Re: [algogeeks] Amazon Question - Find Pythagorean triplet in an unsorted array

[ravindra patel]

@Anshu
looks interesting. A few things -

>> To check the particular number square can be written as sum of two
squares or not. If it has any prime factor x such that x % 4 == 1 then only.
 - What would be the complexity of finding prime factors. Did you factor
in it in overall complexity.
 - "if it has any prime factor x such that x % 4 == 1 then only", this
looks interesting. how did you figire this out? Is there a theorem of this
sort?

>> so time complexity will reduce to O(n * (number of side which can be
largest one for any triplet) ).
   unfortunately, in terms of complexity it will still be O(n*n) because
there is no predictive way to find how many elements can be discarded with
above criteria. In fact in the worst case each element may satisfy the prime
factor (with modulo 4 = 1) condition. That said, I agree that it definitely
reduces the average running time.

Thanks,
- Ravindra

On Thu, Oct 20, 2011 at 3:38 PM, anshu mishra wrote:

> @Ravindra
>
> To check the particular number square can be written as sum of two squares
> or not.
>
> If it has any prime factor x such that x % 4 == 1 then only.
>
> Now about time complexity.
>
> suppose u have given array is.
>
> 10 6 13 9 17 4 18 12 1 5.
>
> now u can easily skip the numbers(1, 4, 6, 9, 12, 18);
>
>
> and u have to check only for these numbers(5, 10, 13, 17);
>
> so time complexity will reduce to O(n * (number of side which can be
> largest one for any triplet) ).
>
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Re: [algogeeks] Amazon Question - Find Pythagorean triplet in an unsorted array

[anshu mishra]

@Ravindra

To check the particular number square can be written as sum of two squares
or not.

If it has any prime factor x such that x % 4 == 1 then only.

Now about time complexity.

suppose u have given array is.

10 6 13 9 17 4 18 12 1 5.

now u can easily skip the numbers(1, 4, 6, 9, 12, 18);


and u have to check only for these numbers(5, 10, 13, 17);

so time complexity will reduce to O(n * (number of side which can be largest
one for any triplet) ).

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Re: [algogeeks] Amazon Question - Find Pythagorean triplet in an unsorted array

[sravanreddy001]

Sorry.. 
this is good one, 
but works for consecutive numbers only from 1..N

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Re: [algogeeks] Amazon Question - Find Pythagorean triplet in an unsorted array

[ravindra patel]

@Anshu

>> first check that particular number can be written as the sum of two
squares or not
What would be the way to figure it out.

>> O(n * (number of side which is largest one for any triplet))
Didn't get it.

Thanks,
- Ravindra

On Wed, Oct 19, 2011 at 11:09 AM, anshu mishra wrote:

> @Ravindra
> may be the interviewer wants from u that instead of blindly checking for
> every number. first check that particular number can be written as the sum
> of two squares or not if yes than only search for that number. So the order
> will be decrease from O(n^2) to O(n * (number of side which is largest one
> for any triplet)) and in practical it will be much less compare to O(n^2);
>
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Re: [algogeeks] Amazon Question - Find Pythagorean triplet in an unsorted array

[anshu mishra]

@Ravindra
may be the interviewer wants from u that instead of blindly checking for
every number. first check that particular number can be written as the sum
of two squares or not if yes than only search for that number. So the order
will be decrease from O(n^2) to O(n * (number of side which is largest one
for any triplet)) and in practical it will be much less compare to O(n^2);

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Re: [algogeeks] Amazon Question - Find Pythagorean triplet in an unsorted array

[Ankur Garg]

@Shashank ..+1 ..I wud say he must be given a tuning award :D :D  for
solving such eternal conundrum ;)



On Mon, Oct 17, 2011 at 2:37 PM, WgpShashank wrote:

> @wladimir , its PPT (Pythagoras triplets ) but its number theory based
> approach  http://en.wikipedia.org/wiki/Pythagorean_triple might not be
> good idea
>
> Here is approach :
> *
> *
> *Euclid's 
> formula*[1] is
> a fundamental formula for generating Pythagorean triples given an arbitrary
> pair of positive integers *m* and *n* with *m* > *n*. The formula states
> that the integers p=m^2-n^2 , q=2mn r=m^2+n^2  , we have to sort the array
> in non-increasing order  , then for each m>n we have to generate the  all
> such p,q,r in worst case it will also requires O(N^2) such p,q,r for each
> M>N isn't it ? then its not less then O(n^2) ??
> Even with this approach,The triple generated by Euclid's formula is
> primitive if and only if *m* and *n* are coprime and *m*-*n* is odd. If
> both *m* and *n* are odd, then *a*, *b*, and *c* will be even, and so the
> triple will not be primitive; however, dividing *a*, *b*, and *c* by 2
> will yield a primitive triple if *m* and *n* are coprime.
>
> @all other , its similar to 3 sun , can't be done in less then O(N^2) if
> number are not in range , When the integers are in the range [-*u* ... *u*],
> 3SUM can be solved in time O(n + *u* lg *u*) by representing *S* as a bit
> vector and performing a discrete convolution using FFT.
>
> i wondered if any other  algo/code/link you have which works in less then
> O(N^2) , Better if One Explain The Approach or Algorithm , You Might able to
> fill Patent :D
>
> Thanks
> Shashank
> CSE, BIT Mesra
>
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Re: [algogeeks] Amazon Question - Find Pythagorean triplet in an unsorted array

[Ankur Garg]

*Turing :P

On Mon, Oct 17, 2011 at 3:51 PM, Ankur Garg  wrote:

> @Shashank ..+1 ..I wud say he must be given a tuning award :D :D  for
> solving such eternal conundrum ;)
>
>
>
> On Mon, Oct 17, 2011 at 2:37 PM, WgpShashank 
> wrote:
>
>> @wladimir , its PPT (Pythagoras triplets ) but its number theory based
>> approach  http://en.wikipedia.org/wiki/Pythagorean_triple might not be
>> good idea
>>
>> Here is approach :
>> *
>> *
>> *Euclid's 
>> formula*[1] is
>> a fundamental formula for generating Pythagorean triples given an arbitrary
>> pair of positive integers *m* and *n* with *m* > *n*. The formula states
>> that the integers p=m^2-n^2 , q=2mn r=m^2+n^2  , we have to sort the array
>> in non-increasing order  , then for each m>n we have to generate the  all
>> such p,q,r in worst case it will also requires O(N^2) such p,q,r for each
>> M>N isn't it ? then its not less then O(n^2) ??
>> Even with this approach,The triple generated by Euclid's formula is
>> primitive if and only if *m* and *n* are coprime and *m*-*n* is odd. If
>> both *m* and *n* are odd, then *a*, *b*, and *c* will be even, and so the
>> triple will not be primitive; however, dividing *a*, *b*, and *c* by 2
>> will yield a primitive triple if *m* and *n* are coprime.
>>
>> @all other , its similar to 3 sun , can't be done in less then O(N^2) if
>> number are not in range , When the integers are in the range [-*u* ... *u
>> *], 3SUM can be solved in time O(n + *u* lg *u*) by representing *S* as a
>> bit vector and performing a discrete convolution using FFT.
>>
>> i wondered if any other  algo/code/link you have which works in less then
>> O(N^2) , Better if One Explain The Approach or Algorithm , You Might able to
>> fill Patent :D
>>
>> Thanks
>> Shashank
>> CSE, BIT Mesra
>>
>> --
>> You received this message because you are subscribed to the Google Groups
>> "Algorithm Geeks" group.
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>> https://groups.google.com/d/msg/algogeeks/-/JQWWHDKMCiAJ.
>>
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>> http://groups.google.com/group/algogeeks?hl=en.
>>
>
>

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Re: [algogeeks] Amazon Question - Find Pythagorean triplet in an unsorted array

[WgpShashank]

@wladimir , its PPT (Pythagoras triplets ) but its number theory based 
approach  http://en.wikipedia.org/wiki/Pythagorean_triple might not be good 
idea 

Here is approach :
*
*
*Euclid's 
formula*[1] is 
a fundamental formula for generating Pythagorean triples given an arbitrary 
pair of positive integers *m* and *n* with *m* > *n*. The formula states 
that the integers p=m^2-n^2 , q=2mn r=m^2+n^2  , we have to sort the array 
in non-increasing order  , then for each m>n we have to generate the  all 
such p,q,r in worst case it will also requires O(N^2) such p,q,r for each 
M>N isn't it ? then its not less then O(n^2) ??
Even with this approach,The triple generated by Euclid's formula is 
primitive if and only if *m* and *n* are coprime and *m*-*n* is odd. If 
both *m* and *n* are odd, then *a*, *b*, and *c* will be even, and so the 
triple will not be primitive; however, dividing *a*, *b*, and *c* by 2 will 
yield a primitive triple if *m* and *n* are coprime.

@all other , its similar to 3 sun , can't be done in less then O(N^2) if 
number are not in range , When the integers are in the range [-*u* ... *u*], 
3SUM can be solved in time O(n + *u* lg *u*) by representing *S* as a bit 
vector and performing a discrete convolution using FFT. 

i wondered if any other  algo/code/link you have which works in less then 
O(N^2) , Better if One Explain The Approach or Algorithm , You Might able to 
fill Patent :D

Thanks
Shashank 
CSE, BIT Mesra

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Re: [algogeeks] Amazon Question - Find Pythagorean triplet in an unsorted array

[sravanreddy001]

This appears to be n^(3/2) complexity, looking at one of the solutions in 

http://stackoverflow.com/questions/575117/pythagorean-triplets

assuming elements as sorted. (x cannot be greater than sqrt(2z) as x2+y2 = 
z2 --> for the worst value of y2 --> 2x^2 = z2

MaxX = ( 2 * N - 1 ) ** 0.5

for x in 3..MaxX {
  y = x+1
  z = y+1
  m = x*x + y*y
  k = z * z
  while z <= N {
 while k < m {
z = z + 1
k = k + (2*z) - 1
}
if k == m and z <= N then {
// use x, y, z
}
y = y + 1
m = m + (2 * y) - 1
  }
 }

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Re: [algogeeks] Amazon Question - Find Pythagorean triplet in an unsorted array

[Ashish Goel]

http://stackoverflow.com/questions/575117/pythagorean-triplets

Best Regards
Ashish Goel
"Think positive and find fuel in failure"
+919985813081
+919966006652


On Fri, Oct 14, 2011 at 3:14 PM, Ankur Garg  wrote:

> @Rahul
>
> Pls elaborate with an example ...
>
>
> On Fri, Oct 14, 2011 at 2:35 PM, rahul patil <
> rahul.deshmukhpa...@gmail.com> wrote:
>
>> You can take advantage of a basic property of triagle that
>>
>> sum of largest side of triangle < sum of other two sides,
>>
>> After sorting you could easily deside the range in which possible solution
>> could be found for a chosen hypotenuse
>>
>> On Fri, Oct 14, 2011 at 11:10 AM, ravindra patel <
>> ravindra.it...@gmail.com> wrote:
>>
>>> @Wladimir, yeah I have heard about that. Another way of populating
>>> primitive pythagoreans is, for any natural number m > 1  (m^2 - 1, 2m, m^2 +
>>> 1) forms a pythagorean triplet. This is useful in populating pythagorean
>>> tiplets but here the problem is to search such triplets from a given int
>>> array.
>>>
>>> @ rahul, Hash of z^2 - x^2 for each pair of z,x itself will of the size
>>> n*(n-1). I am not sure how it will work in O(n) time then.
>>>
>>> Thanks,
>>> - Ravindra
>>>
>>>
>>> On Fri, Oct 14, 2011 at 12:25 AM, Ankur Garg wrote:
>>>
 @rahul...How do u choose z and x for computing z^2 -x^2 ?

 On Thu, Oct 13, 2011 at 11:34 PM, rahul  wrote:

> You can create a hash with sqrt(z2-x2). This will make it o(n). The
> interviewer just made it lil tricky. That's all
>
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>>>
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>>
>>
>>
>> --
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>> Rahul Patil
>>
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Re: [algogeeks] Amazon Question - Find Pythagorean triplet in an unsorted array

[Bittu Sarkar]

@rahul It still will be O(n^2) time complexity

On 14 October 2011 15:14, Ankur Garg  wrote:

> @Rahul
>
> Pls elaborate with an example ...
>
>
> On Fri, Oct 14, 2011 at 2:35 PM, rahul patil <
> rahul.deshmukhpa...@gmail.com> wrote:
>
>> You can take advantage of a basic property of triagle that
>>
>> sum of largest side of triangle < sum of other two sides,
>>
>> After sorting you could easily deside the range in which possible solution
>> could be found for a chosen hypotenuse
>>
>> On Fri, Oct 14, 2011 at 11:10 AM, ravindra patel <
>> ravindra.it...@gmail.com> wrote:
>>
>>> @Wladimir, yeah I have heard about that. Another way of populating
>>> primitive pythagoreans is, for any natural number m > 1  (m^2 - 1, 2m, m^2 +
>>> 1) forms a pythagorean triplet. This is useful in populating pythagorean
>>> tiplets but here the problem is to search such triplets from a given int
>>> array.
>>>
>>> @ rahul, Hash of z^2 - x^2 for each pair of z,x itself will of the size
>>> n*(n-1). I am not sure how it will work in O(n) time then.
>>>
>>> Thanks,
>>> - Ravindra
>>>
>>>
>>> On Fri, Oct 14, 2011 at 12:25 AM, Ankur Garg wrote:
>>>
 @rahul...How do u choose z and x for computing z^2 -x^2 ?

 On Thu, Oct 13, 2011 at 11:34 PM, rahul  wrote:

> You can create a hash with sqrt(z2-x2). This will make it o(n). The
> interviewer just made it lil tricky. That's all
>
> --
> You received this message because you are subscribed to the Google
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>>>
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>>
>>
>>
>> --
>> Regards,
>> Rahul Patil
>>
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-- 
Bittu Sarkar
5th Year Dual Degree Student
Department of Computer Science & Engineering
Indian Institute of Technology Kharagpur

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Re: [algogeeks] Amazon Question - Find Pythagorean triplet in an unsorted array

[rahul patil]

suppose sorted array is

1,2,3,5,10,12,13,17,19,25

so if u want to find possible combinations, with 25 as hypotenuse, then only
range 10 ... 19 could have answer

as 19 + 10 > 25

On Fri, Oct 14, 2011 at 3:14 PM, Ankur Garg  wrote:

> @Rahul
>
> Pls elaborate with an example ...
>
>
> On Fri, Oct 14, 2011 at 2:35 PM, rahul patil <
> rahul.deshmukhpa...@gmail.com> wrote:
>
>> You can take advantage of a basic property of triagle that
>>
>> sum of largest side of triangle < sum of other two sides,
>>
>> After sorting you could easily deside the range in which possible solution
>> could be found for a chosen hypotenuse
>>
>> On Fri, Oct 14, 2011 at 11:10 AM, ravindra patel <
>> ravindra.it...@gmail.com> wrote:
>>
>>> @Wladimir, yeah I have heard about that. Another way of populating
>>> primitive pythagoreans is, for any natural number m > 1  (m^2 - 1, 2m, m^2 +
>>> 1) forms a pythagorean triplet. This is useful in populating pythagorean
>>> tiplets but here the problem is to search such triplets from a given int
>>> array.
>>>
>>> @ rahul, Hash of z^2 - x^2 for each pair of z,x itself will of the size
>>> n*(n-1). I am not sure how it will work in O(n) time then.
>>>
>>> Thanks,
>>> - Ravindra
>>>
>>>
>>> On Fri, Oct 14, 2011 at 12:25 AM, Ankur Garg wrote:
>>>
 @rahul...How do u choose z and x for computing z^2 -x^2 ?

 On Thu, Oct 13, 2011 at 11:34 PM, rahul  wrote:

> You can create a hash with sqrt(z2-x2). This will make it o(n). The
> interviewer just made it lil tricky. That's all
>
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Re: [algogeeks] Amazon Question - Find Pythagorean triplet in an unsorted array

[Siddharth Pipriya]

using properties of tiangle wont help i guess. the will give the range
of VALUES you want to restrict yourself to. not the range of INDEX's
of the array...

On Fri, Oct 14, 2011 at 3:14 PM, Ankur Garg  wrote:
> @Rahul
> Pls elaborate with an example ...
>
> On Fri, Oct 14, 2011 at 2:35 PM, rahul patil 
> wrote:
>>
>> You can take advantage of a basic property of triagle that
>>
>> sum of largest side of triangle < sum of other two sides,
>>
>> After sorting you could easily deside the range in which possible solution
>> could be found for a chosen hypotenuse
>>
>> On Fri, Oct 14, 2011 at 11:10 AM, ravindra patel
>>  wrote:
>>>
>>> @Wladimir, yeah I have heard about that. Another way of populating
>>> primitive pythagoreans is, for any natural number m > 1  (m^2 - 1, 2m, m^2 +
>>> 1) forms a pythagorean triplet. This is useful in populating pythagorean
>>> tiplets but here the problem is to search such triplets from a given int
>>> array.
>>>
>>> @ rahul, Hash of z^2 - x^2 for each pair of z,x itself will of the size
>>> n*(n-1). I am not sure how it will work in O(n) time then.
>>>
>>> Thanks,
>>> - Ravindra
>>>
>>> On Fri, Oct 14, 2011 at 12:25 AM, Ankur Garg 
>>> wrote:

 @rahul...How do u choose z and x for computing z^2 -x^2 ?
 On Thu, Oct 13, 2011 at 11:34 PM, rahul  wrote:
>
> You can create a hash with sqrt(z2-x2). This will make it o(n). The
> interviewer just made it lil tricky. That's all
>
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Re: [algogeeks] Amazon Question - Find Pythagorean triplet in an unsorted array

[Ankur Garg]

@Rahul

Pls elaborate with an example ...

On Fri, Oct 14, 2011 at 2:35 PM, rahul patil
wrote:

> You can take advantage of a basic property of triagle that
>
> sum of largest side of triangle < sum of other two sides,
>
> After sorting you could easily deside the range in which possible solution
> could be found for a chosen hypotenuse
>
> On Fri, Oct 14, 2011 at 11:10 AM, ravindra patel  > wrote:
>
>> @Wladimir, yeah I have heard about that. Another way of populating
>> primitive pythagoreans is, for any natural number m > 1  (m^2 - 1, 2m, m^2 +
>> 1) forms a pythagorean triplet. This is useful in populating pythagorean
>> tiplets but here the problem is to search such triplets from a given int
>> array.
>>
>> @ rahul, Hash of z^2 - x^2 for each pair of z,x itself will of the size
>> n*(n-1). I am not sure how it will work in O(n) time then.
>>
>> Thanks,
>> - Ravindra
>>
>>
>> On Fri, Oct 14, 2011 at 12:25 AM, Ankur Garg wrote:
>>
>>> @rahul...How do u choose z and x for computing z^2 -x^2 ?
>>>
>>> On Thu, Oct 13, 2011 at 11:34 PM, rahul  wrote:
>>>
 You can create a hash with sqrt(z2-x2). This will make it o(n). The
 interviewer just made it lil tricky. That's all

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>
>
>
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> Rahul Patil
>
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Re: [algogeeks] Amazon Question - Find Pythagorean triplet in an unsorted array

[rahul patil]

You can take advantage of a basic property of triagle that

sum of largest side of triangle < sum of other two sides,

After sorting you could easily deside the range in which possible solution
could be found for a chosen hypotenuse

On Fri, Oct 14, 2011 at 11:10 AM, ravindra patel
wrote:

> @Wladimir, yeah I have heard about that. Another way of populating
> primitive pythagoreans is, for any natural number m > 1  (m^2 - 1, 2m, m^2 +
> 1) forms a pythagorean triplet. This is useful in populating pythagorean
> tiplets but here the problem is to search such triplets from a given int
> array.
>
> @ rahul, Hash of z^2 - x^2 for each pair of z,x itself will of the size
> n*(n-1). I am not sure how it will work in O(n) time then.
>
> Thanks,
> - Ravindra
>
>
> On Fri, Oct 14, 2011 at 12:25 AM, Ankur Garg  wrote:
>
>> @rahul...How do u choose z and x for computing z^2 -x^2 ?
>>
>> On Thu, Oct 13, 2011 at 11:34 PM, rahul  wrote:
>>
>>> You can create a hash with sqrt(z2-x2). This will make it o(n). The
>>> interviewer just made it lil tricky. That's all
>>>
>>> --
>>> You received this message because you are subscribed to the Google Groups
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Re: [algogeeks] Amazon Question - Find Pythagorean triplet in an unsorted array

[ravindra patel]

@Wladimir, yeah I have heard about that. Another way of populating primitive
pythagoreans is, for any natural number m > 1  (m^2 - 1, 2m, m^2 + 1) forms
a pythagorean triplet. This is useful in populating pythagorean tiplets but
here the problem is to search such triplets from a given int array.

@ rahul, Hash of z^2 - x^2 for each pair of z,x itself will of the size
n*(n-1). I am not sure how it will work in O(n) time then.

Thanks,
- Ravindra

On Fri, Oct 14, 2011 at 12:25 AM, Ankur Garg  wrote:

> @rahul...How do u choose z and x for computing z^2 -x^2 ?
>
> On Thu, Oct 13, 2011 at 11:34 PM, rahul  wrote:
>
>> You can create a hash with sqrt(z2-x2). This will make it o(n). The
>> interviewer just made it lil tricky. That's all
>>
>> --
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>>
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Re: [algogeeks] Amazon Question - Find Pythagorean triplet in an unsorted array

[Ankur Garg]

@rahul...How do u choose z and x for computing z^2 -x^2 ?

On Thu, Oct 13, 2011 at 11:34 PM, rahul  wrote:

> You can create a hash with sqrt(z2-x2). This will make it o(n). The
> interviewer just made it lil tricky. That's all
>
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[algogeeks] Amazon Question - Find Pythagorean triplet in an unsorted array

[rahul]

You can create a hash with sqrt(z2-x2). This will make it o(n). The interviewer 
just made it lil tricky. That's all

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Re: [algogeeks] Amazon Question - Find Pythagorean triplet in an unsorted array

[Ankur Garg]

BTW can we solve this by hashing..That is the only feasible solution which
comes to my mind to reduce the time complexity ?

On Thu, Oct 13, 2011 at 11:20 PM, Ankur Garg  wrote:

> Dude this is nothing but 3 sum problem
>
> http://en.wikipedia.org/wiki/3SUM
>
> Ask interviewer to check this link and say he has gone mad!! :P
>
> Regards
> Ankur
>
> On Thu, Oct 13, 2011 at 10:29 PM, ravindra patel  > wrote:
>
>> Hi,
>> Another question I faced in Amazon F2F.
>>
>> Given an unsorted array of integers, find all triplets that satisfy x^2 +
>> y^2 = z^2.
>>
>> For example if given array is -  1, 3, 7, 5, 4, 12, 13
>> The answer should be -
>> 5, 12, 13 and
>> 3, 4, 5
>>
>> I suggested below algo with complexity O(n^2) -
>>
>> - Sort the array in descending order. - O(nlogn)
>> - square each element. - O(n)
>>
>> Now it reduces to the problem of  finding all triplets(a,b,c) in a
>> sorted array such that a = b+c.
>>
>> The interviewer was insisting on a solution better than O(n^2) which I
>> dont think is feasible, but I couldn't prove that. Anyone has any idea.
>>
>>
>>
>> Thanks,
>> - Ravindra
>>
>> --
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>
>

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Re: [algogeeks] Amazon Question - Find Pythagorean triplet in an unsorted array

[praveen raj]

N2 would me minimum
On 13-Oct-2011 11:08 PM, "ravindra patel"  wrote:

> Hi,
> Another question I faced in Amazon F2F.
>
> Given an unsorted array of integers, find all triplets that satisfy x^2 +
> y^2 = z^2.
>
> For example if given array is -  1, 3, 7, 5, 4, 12, 13
> The answer should be -
> 5, 12, 13 and
> 3, 4, 5
>
> I suggested below algo with complexity O(n^2) -
>
> - Sort the array in descending order. - O(nlogn)
> - square each element. - O(n)
>
> Now it reduces to the problem of  finding all triplets(a,b,c) in a
> sorted array such that a = b+c.
>
> The interviewer was insisting on a solution better than O(n^2) which I dont
> think is feasible, but I couldn't prove that. Anyone has any idea.
>
>
>
> Thanks,
> - Ravindra
>
> --
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Re: [algogeeks] Amazon Question - Find Pythagorean triplet in an unsorted array

[Ankur Garg]

Dude this is nothing but 3 sum problem

http://en.wikipedia.org/wiki/3SUM

Ask interviewer to check this link and say he has gone mad!! :P

Regards
Ankur

On Thu, Oct 13, 2011 at 10:29 PM, ravindra patel
wrote:

> Hi,
> Another question I faced in Amazon F2F.
>
> Given an unsorted array of integers, find all triplets that satisfy x^2 +
> y^2 = z^2.
>
> For example if given array is -  1, 3, 7, 5, 4, 12, 13
> The answer should be -
> 5, 12, 13 and
> 3, 4, 5
>
> I suggested below algo with complexity O(n^2) -
>
> - Sort the array in descending order. - O(nlogn)
> - square each element. - O(n)
>
> Now it reduces to the problem of  finding all triplets(a,b,c) in a
> sorted array such that a = b+c.
>
> The interviewer was insisting on a solution better than O(n^2) which I dont
> think is feasible, but I couldn't prove that. Anyone has any idea.
>
>
>
> Thanks,
> - Ravindra
>
> --
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Re: [algogeeks] Amazon Question - Find Pythagorean triplet in an unsorted array

[Wladimir Tavares]

I thinking in this property but i dont know how to use :(


Euclid, in his book Elements, demonstrated that there is a infinnity of
suits early Pythagoreans. Moreover, he found a formula that generates all
primitive Pythagorean suits. Given two natural numbers m> n, the suit (a, b,
c), where:

 a = m ^ 2 - n ^ 2,
 b = 2mn,
 c = m ^ 2 + n ^ 2,




Wladimir Araujo Tavares
*Federal University of Ceará 
Homepage  |
Maratona|
*




On Thu, Oct 13, 2011 at 1:59 PM, ravindra patel wrote:

> Hi,
> Another question I faced in Amazon F2F.
>
> Given an unsorted array of integers, find all triplets that satisfy x^2 +
> y^2 = z^2.
>
> For example if given array is -  1, 3, 7, 5, 4, 12, 13
> The answer should be -
> 5, 12, 13 and
> 3, 4, 5
>
> I suggested below algo with complexity O(n^2) -
>
> - Sort the array in descending order. - O(nlogn)
> - square each element. - O(n)
>
> Now it reduces to the problem of  finding all triplets(a,b,c) in a
> sorted array such that a = b+c.
>
> The interviewer was insisting on a solution better than O(n^2) which I dont
> think is feasible, but I couldn't prove that. Anyone has any idea.
>
>
>
> Thanks,
> - Ravindra
>
> --
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[algogeeks] Amazon Question - Find Pythagorean triplet in an unsorted array

[ravindra patel]

Hi,
Another question I faced in Amazon F2F.

Given an unsorted array of integers, find all triplets that satisfy x^2 +
y^2 = z^2.

For example if given array is -  1, 3, 7, 5, 4, 12, 13
The answer should be -
5, 12, 13 and
3, 4, 5

I suggested below algo with complexity O(n^2) -

- Sort the array in descending order. - O(nlogn)
- square each element. - O(n)

Now it reduces to the problem of  finding all triplets(a,b,c) in a
sorted array such that a = b+c.

The interviewer was insisting on a solution better than O(n^2) which I dont
think is feasible, but I couldn't prove that. Anyone has any idea.



Thanks,
- Ravindra

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