Formula calculation C# code needed

[GB]

Hello,
How to calculate value for the following formula (I need C# code):

res = (((m+1)(m+2)... (m+(k-1)))/1.2...(k-1))

or more generalized formula is:

k-1
__
| | (m+i)
i=1
res = ---------------
k-1
__
| | i
i=1
Thanks,
GB

[Jon Skeet [C# MVP]]

GB <ge*****@telus. netwrote:

Hello,
How to calculate value for the following formula (I need C# code):

res = (((m+1)(m+2)... (m+(k-1)))/1.2...(k-1))

or more generalized formula is:

k-1
__
| | (m+i)
i=1
res = ---------------
k-1
__
| | i
i=1

Well, why not just do the calculation in a loop? Loop round doing the
multiplication, then loop round doing the division. You'll lose a fair
amount of precision, but that may be okay depending on what your use
is...

--
Jon Skeet - <sk***@pobox.co m>
http://www.pobox.com/~skeet Blog: http://www.msmvps.com/jon.skeet
If replying to the group, please do not mail me too

[GB]

Please, give me an example.

GB
"Jon Skeet [C# MVP]" <sk***@pobox.co mwrote in message
news:MP******** *************** @msnews.microso ft.com...

GB <ge*****@telus. netwrote:

>Hello,
How to calculate value for the following formula (I need C# code):

res = (((m+1)(m+2)... (m+(k-1)))/1.2...(k-1))

or more generalized formula is:

k-1
__
| | (m+i)
i=1
res = ---------------
k-1
__
| | i
i=1

Well, why not just do the calculation in a loop? Loop round doing the
multiplication, then loop round doing the division. You'll lose a fair
amount of precision, but that may be okay depending on what your use
is...

--
Jon Skeet - <sk***@pobox.co m>
http://www.pobox.com/~skeet Blog: http://www.msmvps.com/jon.skeet
If replying to the group, please do not mail me too

[Ben Newsam]

On Wed, 30 Aug 2006 06:26:21 GMT, "GB" <ge*****@telus. netwrote:

>Please, give me an example.

GB
"Jon Skeet [C# MVP]" <sk***@pobox.co mwrote in message
news:MP******* *************** *@msnews.micros oft.com...

>GB <ge*****@telus. netwrote:

>>Hello,
How to calculate value for the following formula (I need C# code):

res = (((m+1)(m+2)... (m+(k-1)))/1.2...(k-1))

or more generalized formula is:

k-1
__
| | (m+i)
i=1
res = ---------------
k-1
__
| | i
i=1

Let me get this right...

In your example, say, if m=3 and k=10, and i=1 (is i *always* 1?),
then you need to calculate:

(4.5.6.7.8.9) / (1.2.3.4.5.6.7. 8.9), which works out at 0.16667 (same
as 1/6)

and m=4 and k=9 would be (5.6.7.8)/(1.2.3.4.5.6.7. 8), which is
0.041667

If this is correct, then I would do it recursively:
long MyFunc ( long n, long Limit, long i )
{
long Result = n;
if ( n <= Limit )
return Result;
return ( n * MyFunc ( n - i, Limit, i ) );
}

Then you can do:

long k = 10;
long m = 3;
long i = 1;
double res1 = 0.0, res2 = 0.0;
double result = 0.0;

res1 = (double) MyFunc(k - 1, m + 1, i);
res2 = (double) MyFunc(k - 1, 1, 1);
result = res1 / res2;

and
k = 9;
m = 4;
res1 = (double) MyFunc(k - 1, m + 1, i);
res2 = (double) MyFunc(k - 1, 1, 1);
result = res1 / res2;

The last one gives 0.041666...664
Oh well, it's close.

--
Posted via a free Usenet account from http://www.teranews.com

[DaanishRumani]

I would do it this way.

// Numerator
double Pi_MplusI(int start, int end, int m)
{
double result = 1.0;

if(start end)
{
// swap start and end
int temp = start;
start = end;
end = temp;
}

if(start == end)
{
// not sure about this!!!
return 1.0;
}

for(int i= start; i < end; ++i)
{
result *= m + i;
}

return result;
}

// Denominator
double Pi_I(int start, int end)
{
double result = 1.0;

if(start end)
{
// swap start and end
int temp = start;
start = end;
end = temp;
}

if(start == end)
{
// not sure about this!!!
return 1.0;
}

for(int i= start; i < end; ++i)
{
result *= i;
}

return result;
}

// Result
double res(int i, int m)
{
double result = 1.0;
int i;
int k;
int m;

// get your values here
i = 1;
k = 10;
m = 100;

result = Pi_MplusI(1, k) / Pi_I(1, k);

return result;
}

[Marc Gravell]

actually, if my math is right that would be 4.5.6.7.8.9.10. 11.12 /
1.2.3.4.5.6.7.8 .9, leaving 10.11.12 / 1.2.3, leaving 220 [i is just the
product-indexer in the range 1 to k-1 inclusive]

Perhaps the trick here is to look for those terms that are not cancelled;
you could probably do this by looking at the figures and doing a lot of
thinking, but you'd need to think for each and every formula; how about this
instead? It detects cancelled terms before they are multiplied (reducing
both rounding error and the FLOP count), and could be applied to any such
formula.

Marc

class Product {
// dictionary key is the factor, value is the power
readonly Dictionary<int, intfactors = new Dictionary<int, int>();
public void Multiply(int factor) {
int power;
factors.TryGetV alue(factor, out power);
factors[factor] = power + 1;
}
public void Divide(int quotient) {
int power;
factors.TryGetV alue(quotient, out power);
factors[quotient] = power - 1;
}
public double Evaluate() {
// could also perhaps do with logarithms?
double result = 1.0;
foreach (KeyValuePair<i nt, intpair in factors) {
int power = pair.Value;
if (power == 0) continue; // nothing to do
result *= Math.Pow(pair.K ey, power);
}
return result;
}

}
static class Program {
static void Main() {
int k = 10, m = 3;
Product p = new Product();
// could actually do both loops at once, but
// keep it simple for easy re-use with different
// maths...
for(int i = 1; i <= k - 1; i++) {
p.Multiply(m+i) ;
}
for (int i = 1; i <= k - 1; i++) {
p.Divide(i);
}
MessageBox.Show (p.Evaluate().T oString());
}
}

[Marc Gravell]

Some refinements below:
* handles zero multipliers much more efficiently (short-circuits everything)
* throws exception on zero quotients
* tracks "sign" separately, so that -17 can cancel 17
* discards "unit" (but tracks sign)
* performs single * and / directly, to avoid a Math.Pow() call

Marc

class Product {
readonly Dictionary<int, intfactors = new Dictionary<int, int>();
bool zero = false, negate = false;
public void Multiply(int factor) {
if (zero) return;
if (factor == 0) {
zero = true;
factors.Clear() ;
return; // all over
}
if (factor < 0) {
negate = !negate;
factor = -factor;
}
if (factor == 1) { // unit
return; // nothing more to do
}
int power;
factors.TryGetV alue(factor, out power);
factors[factor] = power + 1;
}
public void Divide(int quotient) {
if (quotient == 0) throw new DivideByZeroExc eption();
if (zero) return;
if (quotient < 0) {
negate = !negate;
quotient = -quotient;
}
if (quotient == 1) { // unit
return; // nothing more to do
}
int power;
factors.TryGetV alue(quotient, out power);
factors[quotient] = power - 1;
}
public double Evaluate() {
if (zero) return 0;
// could also perhaps do with logarithms?
double result = 1.0;
foreach (KeyValuePair<i nt, intpair in factors) {
int factor = pair.Key, power = pair.Value;
switch (power) {
case 0: break; // do nothing (cancelled factor)
case 1: result *= factor; break; // single mult
case -1: result /= factor; break; // single div
default: result *= Math.Pow(factor , power); break; //
everything else
}
}
return negate ? -result : result;
}
}

[Rick Lones]

So you are evalulating C(m+k-1, k-1), the number of combinations of (m+k-1)
things taken (k-1) at a time, correct?

Then you want:

Prod((m+1),(m+k-1)) / Prod(1, (k-1)), where:

(warning, untested code!)

long Prod(int low, int high)
{
long result = low;
int multiplier = low;

while (++multiplier <= high)
result *= multiplier;

return result;
}

HTH,
-rick-

GB wrote:

Hello,
How to calculate value for the following formula (I need C# code):

res = (((m+1)(m+2)... (m+(k-1)))/1.2...(k-1))

or more generalized formula is:

k-1
__
| | (m+i)
i=1
res = ---------------
k-1
__
| | i
i=1
Thanks,
GB

[GB]

Thank you , Rick.
It works perfectly for me!

GB

2
"Rick Lones" <Wr******@Ychar terZ.netwrote in message
news:t6******** *****@newsfe07. lga...

So you are evalulating C(m+k-1, k-1), the number of combinations of

(m+k-1)

things taken (k-1) at a time, correct?

Then you want:

Prod((m+1),(m+k-1)) / Prod(1, (k-1)), where:

(warning, untested code!)

long Prod(int low, int high)
{
long result = low;
int multiplier = low;

while (++multiplier <= high)
result *= multiplier;

return result;
}

HTH,
-rick-

GB wrote:

Hello,
How to calculate value for the following formula (I need C# code):

res = (((m+1)(m+2)... (m+(k-1)))/1.2...(k-1))

or more generalized formula is:

k-1
__
| | (m+i)
i=1
res = ---------------
k-1
__
| | i
i=1
Thanks,
GB