distribution algorithm question

[Koen]

Hi,

I am looking for an algorithm that figures out which numbers from a
given set add up to another number. I am sure this has been done
before, but I have no idea how such a calculation is called, which
kind of limits my further searching.

An example. The set contains the numbers 1-2-3-4-5. Now the algorithm
should calculate all possible combinations of these numbers that add
up to 10. Each number can be used more than one time or not at all.

possible solutions are:

10 x 1
5 x 2
3 x 2 + 4
1 + 4 + 5
2 + 3 + 5
1 + 2 + 3 + 4

etc.


In this case it's pretty easy to do it on paper, but when the numbers
become larger (>1000) it would be nice to have a program to do this.


Any suggestions how to do this and/or where to start looking ?


thanks,

- Koen.

 

[Thomas Matthews]

Hi,

I am looking for an algorithm that figures out which numbers from a
given set add up to another number. I am sure this has been done
before, but I have no idea how such a calculation is called, which
kind of limits my further searching.

Are you talking addition or multiplication or both?
The above paragraph talks about addition, but the solutions show
multiplication.

An example. The set contains the numbers 1-2-3-4-5. Now the algorithm
should calculate all possible combinations of these numbers that add
up to 10. Each number can be used more than one time or not at all.

Again, you state addition, but the example shows multiplication.
What is exact definition of the problem?

possible solutions are:

10 x 1
5 x 2
3 x 2 + 4
1 + 4 + 5
2 + 3 + 5
1 + 2 + 3 + 4

etc.

Let us see, the first solution is invalid according to the given rules.
"10 x 1" is not a solution because the number "10" is not a member of
the set [1,2,3,4,5].

According to your problem definition, the first three solutions:
10 x 1
5 x 2
3 x 2 + 4
are all invalid solutions since they involve multiplication.

In this case it's pretty easy to do it on paper, but when the numbers
become larger (>1000) it would be nice to have a program to do this.

As I've been thinking about this problem, it is not easy.
The given solution set does not match the problem definition.
The number of solutions involving mulitiplication is not a finitie
set, given the rule that any number may be used more than once and
the rule of multiplication by 1.

Addition, on the other hand, is a finite set, as long a zero is not
within the set. The rule of addition with zero provides an infinite
quantity of terms for a solution.

Any suggestions how to do this and/or where to start looking ?

Yes, get your problem definition correct before proceeding.
Start looking at:
combinatorics
recursion
linked list
stack
Identity Theorum for Multiplication
Identity Theorum for Addition
Programming loop constructs.
Greatest Common Factor (GCF)
Lowest Common Denominator (LCD)
logarithms (sp?)
Series expansion

If this is homework, slap your instructor and say "bad assignment"
then ramble off the Identity Theorums and say this is a never
ending waste of computer cycles (the same as an infinite loop).

thanks,

- Koen.

I would first start out with either multiplication or addition and
get them working. The multiplication with addition adds more
complexity to the function (as well as combinations).

Since "Each number can be used more than one time",
how does one know when to stop?
For example,
5 x 2
5 x 2 x 1
5 x 2 x 1 x 1
5 x 2 x 1 x 1 x 1 ...

 

[Ivan Vecerina]

| I am looking for an algorithm that figures out which numbers from a
| given set add up to another number. I am sure this has been done
| before, but I have no idea how such a calculation is called, which
| kind of limits my further searching.
|
| An example. The set contains the numbers 1-2-3-4-5. Now the algorithm
| should calculate all possible combinations of these numbers that add
| up to 10. Each number can be used more than one time or not at all.
.....
| In this case it's pretty easy to do it on paper, but when the numbers
| become larger (>1000) it would be nice to have a program to do this.
.....
| Any suggestions how to do this and/or where to start looking ?

Not really a question about C... but anyway:

A somewhat similar classic is the "knapsack problem".
A classic approach to solve this type of thing is "Dynamic programming".
(NB: this is not about dynamic code generation, 'programming' is
to be taken in a mathematical sense).

Googling for these terms should take you in the right direction.


I hope this helps,
Ivan

 

[Fred L. Kleinschmidt]

Hi,

I am looking for an algorithm that figures out which numbers from a
given set add up to another number. I am sure this has been done
before, but I have no idea how such a calculation is called, which
kind of limits my further searching.

Are you talking addition or multiplication or both?
The above paragraph talks about addition, but the solutions show
multiplication.

An example. The set contains the numbers 1-2-3-4-5. Now the algorithm
should calculate all possible combinations of these numbers that add
up to 10. Each number can be used more than one time or not at all.

Again, you state addition, but the example shows multiplication.
What is exact definition of the problem?

possible solutions are:

10 x 1
5 x 2
3 x 2 + 4
1 + 4 + 5
2 + 3 + 5
1 + 2 + 3 + 4

etc.

Let us see, the first solution is invalid according to the given rules.
"10 x 1" is not a solution because the number "10" is not a member of
the set [1,2,3,4,5].

According to your problem definition, the first three solutions:
10 x 1
5 x 2
3 x 2 + 4
are all invalid solutions since they involve multiplication.

In this case it's pretty easy to do it on paper, but when the numbers
become larger (>1000) it would be nice to have a program to do this.

As I've been thinking about this problem, it is not easy.
The given solution set does not match the problem definition.
The number of solutions involving mulitiplication is not a finitie
set, given the rule that any number may be used more than once and
the rule of multiplication by 1.

Addition, on the other hand, is a finite set, as long a zero is not
within the set. The rule of addition with zero provides an infinite
quantity of terms for a solution.

Any suggestions how to do this and/or where to start looking ?

Yes, get your problem definition correct before proceeding.
Start looking at:
combinatorics
recursion
linked list
stack
Identity Theorum for Multiplication
Identity Theorum for Addition
Programming loop constructs.
Greatest Common Factor (GCF)
Lowest Common Denominator (LCD)
logarithms (sp?)
Series expansion

If this is homework, slap your instructor and say "bad assignment"
then ramble off the Identity Theorums and say this is a never
ending waste of computer cycles (the same as an infinite loop).

thanks,

- Koen.

I would first start out with either multiplication or addition and
get them working. The multiplication with addition adds more
complexity to the function (as well as combinations).

Since "Each number can be used more than one time",
how does one know when to stop?
For example,
5 x 2
5 x 2 x 1
5 x 2 x 1 x 1
5 x 2 x 1 x 1 x 1 ...

--
Thomas Matthews
C Faq: http://www.eskimo.com/~scs/c-faq/top.html
alt.comp.lang.learn.c-c++ faq:
http://www.raos.demon.uk/acllc-c++/faq.html

Aw, come on!
It seems obvious that the original posting
10x1
is just a shorthand for saying "1+1+1+1+1+1+1+1+1+1"
and was not meant to say that multiplication was part of the deal.

 

[Koen]

A somewhat similar classic is the "knapsack problem".
A classic approach to solve this type of thing is "Dynamic programming".
(NB: this is not about dynamic code generation, 'programming' is
to be taken in a mathematical sense).

Googling for these terms should take you in the right direction.


I hope this helps,
Ivan

Thanks Ivan for a grown-up response I will look into the knapsack
problem.

- Koen.

 

[Koen]

Are you talking addition or multiplication or both?
The above paragraph talks about addition, but the solutions show
multiplication.

If this is homework, slap your instructor and say "bad assignment"
then ramble off the Identity Theorums and say this is a never
ending waste of computer cycles (the same as an infinite loop).

Sorry Thomas, I don't understand your replies. I am glad another reader
gave a more mature reply and pointed me in the correct direction (my
problem is similar to the 'knapsack problem').


have a nice day,

- Koen.