirates (of different ages) have 100 gold coins to divide
> amongst themselves. They decide on the following approach to determine
> how much each pirate receives:
>
> The eldest pirate proposes an allocation. All pirates (including the
> eldest) then vote on the proposal. If the majority accept the proposal
> then the coins are divided in the way suggested. If not, then the
> eldest pirate is executed and the new eldest amongst the remaining
> pirates proposes a new allocation. If the votes are tied then this is
> enough for the proposal to be accepted.
>
> Assuming that the pirates are motivated primarily by survival, then to
> a lesser extent by greed and finally to the least extent by sadism
> (i.e. they'd prefer to receive a gold coin and see someone get
> executed than just receive one coin earlier, but would prefer one coin
> to none and an execution; and obviously would prefer 0 coins and
> surviving to 100 coins and being executed), and act in a logical way,
> what is the maximum number of coins the eldest pirate can get?
>
> please provide a source code
>
> thanks in advance

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Re: [algogeeks] Re: To sort an array of 0,1,2

2010-08-23 Thread Manjunath Manohar
@sathiah..i can get u ..but dont seem to understand the part where in we
must keep track of the 1's...can u pls post the code..

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[algogeeks] Re: To sort an array of 0,1,2

2010-08-23 Thread luckyzoner
You can refer to this sample code i had tried to sort in a single
pass:

#include
#include

using namespace std;

int main()
{
int a = 0, b=1, c=9;

int s[10]= { 2,1,0,1,1,0,2,1,0,1};

while(ab)
  c--;

 if(!(a>=b) && !(b>=c))
  {
if(s[b]==0)
 {
  s[b]=s[a];
  s[a]=0;
 }

   if(s[b]==2)
{
s[b]=s[c];
 s[c]=2;
 }
}

  for(int i = 0; i<10; i++)
  {
  cout

Re: [algogeeks] Re: BST Problem

2010-08-23 Thread TurksHead Education
I am not sure if I am repeating the answer:

The problem will reduce to find the pair of elements which will sum up to a
particular number. Then read the below article,

http://www.rawkam.com/?p=345



On Mon, Aug 23, 2010 at 9:29 AM, R.ARAVINDH  wrote:

> @giri:
>
> can u post d correct answer??
>
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Re: [algogeeks] Sorting algorithm

2010-08-23 Thread TurksHead Education
Comparison Sort Algorithms cannot sort in linear time(
http://www.rawkam.com/?p=886) so we have to use some non-comparison sorting
algorithm like Counting Sort,Bucket Sort, Radix Sort etc.

But all the non-comparison sort algorithms requires the input to be in a
particular order. (For example: Counting Sort will not be a good option if
range of numbers is high.

On Mon, Aug 23, 2010 at 4:20 PM, Tanveer Asif wrote:

> Count sort..
>
>
> --
> *From:* Subhranil Banerjee 
> *To:* algogeeks@googlegroups.com
> *Sent:* Mon, August 23, 2010 3:36:12 AM
> *Subject:* [algogeeks] Sorting algorithm
>
> Can anyone suggest a sorting algorithm that sorts in linear time without
> using extra space.
>
> --
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Re: [algogeeks] Re: To sort an array of 0,1,2

2010-08-23 Thread Sathaiah Dontula
Yes, it is possible in one pass without extra memory, I think this is a CLRS
exercise problem.

It is possible in one pass without using extra memory.

Keep the 0's at left and 2's at right and scan the middle portion from left
to right and if you see 0 keep at left side and if you see 2 keep it right
side, what is left in the middle is the 1's. Keep track of 1's the tricky
part and have a index at start of 1's.

I think it is possible, I have a tested code, I will post, but you can try
once.



Thanks,
Sathaiah Dontula




On Mon, Aug 23, 2010 at 12:10 PM, Manjunath Manohar <
manjunath.n...@gmail.com> wrote:

> is it possible to do without any extra space...
>
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Re: [algogeeks] Sorting algorithm

2010-08-23 Thread varun bhatia
Who said count sort does not uses extra space???

As faras I know, it does need extra space to need thr frequency of each and
every element within a given range..

Regards,

Varun Bhatia



On Mon, Aug 23, 2010 at 4:20 PM, Tanveer Asif wrote:

> Count sort..
>
>
> --
> *From:* Subhranil Banerjee 
> *To:* algogeeks@googlegroups.com
> *Sent:* Mon, August 23, 2010 3:36:12 AM
> *Subject:* [algogeeks] Sorting algorithm
>
> Can anyone suggest a sorting algorithm that sorts in linear time without
> using extra space.
>
> --
> You received this message because you are subscribed to the Google Groups
> "Algorithm Geeks" group.
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Re: [algogeeks] Re: BST Problem

2010-08-23 Thread Raj N
Perform inorder traversal and store in an array.
low = 0, high = size-1

while(low<=high)
{
if ( a[low] + a[high] < sum)
low++;
else if (a[low] + a[high] > sum)
high--;
else
return a[high] and [low]
}
On Mon, Aug 23, 2010 at 9:29 AM, R.ARAVINDH  wrote:

> @giri:
>
> can u post d correct answer??
>
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Re: [algogeeks] Re: To sort an array of 0,1,2

2010-08-23 Thread Raj N
Refer Dutch National Flag Algorithm

On Mon, Aug 23, 2010 at 12:10 PM, Manjunath Manohar <
manjunath.n...@gmail.com> wrote:

> is it possible to do without any extra space...
>
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[algogeeks] linked list as tree

2010-08-23 Thread Raj N
Hi,
Could anyone help me representing linked list in the form a binary
tree ?

Thanks !!

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Re: [algogeeks] Re: To sort an array of 0,1,2

2010-08-23 Thread TurksHead Education
I think the first 3 methods of the total 4 specified at

http://www.rawkam.com/?p=168

will be applicable for sorting arrays with 0,1 &2

On Mon, Aug 23, 2010 at 11:07 AM, Jameel Mohamed
wrote:

> Use counting sort. time complexity is O(n)
>
> On Aug 22, 1:11 pm, AlgoBoy  wrote:
> > An algorithm to sort an array of 0's,1's,2's in a single pass...
>
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Re: [algogeeks] Re: To sort an array of 0,1,2

2010-08-23 Thread Kumar Vishal
yes we can
 a possible solution what i can think is
treat 1&2 (same entity )
and 0 as other so in first pass we will short array which will have (all
zeros first , then 1&2 in some random order )
take index number of zero then in second pass short for 1 & 2

still O(n) but takes 2 pass



On Mon, Aug 23, 2010 at 12:10 PM, Manjunath Manohar <
manjunath.n...@gmail.com> wrote:

> is it possible to do without any extra space...
>
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-- 
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Contact No:- 09560193839

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[algogeeks] 5 pirate problem

2010-08-23 Thread hari
Five  pirates (of different ages) have 100 gold coins to divide
amongst themselves. They decide on the following approach to determine
how much each pirate receives:

The eldest pirate proposes an allocation. All pirates (including the
eldest) then vote on the proposal. If the majority accept the proposal
then the coins are divided in the way suggested. If not, then the
eldest pirate is executed and the new eldest amongst the remaining
pirates proposes a new allocation. If the votes are tied then this is
enough for the proposal to be accepted.

Assuming that the pirates are motivated primarily by survival, then to
a lesser extent by greed and finally to the least extent by sadism
(i.e. they'd prefer to receive a gold coin and see someone get
executed than just receive one coin earlier, but would prefer one coin
to none and an execution; and obviously would prefer 0 coins and
surviving to 100 coins and being executed), and act in a logical way,
what is the maximum number of coins the eldest pirate can get?


please provide a source code

thanks in advance

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[algogeeks] Re: Sorting algorithm

2010-08-23 Thread Chi
Time is measured in O(n^2) where n is the size of the string.
Quicksort can do in O(n * log(n)) but it uses extra spaces on the
stack, as most sorting method using recursion.

On Aug 23, 12:36 pm, Subhranil Banerjee  wrote:
> Can anyone suggest a sorting algorithm that sorts in linear time without
> using extra space.

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Re: [algogeeks] Sorting algorithm

2010-08-23 Thread Tanveer Asif
Count sort..






From: Subhranil Banerjee 
To: algogeeks@googlegroups.com
Sent: Mon, August 23, 2010 3:36:12 AM
Subject: [algogeeks] Sorting algorithm

Can anyone suggest a sorting algorithm that sorts in linear time without using 
extra space. 

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[algogeeks] Sorting algorithm

2010-08-23 Thread Subhranil Banerjee
Can anyone suggest a sorting algorithm that sorts in linear time without
using extra space.

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Re: [algogeeks] Re: Longest Palindromic Substring

2010-08-23 Thread Chi Hoang
I don't think so, I've have wriiten a kart-trie:
http://sourceforge.net/projects/kart-trie which is basically a patricia-tree
or radix-tree. Such a tree has maximum 2 leafs at each branch whilst a
suffix-tree can has more then 2 leafs at each branch (BTW. can you explain
to me what does edge means when talking about trees?). This is my
understanding of a suffix-tree so far. I'm awaiting your anwser!
2010/8/21 Chonku 

> You use a trie when you want to model a number of strings. Suffix Tree is
> used only when you have one string in your model. Suffix Tree is a type of
> trie, but the difference lies in the intent.
>
>
> On Sat, Aug 21, 2010 at 7:22 PM, Chi  wrote:
>
>> Isn't that by definition a compressed trie, i.e patricia-tree, crit-
>> bit tree (suffix-tree)? Or what is the difference?
>>
>> On Aug 20, 5:17 pm, Nikhil Jindal  wrote:
>> > @chonku
>> > As i understand, a trie is used when we have a lot of strings (such as a
>> > dictionary).
>> > Here we just have a single string. The resultant trie will be:
>> >
>> > a
>> >  \
>> >   b
>> >\
>> > c
>> >  \
>> >   l
>> >\
>> > e
>> >  \
>> >   v
>> >\
>> > e
>> >  \
>> >   l
>> >\
>> > a
>> >  \
>> >   b
>> >\
>> > c
>> >
>> > We get a similar trie for the reverse string.
>> >
>> > So why are you using a trie here? I cant see any advantage of it here.
>> >
>> >
>> >
>> >
>> >
>> > On Fri, Aug 20, 2010 at 8:36 AM, Chonku  wrote:
>> > > Can we use a trie here.
>> > > Make first pass from left to right and construct the trie.
>> > > Make second pass from right to left and look for the trie branch with
>> > > maximum nodes that match the characters.
>> >
>> > > On Thu, Aug 19, 2010 at 7:46 PM, Nikhil Jindal <
>> fundoon...@yahoo.co.in>wrote:
>> >
>> > >> Hi All,
>> >
>> > >> Givan a string, you have to find the longest palindromic substring.
>> > >> For ex: Longest Palindromic substring for abclevelabc is level.
>> >
>> > >> What is the most optimised solution possible?
>> >
>> > >> Please access the attached hyperlink for an important electronic
>> communications disclaimer:
>> http://dce.edu/web/Sections/Standalone/Email_Disclaimer.php
>> >
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Re: [algogeeks] Permutation of Array.

2010-08-23 Thread BALARUKESH SIVARAMAN
now its clear.. thank you..

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