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Simple but confusing algorith question

Hey all,
I was asked this question in an interview recently:

Suppose you have the method signature

bool MyPairSum(int [] array, int sum)

the array has all unique values (no repeats), your task is to find two
indices in the array whose sum equals the input parameter sum. If there
exists two entries in the array that sum together to equal the input
parameter of sum, then return true, otherwise return false. what's the
most efficient implementation?

My question is can we have a better worse case runtime of O(n) ??
I'm thinking that in the worse case, you'd have to compare each index
against all the other indices and test each sum until you find one that
matches the input sum. In the worse case, there will be no pair of
indices that equal the input sum parameter. Am I overlooking a very
basic trick? I figured with all the sharp people in here, somebody can
discern whether I'm off base or not :)

Here's the sample implementation I was thinking of:
bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
for (int j = i + 1; j < array.Length; j++)
{
if ( array[i] + array[j] == sum)
return true;
}
}
return false;
}
Tks, Karan S.

Apr 27 '06 #1
27 1641
If the data were sorted you could do much better. If they are not sorted you
would have n^2 as your worst case as you have to check every index of the
array for each value.

even so you could still do slightly better by only issuing a single add/sub
instead of a operation on every iteration ... see example.

bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
int need = sum - array[j];
for (int j = 0; j < array.Length; j++)
{
if (array[j] == sum)
return true;
}
}
return false;
}

Also your code has failure modes because int j = i + 1 ... what about the
following data?

array 0,1,2 sum = 3 by using i+1 you say it doesn't exist.

Another quick question ... what should the behavior be for the following?

array 1,2,3,4 sum = 5

Cheers,

Greg

<ka**********@gmail.com> wrote in message
news:11*********************@i39g2000cwa.googlegro ups.com...
Hey all,
I was asked this question in an interview recently:

Suppose you have the method signature

bool MyPairSum(int [] array, int sum)

the array has all unique values (no repeats), your task is to find two
indices in the array whose sum equals the input parameter sum. If there
exists two entries in the array that sum together to equal the input
parameter of sum, then return true, otherwise return false. what's the
most efficient implementation?

My question is can we have a better worse case runtime of O(n) ??
I'm thinking that in the worse case, you'd have to compare each index
against all the other indices and test each sum until you find one that
matches the input sum. In the worse case, there will be no pair of
indices that equal the input sum parameter. Am I overlooking a very
basic trick? I figured with all the sharp people in here, somebody can
discern whether I'm off base or not :)

Here's the sample implementation I was thinking of:
bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
for (int j = i + 1; j < array.Length; j++)
{
if ( array[i] + array[j] == sum)
return true;
}
}
return false;
}
Tks, Karan S.
Apr 27 '06 #2
This is Sorted
array 1,2,3,4 sum = 5

This is not Sorted
array 1,4,2,3 sum = 5

Which one is faster??

SA

"Greg Young [MVP]" <Dr*************@hotmail.com> wrote in message
news:OM*************@TK2MSFTNGP05.phx.gbl...
If the data were sorted you could do much better. If they are not sorted
you
would have n^2 as your worst case as you have to check every index of the
array for each value.

even so you could still do slightly better by only issuing a single
add/sub
instead of a operation on every iteration ... see example.

bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
int need = sum - array[j];
for (int j = 0; j < array.Length; j++)
{
if (array[j] == sum)
return true;
}
}
return false;
}

Also your code has failure modes because int j = i + 1 ... what about the
following data?

array 0,1,2 sum = 3 by using i+1 you say it doesn't exist.

Another quick question ... what should the behavior be for the following?

array 1,2,3,4 sum = 5

Cheers,

Greg

<ka**********@gmail.com> wrote in message
news:11*********************@i39g2000cwa.googlegro ups.com...
Hey all,
I was asked this question in an interview recently:

Suppose you have the method signature

bool MyPairSum(int [] array, int sum)

the array has all unique values (no repeats), your task is to find two
indices in the array whose sum equals the input parameter sum. If there
exists two entries in the array that sum together to equal the input
parameter of sum, then return true, otherwise return false. what's the
most efficient implementation?

My question is can we have a better worse case runtime of O(n) ??
I'm thinking that in the worse case, you'd have to compare each index
against all the other indices and test each sum until you find one that
matches the input sum. In the worse case, there will be no pair of
indices that equal the input sum parameter. Am I overlooking a very
basic trick? I figured with all the sharp people in here, somebody can
discern whether I'm off base or not :)

Here's the sample implementation I was thinking of:
bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
for (int j = i + 1; j < array.Length; j++)
{
if ( array[i] + array[j] == sum)
return true;
}
}
return false;
}
Tks, Karan S.

Apr 27 '06 #3
if (array[j] == sum) < == need
return true;

"Greg Young [MVP]" <Dr*************@hotmail.com> wrote in message
news:OM*************@TK2MSFTNGP05.phx.gbl...
If the data were sorted you could do much better. If they are not sorted
you
would have n^2 as your worst case as you have to check every index of the
array for each value.

even so you could still do slightly better by only issuing a single
add/sub
instead of a operation on every iteration ... see example.

bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
int need = sum - array[j];
for (int j = 0; j < array.Length; j++)
{
if (array[j] == sum)
return true;
}
}
return false;
}

Also your code has failure modes because int j = i + 1 ... what about the
following data?

array 0,1,2 sum = 3 by using i+1 you say it doesn't exist.

Another quick question ... what should the behavior be for the following?

array 1,2,3,4 sum = 5

Cheers,

Greg

<ka**********@gmail.com> wrote in message
news:11*********************@i39g2000cwa.googlegro ups.com...
Hey all,
I was asked this question in an interview recently:

Suppose you have the method signature

bool MyPairSum(int [] array, int sum)

the array has all unique values (no repeats), your task is to find two
indices in the array whose sum equals the input parameter sum. If there
exists two entries in the array that sum together to equal the input
parameter of sum, then return true, otherwise return false. what's the
most efficient implementation?

My question is can we have a better worse case runtime of O(n) ??
I'm thinking that in the worse case, you'd have to compare each index
against all the other indices and test each sum until you find one that
matches the input sum. In the worse case, there will be no pair of
indices that equal the input sum parameter. Am I overlooking a very
basic trick? I figured with all the sharp people in here, somebody can
discern whether I'm off base or not :)

Here's the sample implementation I was thinking of:
bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
for (int j = i + 1; j < array.Length; j++)
{
if ( array[i] + array[j] == sum)
return true;
}
}
return false;
}
Tks, Karan S.

Apr 27 '06 #4
If you can count on sorted data you can make assumptions in your looping and
get your worst case a whole lot better than O(n^2)

i.e
if current + array[i] > sum {
//skip rest of list
}

"MSDN" <sq**********@hotmail.com> wrote in message
news:%2****************@TK2MSFTNGP03.phx.gbl...
This is Sorted
array 1,2,3,4 sum = 5

This is not Sorted
array 1,4,2,3 sum = 5

Which one is faster??

SA

"Greg Young [MVP]" <Dr*************@hotmail.com> wrote in message
news:OM*************@TK2MSFTNGP05.phx.gbl...
If the data were sorted you could do much better. If they are not sorted
you
would have n^2 as your worst case as you have to check every index of the
array for each value.

even so you could still do slightly better by only issuing a single
add/sub
instead of a operation on every iteration ... see example.

bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
int need = sum - array[j];
for (int j = 0; j < array.Length; j++)
{
if (array[j] == sum)
return true;
}
}
return false;
}

Also your code has failure modes because int j = i + 1 ... what about the
following data?

array 0,1,2 sum = 3 by using i+1 you say it doesn't exist.

Another quick question ... what should the behavior be for the following?

array 1,2,3,4 sum = 5

Cheers,

Greg

<ka**********@gmail.com> wrote in message
news:11*********************@i39g2000cwa.googlegro ups.com...
Hey all,
I was asked this question in an interview recently:

Suppose you have the method signature

bool MyPairSum(int [] array, int sum)

the array has all unique values (no repeats), your task is to find two
indices in the array whose sum equals the input parameter sum. If there
exists two entries in the array that sum together to equal the input
parameter of sum, then return true, otherwise return false. what's the
most efficient implementation?

My question is can we have a better worse case runtime of O(n) ??
I'm thinking that in the worse case, you'd have to compare each index
against all the other indices and test each sum until you find one that
matches the input sum. In the worse case, there will be no pair of
indices that equal the input sum parameter. Am I overlooking a very
basic trick? I figured with all the sharp people in here, somebody can
discern whether I'm off base or not :)

Here's the sample implementation I was thinking of:
bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
for (int j = i + 1; j < array.Length; j++)
{
if ( array[i] + array[j] == sum)
return true;
}
}
return false;
}
Tks, Karan S.


Apr 27 '06 #5
Also O(n^2) is talking about the worst case ... you have provided the best
case as a comparison ...

to compare the worst case in this problem you would actually be looking at
iterations on a miss ..

array 1,2,3,4 sum 12
array 3,2,1,4 sum 12

in the onsorted case you have O^2 (loop through all twice) .. 16

in the sorted case you would be with almost no effort at 9 comparisons on
the worst case as it would allow you to do the simple change in the original
code (use i+1 for j instead of 0)
"MSDN" <sq**********@hotmail.com> wrote in message
news:%2****************@TK2MSFTNGP03.phx.gbl...
This is Sorted
array 1,2,3,4 sum = 5

This is not Sorted
array 1,4,2,3 sum = 5

Which one is faster??

SA

"Greg Young [MVP]" <Dr*************@hotmail.com> wrote in message
news:OM*************@TK2MSFTNGP05.phx.gbl...
If the data were sorted you could do much better. If they are not sorted
you
would have n^2 as your worst case as you have to check every index of the
array for each value.

even so you could still do slightly better by only issuing a single
add/sub
instead of a operation on every iteration ... see example.

bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
int need = sum - array[j];
for (int j = 0; j < array.Length; j++)
{
if (array[j] == sum)
return true;
}
}
return false;
}

Also your code has failure modes because int j = i + 1 ... what about the
following data?

array 0,1,2 sum = 3 by using i+1 you say it doesn't exist.

Another quick question ... what should the behavior be for the following?

array 1,2,3,4 sum = 5

Cheers,

Greg

<ka**********@gmail.com> wrote in message
news:11*********************@i39g2000cwa.googlegro ups.com...
Hey all,
I was asked this question in an interview recently:

Suppose you have the method signature

bool MyPairSum(int [] array, int sum)

the array has all unique values (no repeats), your task is to find two
indices in the array whose sum equals the input parameter sum. If there
exists two entries in the array that sum together to equal the input
parameter of sum, then return true, otherwise return false. what's the
most efficient implementation?

My question is can we have a better worse case runtime of O(n) ??
I'm thinking that in the worse case, you'd have to compare each index
against all the other indices and test each sum until you find one that
matches the input sum. In the worse case, there will be no pair of
indices that equal the input sum parameter. Am I overlooking a very
basic trick? I figured with all the sharp people in here, somebody can
discern whether I'm off base or not :)

Here's the sample implementation I was thinking of:
bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
for (int j = i + 1; j < array.Length; j++)
{
if ( array[i] + array[j] == sum)
return true;
}
}
return false;
}
Tks, Karan S.


Apr 27 '06 #6
n/m on i+1 must need coffee :)

"Greg Young [MVP]" <Dr*************@hotmail.com> wrote in message
news:OM*************@TK2MSFTNGP05.phx.gbl...
If the data were sorted you could do much better. If they are not sorted
you
would have n^2 as your worst case as you have to check every index of the
array for each value.

even so you could still do slightly better by only issuing a single
add/sub
instead of a operation on every iteration ... see example.

bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
int need = sum - array[j];
for (int j = 0; j < array.Length; j++)
{
if (array[j] == sum)
return true;
}
}
return false;
}

Also your code has failure modes because int j = i + 1 ... what about the
following data?

array 0,1,2 sum = 3 by using i+1 you say it doesn't exist.

Another quick question ... what should the behavior be for the following?

array 1,2,3,4 sum = 5

Cheers,

Greg

<ka**********@gmail.com> wrote in message
news:11*********************@i39g2000cwa.googlegro ups.com...
Hey all,
I was asked this question in an interview recently:

Suppose you have the method signature

bool MyPairSum(int [] array, int sum)

the array has all unique values (no repeats), your task is to find two
indices in the array whose sum equals the input parameter sum. If there
exists two entries in the array that sum together to equal the input
parameter of sum, then return true, otherwise return false. what's the
most efficient implementation?

My question is can we have a better worse case runtime of O(n) ??
I'm thinking that in the worse case, you'd have to compare each index
against all the other indices and test each sum until you find one that
matches the input sum. In the worse case, there will be no pair of
indices that equal the input sum parameter. Am I overlooking a very
basic trick? I figured with all the sharp people in here, somebody can
discern whether I'm off base or not :)

Here's the sample implementation I was thinking of:
bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
for (int j = i + 1; j < array.Length; j++)
{
if ( array[i] + array[j] == sum)
return true;
}
}
return false;
}
Tks, Karan S.

Apr 27 '06 #7
"Greg Young [MVP]" <Dr*************@hotmail.com> wrote:
If you can count on sorted data you can make assumptions in your looping and
get your worst case a whole lot better than O(n^2)


I think it's O(n) if the list is sorted...

(1) Sort the list from smallest to largest
(2) Have two pointers, "left" at the start of the list, "right" at the
end.
(3) If the sum of your two pointers is too big, then "right" has to
move left
(4) If the sum is too small, then "left" has to move right
(5) If the two pointers meet then there is no solution

Proof: suppose there exists a solution x+y where x is smaller. If
left<x and right>y then any move we can make is acceptable. If left=x
then no move will make right<y. Similarly if right=y then no move will
make left>x.

--
Lucian
Apr 27 '06 #8
The array isn't sorted I believe, just no dupes.Also, it just checks if
two indexes summed equals sum like array[3] + array[33] = sum !!

Thanks for your input though :)
Greg Young [MVP] wrote:
If the data were sorted you could do much better. If they are not sorted you
would have n^2 as your worst case as you have to check every index of the
array for each value.

even so you could still do slightly better by only issuing a single add/sub
instead of a operation on every iteration ... see example.

bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
int need = sum - array[j];
for (int j = 0; j < array.Length; j++)
{
if (array[j] == sum)
return true;
}
}
return false;
}

Also your code has failure modes because int j = i + 1 ... what about the
following data?

array 0,1,2 sum = 3 by using i+1 you say it doesn't exist.

Another quick question ... what should the behavior be for the following?

array 1,2,3,4 sum = 5

Cheers,

Greg

<ka**********@gmail.com> wrote in message
news:11*********************@i39g2000cwa.googlegro ups.com...
Hey all,
I was asked this question in an interview recently:

Suppose you have the method signature

bool MyPairSum(int [] array, int sum)

the array has all unique values (no repeats), your task is to find two
indices in the array whose sum equals the input parameter sum. If there
exists two entries in the array that sum together to equal the input
parameter of sum, then return true, otherwise return false. what's the
most efficient implementation?

My question is can we have a better worse case runtime of O(n) ??
I'm thinking that in the worse case, you'd have to compare each index
against all the other indices and test each sum until you find one that
matches the input sum. In the worse case, there will be no pair of
indices that equal the input sum parameter. Am I overlooking a very
basic trick? I figured with all the sharp people in here, somebody can
discern whether I'm off base or not :)

Here's the sample implementation I was thinking of:
bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
for (int j = i + 1; j < array.Length; j++)
{
if ( array[i] + array[j] == sum)
return true;
}
}
return false;
}


Tks, Karan S.


Apr 27 '06 #9
It does seem like there's no way around checking all possibilties
unless some other data structure was involved. I was trying to cut down
on comparisons/summations by eliminating the first element, then the
second, so the over run time would be on the order of

n ( n - 1 )
----------------
2

in the worse case, which basically is O(n).

like from your example
comparisons: 1 with 2, 1 with 3, 1 with 4, 2 with 3, 2 with 4, 3 with 4
(done, all combos tested). You wouldn't compare 1 with 1, 2 with 2, and
the like since they're not different indexes. worse case runtime = 1/2
n which amounts to O(n) unfortunately.

Thanks for your reply

Greg Young [MVP] wrote:
Also O(n^2) is talking about the worst case ... you have provided the best
case as a comparison ...

to compare the worst case in this problem you would actually be looking at
iterations on a miss ..

array 1,2,3,4 sum 12
array 3,2,1,4 sum 12

in the onsorted case you have O^2 (loop through all twice) .. 16

in the sorted case you would be with almost no effort at 9 comparisons on
the worst case as it would allow you to do the simple change in the original
code (use i+1 for j instead of 0)
"MSDN" <sq**********@hotmail.com> wrote in message
news:%2****************@TK2MSFTNGP03.phx.gbl...
This is Sorted
array 1,2,3,4 sum = 5

This is not Sorted
array 1,4,2,3 sum = 5

Which one is faster??

SA

"Greg Young [MVP]" <Dr*************@hotmail.com> wrote in message
news:OM*************@TK2MSFTNGP05.phx.gbl...
If the data were sorted you could do much better. If they are not sorted
you
would have n^2 as your worst case as you have to check every index of the
array for each value.

even so you could still do slightly better by only issuing a single
add/sub
instead of a operation on every iteration ... see example.

bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
int need = sum - array[j];
for (int j = 0; j < array.Length; j++)
{
if (array[j] == sum)
return true;
}
}
return false;
}

Also your code has failure modes because int j = i + 1 ... what about the
following data?

array 0,1,2 sum = 3 by using i+1 you say it doesn't exist.

Another quick question ... what should the behavior be for the following?

array 1,2,3,4 sum = 5

Cheers,

Greg

<ka**********@gmail.com> wrote in message
news:11*********************@i39g2000cwa.googlegro ups.com...
Hey all,
I was asked this question in an interview recently:

Suppose you have the method signature

bool MyPairSum(int [] array, int sum)

the array has all unique values (no repeats), your task is to find two
indices in the array whose sum equals the input parameter sum. If there
exists two entries in the array that sum together to equal the input
parameter of sum, then return true, otherwise return false. what's the
most efficient implementation?

My question is can we have a better worse case runtime of O(n) ??
I'm thinking that in the worse case, you'd have to compare each index
against all the other indices and test each sum until you find one that
matches the input sum. In the worse case, there will be no pair of
indices that equal the input sum parameter. Am I overlooking a very
basic trick? I figured with all the sharp people in here, somebody can
discern whether I'm off base or not :)

Here's the sample implementation I was thinking of:
bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
for (int j = i + 1; j < array.Length; j++)
{
if ( array[i] + array[j] == sum)
return true;
}
}
return false;
}
Tks, Karan S.



Apr 27 '06 #10
ka**********@gmail.com wrote:
The array isn't sorted I believe, just no dupes.Also, it just checks if
two indexes summed equals sum like array[3] + array[33] = sum !!


Well then, sort the list first O(n.log n) and then run an O(n) search
for pairs on the sorted list! After all, O(n)+O(n.log n) = O(n.log n).

--
Lucian
Apr 27 '06 #11
I think you are missing the point about the subtraction part ..

You lower your constant by using the code as I wrote it .. by doing the
subtraction up front you avoid doing the additions.

on a given iteration yours ... is j comparisons + j additions .. mine is j
comparisons + 1 subtraction.

bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
int need = sum - array[j];
for (int j = i+1; j < array.Length; j++)
{
if (array[j] == need)
return true;
}
}
return false;
}

Another interesting question is how much data is being passed into this and
how often to you expect to be in your worst case? Since the data if sorted
can be done in linear time, if you expected to be in your worst case (miss)
most of the time with rather large datasets being passed in it might be
worth while to take a look at sorting the data first as it could end up
lowerring your average case.

Greg
<ka**********@gmail.com> wrote in message
news:11**********************@g10g2000cwb.googlegr oups.com...
The array isn't sorted I believe, just no dupes.Also, it just checks if
two indexes summed equals sum like array[3] + array[33] = sum !!

Thanks for your input though :)
Greg Young [MVP] wrote:
If the data were sorted you could do much better. If they are not sorted
you
would have n^2 as your worst case as you have to check every index of the
array for each value.

even so you could still do slightly better by only issuing a single
add/sub
instead of a operation on every iteration ... see example.

bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
int need = sum - array[j];
for (int j = 0; j < array.Length; j++)
{
if (array[j] == sum)
return true;
}
}
return false;
}

Also your code has failure modes because int j = i + 1 ... what about the
following data?

array 0,1,2 sum = 3 by using i+1 you say it doesn't exist.

Another quick question ... what should the behavior be for the following?

array 1,2,3,4 sum = 5

Cheers,

Greg

<ka**********@gmail.com> wrote in message
news:11*********************@i39g2000cwa.googlegro ups.com...
Hey all,
I was asked this question in an interview recently:

Suppose you have the method signature

bool MyPairSum(int [] array, int sum)

the array has all unique values (no repeats), your task is to find two
indices in the array whose sum equals the input parameter sum. If there
exists two entries in the array that sum together to equal the input
parameter of sum, then return true, otherwise return false. what's the
most efficient implementation?

My question is can we have a better worse case runtime of O(n) ??
I'm thinking that in the worse case, you'd have to compare each index
against all the other indices and test each sum until you find one that
matches the input sum. In the worse case, there will be no pair of
indices that equal the input sum parameter. Am I overlooking a very
basic trick? I figured with all the sharp people in here, somebody can
discern whether I'm off base or not :)

Here's the sample implementation I was thinking of:
bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
for (int j = i + 1; j < array.Length; j++)
{
if ( array[i] + array[j] == sum)
return true;
}
}
return false;
}
Tks, Karan S.

Apr 27 '06 #12
I guess in my code, the unSorted one would be faster in this specific
test case :). I'm trying to think of way to implement some pre-made
data structure in .NET where you'd add each value to it as you pass
through the array, then query against the structure somehow. Although,
this would a best case run time of one pass and adding to the data
structure (cn) and the cost of querying the data structure (c). This
should result in a run time of cn. Then again, the time cost of the
data structure may be quite big too. I was thinking of something like a
SortedList and then going from there. This interview question may have
more of a way to see how I approach problems than what sort of
solutions I come up with.

Thanks for your reply!
MSDN wrote:
This is Sorted
array 1,2,3,4 sum = 5

This is not Sorted
array 1,4,2,3 sum = 5

Which one is faster??

SA

"Greg Young [MVP]" <Dr*************@hotmail.com> wrote in message
news:OM*************@TK2MSFTNGP05.phx.gbl...
If the data were sorted you could do much better. If they are not sorted
you
would have n^2 as your worst case as you have to check every index of the
array for each value.

even so you could still do slightly better by only issuing a single
add/sub
instead of a operation on every iteration ... see example.

bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
int need = sum - array[j];
for (int j = 0; j < array.Length; j++)
{
if (array[j] == sum)
return true;
}
}
return false;
}

Also your code has failure modes because int j = i + 1 ... what aboutthe
following data?

array 0,1,2 sum = 3 by using i+1 you say it doesn't exist.

Another quick question ... what should the behavior be for the following?

array 1,2,3,4 sum = 5

Cheers,

Greg

<ka**********@gmail.com> wrote in message
news:11*********************@i39g2000cwa.googlegro ups.com...
Hey all,
I was asked this question in an interview recently:

Suppose you have the method signature

bool MyPairSum(int [] array, int sum)

the array has all unique values (no repeats), your task is to find two
indices in the array whose sum equals the input parameter sum. If there
exists two entries in the array that sum together to equal the input
parameter of sum, then return true, otherwise return false. what's the
most efficient implementation?

My question is can we have a better worse case runtime of O(n) ??
I'm thinking that in the worse case, you'd have to compare each index
against all the other indices and test each sum until you find one that
matches the input sum. In the worse case, there will be no pair of
indices that equal the input sum parameter. Am I overlooking a very
basic trick? I figured with all the sharp people in here, somebody can
discern whether I'm off base or not :)

Here's the sample implementation I was thinking of:
bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
for (int j = i + 1; j < array.Length; j++)
{
if ( array[i] + array[j] == sum)
return true;
}
}
return false;
}
Tks, Karan S.


Apr 27 '06 #13
It does seem like there's no way around checking all possibilties
unless some other data structure was involved. I was trying to cut down
on comparisons/summations by eliminating the first element, then the
second, so the over run time would be on the order of

n ( n - 1 )
----------------
2

in the worse case, which basically is O(n).

like from your example
comparisons: 1 with 2, 1 with 3, 1 with 4, 2 with 3, 2 with 4, 3 with 4
(done, all combos tested). You wouldn't compare 1 with 1, 2 with 2, and
the like since they're not different indexes. worse case runtime = 1/2
n which amounts to O(n) unfortunately.

Thanks for your reply

Greg Young [MVP] wrote:
Also O(n^2) is talking about the worst case ... you have provided the best
case as a comparison ...

to compare the worst case in this problem you would actually be looking at
iterations on a miss ..

array 1,2,3,4 sum 12
array 3,2,1,4 sum 12

in the onsorted case you have O^2 (loop through all twice) .. 16

in the sorted case you would be with almost no effort at 9 comparisons on
the worst case as it would allow you to do the simple change in the original
code (use i+1 for j instead of 0)
"MSDN" <sq**********@hotmail.com> wrote in message
news:%2****************@TK2MSFTNGP03.phx.gbl...
This is Sorted
array 1,2,3,4 sum = 5

This is not Sorted
array 1,4,2,3 sum = 5

Which one is faster??

SA

"Greg Young [MVP]" <Dr*************@hotmail.com> wrote in message
news:OM*************@TK2MSFTNGP05.phx.gbl...
If the data were sorted you could do much better. If they are not sorted
you
would have n^2 as your worst case as you have to check every index of the
array for each value.

even so you could still do slightly better by only issuing a single
add/sub
instead of a operation on every iteration ... see example.

bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
int need = sum - array[j];
for (int j = 0; j < array.Length; j++)
{
if (array[j] == sum)
return true;
}
}
return false;
}

Also your code has failure modes because int j = i + 1 ... what about the
following data?

array 0,1,2 sum = 3 by using i+1 you say it doesn't exist.

Another quick question ... what should the behavior be for the following?

array 1,2,3,4 sum = 5

Cheers,

Greg

<ka**********@gmail.com> wrote in message
news:11*********************@i39g2000cwa.googlegro ups.com...
Hey all,
I was asked this question in an interview recently:

Suppose you have the method signature

bool MyPairSum(int [] array, int sum)

the array has all unique values (no repeats), your task is to find two
indices in the array whose sum equals the input parameter sum. If there
exists two entries in the array that sum together to equal the input
parameter of sum, then return true, otherwise return false. what's the
most efficient implementation?

My question is can we have a better worse case runtime of O(n) ??
I'm thinking that in the worse case, you'd have to compare each index
against all the other indices and test each sum until you find one that
matches the input sum. In the worse case, there will be no pair of
indices that equal the input sum parameter. Am I overlooking a very
basic trick? I figured with all the sharp people in here, somebody can
discern whether I'm off base or not :)

Here's the sample implementation I was thinking of:
bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
for (int j = i + 1; j < array.Length; j++)
{
if ( array[i] + array[j] == sum)
return true;
}
}
return false;
}
Tks, Karan S.



Apr 27 '06 #14
It does seem like there's no way around checking all possibilties
unless some other data structure was involved. I was trying to cut down
on comparisons/summations by eliminating the first element, then the
second, so the over run time would be on the order of

n ( n - 1 )
----------------
2

in the worse case, which basically is O(n).

like from your example
comparisons: 1 with 2, 1 with 3, 1 with 4, 2 with 3, 2 with 4, 3 with 4
(done, all combos tested). You wouldn't compare 1 with 1, 2 with 2, and
the like since they're not different indexes. worse case runtime = 1/2
n which amounts to O(n) unfortunately.

Thanks for your reply

Greg Young [MVP] wrote:
Also O(n^2) is talking about the worst case ... you have provided the best
case as a comparison ...

to compare the worst case in this problem you would actually be looking at
iterations on a miss ..

array 1,2,3,4 sum 12
array 3,2,1,4 sum 12

in the onsorted case you have O^2 (loop through all twice) .. 16

in the sorted case you would be with almost no effort at 9 comparisons on
the worst case as it would allow you to do the simple change in the original
code (use i+1 for j instead of 0)
"MSDN" <sq**********@hotmail.com> wrote in message
news:%2****************@TK2MSFTNGP03.phx.gbl...
This is Sorted
array 1,2,3,4 sum = 5

This is not Sorted
array 1,4,2,3 sum = 5

Which one is faster??

SA

"Greg Young [MVP]" <Dr*************@hotmail.com> wrote in message
news:OM*************@TK2MSFTNGP05.phx.gbl...
If the data were sorted you could do much better. If they are not sorted
you
would have n^2 as your worst case as you have to check every index of the
array for each value.

even so you could still do slightly better by only issuing a single
add/sub
instead of a operation on every iteration ... see example.

bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
int need = sum - array[j];
for (int j = 0; j < array.Length; j++)
{
if (array[j] == sum)
return true;
}
}
return false;
}

Also your code has failure modes because int j = i + 1 ... what about the
following data?

array 0,1,2 sum = 3 by using i+1 you say it doesn't exist.

Another quick question ... what should the behavior be for the following?

array 1,2,3,4 sum = 5

Cheers,

Greg

<ka**********@gmail.com> wrote in message
news:11*********************@i39g2000cwa.googlegro ups.com...
Hey all,
I was asked this question in an interview recently:

Suppose you have the method signature

bool MyPairSum(int [] array, int sum)

the array has all unique values (no repeats), your task is to find two
indices in the array whose sum equals the input parameter sum. If there
exists two entries in the array that sum together to equal the input
parameter of sum, then return true, otherwise return false. what's the
most efficient implementation?

My question is can we have a better worse case runtime of O(n) ??
I'm thinking that in the worse case, you'd have to compare each index
against all the other indices and test each sum until you find one that
matches the input sum. In the worse case, there will be no pair of
indices that equal the input sum parameter. Am I overlooking a very
basic trick? I figured with all the sharp people in here, somebody can
discern whether I'm off base or not :)

Here's the sample implementation I was thinking of:
bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
for (int j = i + 1; j < array.Length; j++)
{
if ( array[i] + array[j] == sum)
return true;
}
}
return false;
}
Tks, Karan S.



Apr 27 '06 #15
Did you mean to type

int need = sum - array[ i ];

??
On Thu, 27 Apr 2006 00:47:56 -0400, "Greg Young [MVP]"
<Dr*************@hotmail.com> wrote:
I think you are missing the point about the subtraction part ..

You lower your constant by using the code as I wrote it .. by doing the
subtraction up front you avoid doing the additions.

on a given iteration yours ... is j comparisons + j additions .. mine is j
comparisons + 1 subtraction.

bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
int need = sum - array[j];
for (int j = i+1; j < array.Length; j++)
{
if (array[j] == need)
return true;
}
}
return false;
}

Another interesting question is how much data is being passed into this and
how often to you expect to be in your worst case? Since the data if sorted
can be done in linear time, if you expected to be in your worst case (miss)
most of the time with rather large datasets being passed in it might be
worth while to take a look at sorting the data first as it could end up
lowerring your average case.

Greg
<ka**********@gmail.com> wrote in message
news:11**********************@g10g2000cwb.googleg roups.com...
The array isn't sorted I believe, just no dupes.Also, it just checks if
two indexes summed equals sum like array[3] + array[33] = sum !!

Thanks for your input though :)
Greg Young [MVP] wrote:
If the data were sorted you could do much better. If they are not sorted
you
would have n^2 as your worst case as you have to check every index of the
array for each value.

even so you could still do slightly better by only issuing a single
add/sub
instead of a operation on every iteration ... see example.

bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
int need = sum - array[j];
for (int j = 0; j < array.Length; j++)
{
if (array[j] == sum)
return true;
}
}
return false;
}

Also your code has failure modes because int j = i + 1 ... what about the
following data?

array 0,1,2 sum = 3 by using i+1 you say it doesn't exist.

Another quick question ... what should the behavior be for the following?

array 1,2,3,4 sum = 5

Cheers,

Greg

<ka**********@gmail.com> wrote in message
news:11*********************@i39g2000cwa.googlegro ups.com...
Hey all,
I was asked this question in an interview recently:

Suppose you have the method signature

bool MyPairSum(int [] array, int sum)

the array has all unique values (no repeats), your task is to find two
indices in the array whose sum equals the input parameter sum. If there
exists two entries in the array that sum together to equal the input
parameter of sum, then return true, otherwise return false. what's the
most efficient implementation?

My question is can we have a better worse case runtime of O(n) ??
I'm thinking that in the worse case, you'd have to compare each index
against all the other indices and test each sum until you find one that
matches the input sum. In the worse case, there will be no pair of
indices that equal the input sum parameter. Am I overlooking a very
basic trick? I figured with all the sharp people in here, somebody can
discern whether I'm off base or not :)

Here's the sample implementation I was thinking of:
bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
for (int j = i + 1; j < array.Length; j++)
{
if ( array[i] + array[j] == sum)
return true;
}
}
return false;
}
Tks, Karan S.

Apr 27 '06 #16
I guess in my code, the unSorted one would be faster in this specific
test case :). I'm trying to think of way to implement some pre-made
data structure in .NET where you'd add each value to it as you pass
through the array, then query against the structure somehow. Although,
this would a best case run time of one pass and adding to the data
structure (cn) and the cost of querying the data structure (c). This
should result in a run time of cn. Then again, the time cost of the
data structure may be quite big too. I was thinking of something like a
SortedList and then going from there. This interview question may have
more of a way to see how I approach problems than what sort of
solutions I come up with.

Thanks for your reply!
MSDN wrote:
This is Sorted
array 1,2,3,4 sum = 5

This is not Sorted
array 1,4,2,3 sum = 5

Which one is faster??

SA

"Greg Young [MVP]" <Dr*************@hotmail.com> wrote in message
news:OM*************@TK2MSFTNGP05.phx.gbl...
If the data were sorted you could do much better. If they are not sorted
you
would have n^2 as your worst case as you have to check every index of the
array for each value.

even so you could still do slightly better by only issuing a single
add/sub
instead of a operation on every iteration ... see example.

bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
int need = sum - array[j];
for (int j = 0; j < array.Length; j++)
{
if (array[j] == sum)
return true;
}
}
return false;
}

Also your code has failure modes because int j = i + 1 ... what aboutthe
following data?

array 0,1,2 sum = 3 by using i+1 you say it doesn't exist.

Another quick question ... what should the behavior be for the following?

array 1,2,3,4 sum = 5

Cheers,

Greg

<ka**********@gmail.com> wrote in message
news:11*********************@i39g2000cwa.googlegro ups.com...
Hey all,
I was asked this question in an interview recently:

Suppose you have the method signature

bool MyPairSum(int [] array, int sum)

the array has all unique values (no repeats), your task is to find two
indices in the array whose sum equals the input parameter sum. If there
exists two entries in the array that sum together to equal the input
parameter of sum, then return true, otherwise return false. what's the
most efficient implementation?

My question is can we have a better worse case runtime of O(n) ??
I'm thinking that in the worse case, you'd have to compare each index
against all the other indices and test each sum until you find one that
matches the input sum. In the worse case, there will be no pair of
indices that equal the input sum parameter. Am I overlooking a very
basic trick? I figured with all the sharp people in here, somebody can
discern whether I'm off base or not :)

Here's the sample implementation I was thinking of:
bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
for (int j = i + 1; j < array.Length; j++)
{
if ( array[i] + array[j] == sum)
return true;
}
}
return false;
}
Tks, Karan S.


Apr 27 '06 #17
Yeah its getting late, I just cant type that example in correctly.
"Michael H." <m@m.m> wrote in message
news:hc********************************@4ax.com...
Did you mean to type

int need = sum - array[ i ];

??
On Thu, 27 Apr 2006 00:47:56 -0400, "Greg Young [MVP]"
<Dr*************@hotmail.com> wrote:
I think you are missing the point about the subtraction part ..

You lower your constant by using the code as I wrote it .. by doing the
subtraction up front you avoid doing the additions.

on a given iteration yours ... is j comparisons + j additions .. mine is j
comparisons + 1 subtraction.

bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
int need = sum - array[j];
for (int j = i+1; j < array.Length; j++)
{
if (array[j] == need)
return true;
}
}
return false;
}

Another interesting question is how much data is being passed into this
and
how often to you expect to be in your worst case? Since the data if sorted
can be done in linear time, if you expected to be in your worst case
(miss)
most of the time with rather large datasets being passed in it might be
worth while to take a look at sorting the data first as it could end up
lowerring your average case.

Greg
<ka**********@gmail.com> wrote in message
news:11**********************@g10g2000cwb.google groups.com...
The array isn't sorted I believe, just no dupes.Also, it just checks if
two indexes summed equals sum like array[3] + array[33] = sum !!

Thanks for your input though :)
Greg Young [MVP] wrote:
If the data were sorted you could do much better. If they are not sorted
you
would have n^2 as your worst case as you have to check every index of
the
array for each value.

even so you could still do slightly better by only issuing a single
add/sub
instead of a operation on every iteration ... see example.

bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
int need = sum - array[j];
for (int j = 0; j < array.Length; j++)
{
if (array[j] == sum)
return true;
}
}
return false;
}

Also your code has failure modes because int j = i + 1 ... what about
the
following data?

array 0,1,2 sum = 3 by using i+1 you say it doesn't exist.

Another quick question ... what should the behavior be for the
following?

array 1,2,3,4 sum = 5

Cheers,

Greg

<ka**********@gmail.com> wrote in message
news:11*********************@i39g2000cwa.googlegro ups.com...
Hey all,
I was asked this question in an interview recently:

Suppose you have the method signature

bool MyPairSum(int [] array, int sum)

the array has all unique values (no repeats), your task is to find two
indices in the array whose sum equals the input parameter sum. If there
exists two entries in the array that sum together to equal the input
parameter of sum, then return true, otherwise return false. what's the
most efficient implementation?

My question is can we have a better worse case runtime of O(n) ??
I'm thinking that in the worse case, you'd have to compare each index
against all the other indices and test each sum until you find one that
matches the input sum. In the worse case, there will be no pair of
indices that equal the input sum parameter. Am I overlooking a very
basic trick? I figured with all the sharp people in here, somebody can
discern whether I'm off base or not :)

Here's the sample implementation I was thinking of:
bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
for (int j = i + 1; j < array.Length; j++)
{
if ( array[i] + array[j] == sum)
return true;
}
}
return false;
}
Tks, Karan S.

Apr 27 '06 #18
As you mention that this is an interview question ...

My guess is that they were looking to see how you approached the problem
(and what questions you asked like "is the data sorted", "What's the general
usage of the method i.e. 3 items vs 300")

All of those items have alot to do with how you would want to implement the
routine.
<ka**********@gmail.com> wrote in message
news:11*********************@y43g2000cwc.googlegro ups.com...
I guess in my code, the unSorted one would be faster in this specific
test case :). I'm trying to think of way to implement some pre-made
data structure in .NET where you'd add each value to it as you pass
through the array, then query against the structure somehow. Although,
this would a best case run time of one pass and adding to the data
structure (cn) and the cost of querying the data structure (c). This
should result in a run time of cn. Then again, the time cost of the
data structure may be quite big too. I was thinking of something like a
SortedList and then going from there. This interview question may have
more of a way to see how I approach problems than what sort of
solutions I come up with.

Thanks for your reply!
MSDN wrote:
This is Sorted
array 1,2,3,4 sum = 5

This is not Sorted
array 1,4,2,3 sum = 5

Which one is faster??

SA

"Greg Young [MVP]" <Dr*************@hotmail.com> wrote in message
news:OM*************@TK2MSFTNGP05.phx.gbl...
If the data were sorted you could do much better. If they are not sorted
you
would have n^2 as your worst case as you have to check every index of
the
array for each value.

even so you could still do slightly better by only issuing a single
add/sub
instead of a operation on every iteration ... see example.

bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
int need = sum - array[j];
for (int j = 0; j < array.Length; j++)
{
if (array[j] == sum)
return true;
}
}
return false;
}

Also your code has failure modes because int j = i + 1 ... what about
the
following data?

array 0,1,2 sum = 3 by using i+1 you say it doesn't exist.

Another quick question ... what should the behavior be for the
following?

array 1,2,3,4 sum = 5

Cheers,

Greg

<ka**********@gmail.com> wrote in message
news:11*********************@i39g2000cwa.googlegro ups.com...
Hey all,
I was asked this question in an interview recently:

Suppose you have the method signature

bool MyPairSum(int [] array, int sum)

the array has all unique values (no repeats), your task is to find two
indices in the array whose sum equals the input parameter sum. If there
exists two entries in the array that sum together to equal the input
parameter of sum, then return true, otherwise return false. what's the
most efficient implementation?

My question is can we have a better worse case runtime of O(n) ??
I'm thinking that in the worse case, you'd have to compare each index
against all the other indices and test each sum until you find one that
matches the input sum. In the worse case, there will be no pair of
indices that equal the input sum parameter. Am I overlooking a very
basic trick? I figured with all the sharp people in here, somebody can
discern whether I'm off base or not :)

Here's the sample implementation I was thinking of:
bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
for (int j = i + 1; j < array.Length; j++)
{
if ( array[i] + array[j] == sum)
return true;
}
}
return false;
}
Tks, Karan S.

Apr 27 '06 #19
SP
"Greg Young [MVP]" <Dr*************@hotmail.com> wrote in message
news:OM*************@TK2MSFTNGP05.phx.gbl...
If the data were sorted you could do much better. If they are not sorted
you
would have n^2 as your worst case as you have to check every index of the
array for each value.
How would sorted data change things?

even so you could still do slightly better by only issuing a single
add/sub
instead of a operation on every iteration ... see example.

bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
int need = sum - array[j];
for (int j = 0; j < array.Length; j++)
{
if (array[j] == sum)
return true;
}
}
return false;
}

Also your code has failure modes because int j = i + 1 ... what about the
following data?
int j = i + 1 does not cause a failure. It avoids comparing a number against
itself which you do in your example. In your example you would return True
incorrectly with 0,2,3 sum = 4

array 0,1,2 sum = 3 by using i+1 you say it doesn't exist.
Original return True correctly

Another quick question ... what should the behavior be for the following?

array 1,2,3,4 sum = 5
Same here

Cheers,

Greg

<ka**********@gmail.com> wrote in message
news:11*********************@i39g2000cwa.googlegro ups.com...
Hey all,
I was asked this question in an interview recently:

Suppose you have the method signature

bool MyPairSum(int [] array, int sum)

the array has all unique values (no repeats), your task is to find two
indices in the array whose sum equals the input parameter sum. If there
exists two entries in the array that sum together to equal the input
parameter of sum, then return true, otherwise return false. what's the
most efficient implementation?

My question is can we have a better worse case runtime of O(n) ??
I'm thinking that in the worse case, you'd have to compare each index
against all the other indices and test each sum until you find one that
matches the input sum. In the worse case, there will be no pair of
indices that equal the input sum parameter. Am I overlooking a very
basic trick? I figured with all the sharp people in here, somebody can
discern whether I'm off base or not :)

Here's the sample implementation I was thinking of:
bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
for (int j = i + 1; j < array.Length; j++)
{
if ( array[i] + array[j] == sum)
return true;
}
}
return false;
}
Tks, Karan S.

Apr 27 '06 #20
"Greg Young [MVP]" <Dr*************@hotmail.com> wrote in message
news:es**************@TK2MSFTNGP04.phx.gbl...
As you mention that this is an interview question ...

My guess is that they were looking to see how you approached the problem (and what questions you
asked like "is the data sorted", "What's the general usage of the method i.e. 3 items vs 300")

All of those items have alot to do with how you would want to implement the routine.


I would *hope* that this was the interviewer's intent.
Asking "what's the most efficient implementation?" is a loaded question.

Is the data sorted?
Is it OK to sort the data, or do we need to copy the Array and sort that?
Is the array so large that copying it causes memory issues?
Is the data set small enough that O(N), O(NlogN) etc not come into play?

What does the actual data normally look like? (let me Splain)
If the data has very few gaps in it a brute force approach might be fastest.
Example: Data = all integers from 1-100 Sum = 101
One pass through the data will suffice to find a valid result.

OK, this is an extreme example, but if the data has few gaps, you will tend to get multiple valid
solutions to the problem. In the example above there are 100 pairs that add up to 101 (assuming
(x,y) is different from (y,x))

Thus a brute force search can succeed, possibly faster that the sort

Anyway....food for thought
Bill
Apr 27 '06 #21
Why sorted data? - Well sorted data would allow it to be done in O(n) to
start with ...

I already retracted the i+1 above.

This question - array 1,2,3,4 sum = 5 is because there are 2 answers.
"SP" <ec***********@hotmail.com> wrote in message
news:eC**************@TK2MSFTNGP05.phx.gbl...
"Greg Young [MVP]" <Dr*************@hotmail.com> wrote in message
news:OM*************@TK2MSFTNGP05.phx.gbl...
If the data were sorted you could do much better. If they are not sorted
you
would have n^2 as your worst case as you have to check every index of the
array for each value.


How would sorted data change things?

even so you could still do slightly better by only issuing a single
add/sub
instead of a operation on every iteration ... see example.

bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
int need = sum - array[j];
for (int j = 0; j < array.Length; j++)
{
if (array[j] == sum)
return true;
}
}
return false;
}

Also your code has failure modes because int j = i + 1 ... what about the
following data?


int j = i + 1 does not cause a failure. It avoids comparing a number
against itself which you do in your example. In your example you would
return True incorrectly with 0,2,3 sum = 4

array 0,1,2 sum = 3 by using i+1 you say it doesn't exist.


Original return True correctly

Another quick question ... what should the behavior be for the following?

array 1,2,3,4 sum = 5


Same here

Cheers,

Greg

<ka**********@gmail.com> wrote in message
news:11*********************@i39g2000cwa.googlegro ups.com...
Hey all,
I was asked this question in an interview recently:

Suppose you have the method signature

bool MyPairSum(int [] array, int sum)

the array has all unique values (no repeats), your task is to find two
indices in the array whose sum equals the input parameter sum. If there
exists two entries in the array that sum together to equal the input
parameter of sum, then return true, otherwise return false. what's the
most efficient implementation?

My question is can we have a better worse case runtime of O(n) ??
I'm thinking that in the worse case, you'd have to compare each index
against all the other indices and test each sum until you find one that
matches the input sum. In the worse case, there will be no pair of
indices that equal the input sum parameter. Am I overlooking a very
basic trick? I figured with all the sharp people in here, somebody can
discern whether I'm off base or not :)

Here's the sample implementation I was thinking of:
bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
for (int j = i + 1; j < array.Length; j++)
{
if ( array[i] + array[j] == sum)
return true;
}
}
return false;
}
Tks, Karan S.


Apr 27 '06 #22
One change to this (actually the problem was in every one)

bool MyPairSum(int [] array, int sum)
{
for (int i = 0; i < array.Length -1; i++)
{
int need = sum - array[j];
for (int j = i+1; j < array.Length; j++)
{
if (array[j] == need)
return true;
}
}
return false;
}

Without the "array.Length -1" in the "for (i=" line, j would equal
Length+1, and "array[j]" would blow up (except we would actually enter
the second for()), but we would go through the outer loop one more time
than necessary --- and our goal *is* to be the most efficient.

Apr 27 '06 #23
Here is a minor adaptation that may save some iterations depending upon
the sum you're asking for and what data is in the array. Starting with
James Curran's code:

bool MyPairSum(int [] array, int sum)
{
if (array.Length == 0) { return false; }

int minValue = array[0];
int maxValue = array[0];
int need;

// Do the first pass through the array
need = sum - array[0];
for (int j = 1; j < array.Length; j++)
{
if (array[j] == need) { return true; }
if (array[j] < minValue) minValue = array[j];
if (array[j] > maxValue) maxValue = array[k];
}

// Now do the rest
for (int i = 1; i < array.Length -1; i++)
{
need = sum - array[j];
if (minValue <= need && need <= maxValue)
{
for (int j = i+1; j < array.Length; j++)
{
if (array[j] == need)
return true;
}
}
}
return false;
}

This eliminates cases in which the value at array[i] is such that no
value in the array could possibly combine with it to sum to "sum". If
the array contents were sufficiently disparate this could save time.

Of course, if the array contents and the sum are such that almost any
pair of values could potentially sum to "sum" then the additional test
adds two comparisons and an && operation to the cost.

Apr 27 '06 #24

In addition possibly you can add some "History-Efficiency-Metrics" of
previous executions and predict or guestimate an algorithm to use.
at times it could be the wrong algorithm efficiency wise.
This is done in Microprocessors today when doing look ahead calculations.
Basically you are processing op-code ahead of time predicting that the
processing logic might need the look-ahead calculation.

SA

"Bruce Wood" <br*******@canada.com> wrote in message
news:11*********************@e56g2000cwe.googlegro ups.com...
Here is a minor adaptation that may save some iterations depending upon
the sum you're asking for and what data is in the array. Starting with
James Curran's code:

bool MyPairSum(int [] array, int sum)
{
if (array.Length == 0) { return false; }

int minValue = array[0];
int maxValue = array[0];
int need;

// Do the first pass through the array
need = sum - array[0];
for (int j = 1; j < array.Length; j++)
{
if (array[j] == need) { return true; }
if (array[j] < minValue) minValue = array[j];
if (array[j] > maxValue) maxValue = array[k];
}

// Now do the rest
for (int i = 1; i < array.Length -1; i++)
{
need = sum - array[j];
if (minValue <= need && need <= maxValue)
{
for (int j = i+1; j < array.Length; j++)
{
if (array[j] == need)
return true;
}
}
}
return false;
}

This eliminates cases in which the value at array[i] is such that no
value in the array could possibly combine with it to sum to "sum". If
the array contents were sufficiently disparate this could save time.

Of course, if the array contents and the sum are such that almost any
pair of values could potentially sum to "sum" then the additional test
adds two comparisons and an && operation to the cost.

Apr 27 '06 #25
>> After all, O(n)+O(n.log n) = O(n.log n).

Um... Not really. Or, should I say, "Only in th emost theortic case".
Remember the "O(X)" translates to "time = X*C + K".

Hence you are arguing that "n*Clinearsearch + Klinearsearch +
(n.log.n)*Csort +Ksort) < (n*n) *Csearch + Ksearch)"

The problem is the Csort is *so much* greater than Csearch, n would
have to be turly massive before it becomes the domain factor in the
formula.

e.g., let's assume all the Ks are 0, and Clinearseach == Csearch, then
we get
n*Csearch + (n.log.n)*CSort < (n*n)*Csearch

However, the simple search really isn't n*n, it's (n*(n+1))/2, which
regrouped equas
n*Csearch + (n*CSort) * (log.n) < (n * (n+1)*Csearch) /2

Multply by 2
2*n*Csearch + 2*(n*CSort) * (log.n)< (n * (n-1)*Csearch)

Subtract 2*n*Csearch
2 * n * CSort * log.n < n * (n-3)*Csearch

divide by n:
2 * log.n *CSort < (n-3) * Csearch

Putting that all together,
if CSort == CSearch, sort first is faster when n >=7
if CSort == CSearch*10, sort first is faster when n >=94
if CSort == CSearch*100, sort first is faster when n >=1461
if CSort == CSearch*1000, sort first is faster when n >=19789

Now, considering the Csearch here is simply one comparison, and Csort
involves spliting, joining, comparing & copying array elements, 1:1000
ratio is not out of the question.

Apr 27 '06 #26
As Michael H pointed out above, that should be:

need = sum - array[i];

not

need = sum - array[j];

Apr 27 '06 #27
As was pointed out by some of the other posters, the best algorithm
depends on the number of items in the array. Unless it is specifically
mentioned in the question it is usually best that the algorithm should
work with any indata size and therefore, the O() is the easiest thing
to look at.

An O(n*log n) solution has been posted in this thread. It consists of
cloning the array, sorting it and finally traverse at it from both
ends. Here is some sample code for it:

public static bool MyPairSumSorted(int[] array2, int sum)
{
int[] array = (int[])array2.Clone();
Array.Sort(array);
int i1 = 0;
int i2 = array.Length - 1;

while (i1 != i2)
{
int compare = array[i1] + array[i2] - sum;
if (compare < 0)
{
i1++;
}
else if (compare > 0)
{
i2--;
}
else
return true;
}

return false;
}

If the indata array is small, it will however be more efficent to use
your method and avoid sorting. It will perform significantly when the
indata is small.

public static bool MyPairSum(int[] array, int sum)
{
for (int i = 0; i < array.Length; i++)
{
int need = sum - array[i];
for (int j = i+1; j < array.Length; j++)
{
if (array[j] == need)
return true;
}
}
return false;
}

The point where both method perform equally well seems to be when the
array contains a little more than 100 items.

Finally there is a meta method that is often used when an algorithm
performs well with large data and less well with small data. You
basically use the best of both worlds. It basically looks like this.

const int cutoffPoint = 110;

public static bool MyPairSumBoth(int[] array, int sum)
{
if(array.Length > cutoffPoint)
MyPairSumSorted(array,sum);
else
MyPairSum(array,sum);
}

This will use the method that is best for the specific array. The
disadvantage off this method is that it uses more code since both
solutions has to be provided, but it can work efficently with any data
size.

--
Marcus Andrn
Apr 27 '06 #28

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