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-   -   Calculating Factorial (Recursively & Iteratively) (http://www.go4expert.com/articles/calculating-factorial-recursively-t1757/)

pr1nc3k1d 8Dec2007 15:49

Re: Calculating Factorial (Recursively & Iteratively)
 
Yes but it prints on the screen the factorials in rows from 1 to a value .

Here is the new version which prints the results into a file:

Code:

#include <stdio.h>
#include <conio.h>
#include <fstream.h>
#include <time.h>
void main ()
{
        long int v[259000];
  int i,n;
  double start;
        ofstream fp_out;
  fp_out.open("result.txt", ios::out);
  v[0]=1;
  for(i=1;i<259000;i++) v[i]=0;
  printf("Enter the number: ");
  scanf("%d",&n); clrscr ();
  printf("-_-_- :L:O:A:D:I:N:G: -_-_-");
  if(n==0 || n==1 ) fp_out<<n<<"!=  "<<"1";
  else
  {
      start = clock ();
          long int c=0;
          for(i=1;i<=n;i++)
      {
              long int j;
                    for(j=0;j<=c;j++)
          v[j]*=i;
        for(j=0;j<=c;j++)
        {
                if(v[j]>=10)
            {
                    v[j+1]=v[j+1]+v[j]/10;
              v[j]=v[j]%10;
              int k1=258999,cont=0;
              while(v[k1]==0) { cont++; k1--; }
              c=258999-cont;
            }
        }
        fp_out<<i<<"!=  ";
        for(j=c;j>=0;j--)
                  fp_out<<v[j];

        fp_out<<endl;
          }
  start=clock()-start;
  clrscr ();
  printf("-_-_- :C:O:M:P:L:E:T:E:D: -_-_- \n Check out the result file! \n It took  %f ",start);printf(" seconds to complete. ");
  }
        getch ();
  fp_out.close();
}


pr1nc3k1d 9Dec2007 04:55

Re: Calculating Factorial (Recursively & Iteratively)
 
Here it is. The factorial of the numbers from 1 over to 1000 in 51 seconds.

Code:

#include <stdio.h>
#include <conio.h>
#include <time.h>
void main ()
{
        long int v[4000];
  int i,n;
  double start=0.0;
  v[0]=1;
  for(i=1;i<4000;i++) v[i]=0;
  printf("Enter the number: ");
  scanf("%d",&n);
  if(n==0 || n==1 ) printf("%d",&n,"!=1");
  else
  {
      start = clock ();
          long int c=0;
          for(i=1;i<=n;i++)
      {
              long int j;
                    for(j=0;j<=c;j++)
          v[j]*=i;
        for(j=0;j<=c;j++)
        {
                if(v[j]>=10)
            {
              v[j+1]=v[j+1]+v[j]/10;
              v[j]=v[j]%10;
              int k1=3999,cont=0;
              while(v[k1]==0) { cont++; k1--; }
              c=3999-cont;
            }
        }
        printf("%d",i);printf("!=  ");
        for(j=c;j>=0;j--)
                  printf("%d",v[j]);
                printf("\n");
          }
  start=clock()-start;
  start/=1000;
  printf("It took  %f ",start);printf(" seconds to complete. ");
  }
        getch ();
}


asadullah.ansari 11Jan2008 10:31

Re: Calculating Factorial (Recursively & Iteratively)
 
For big number, You can use Srerling's Approximate Formula>>>>

(n-1) ! ~ (2 Pi / (n))1/2e-(n) (n)(n)

pr1nc3k1d 11Jan2008 15:42

Re: Calculating Factorial (Recursively & Iteratively)
 
Yes, but I wanted the full and correct result, not only an approximation. Here is my result ( the factorials from 1 to 1.000 ) :

Code:

1!=  1
2!=  2
3!=  6
4!=  24
5!=  120
6!=  720
7!=  5040
8!=  40320
9!=  362880
10!=  3628800
11!=  39916800
12!=  479001600
13!=  6227020800
14!=  87178291200
15!=  1307674368000
16!=  20922789888000
17!=  355687428096000
18!=  6402373705728000
19!=  121645100408832000
20!=  2432902008176640000
21!=  51090942171709440000
22!=  1124000727777607680000
23!=  25852016738884976640000
24!=  620448401733239439360000
25!=  15511210043330985984000000
26!=  403291461126605635584000000
27!=  10888869450418352160768000000
28!=  304888344611713860501504000000
29!=  8841761993739701954543616000000
30!=  265252859812191058636308480000000
...................................................................
998!=  402790050127220994538240674597601587306681545756471103647447357787726238637266286878923131618587992793273261872069265323955622495490298857759082912582527118115540044131204964883707335062250983503282788739735011132006982444941985587005283378024520811868262149587473961298417598644470253901751728741217850740576532267700213398722681144219777186300562980454804151705133780356968636433830499319610818197341194914502752560687555393768328059805942027406941465687273867068997087966263572003396240643925156715326363340141498803019187935545221092440752778256846166934103235684110346477890399179387387649332483510852680658363147783651821986351375529220618900164975188281042287183543472177292257232652561904125692525097177999332518635447000616452999984030739715318219169707323799647375797687367013258203364129482891089991376819307292252205524626349705261864003453853589870620758596211518646408335184218571196396412300835983314926628732700876798309217005024417595709904449706930796337798861753941902125964936412501007284147114260935633196107341423863071231385166055949914432695939611227990169338248027939843597628903525815803809004448863145157344706452445088044626373001304259830129153477630812429640105937974761667785045203987508259776060285826091261745049275419393680613675366264232715305430889216384611069135662432391043725998805881663054913091981633842006354699525518784828195856033032645477338126512662942408363494651203239333321502114252811411713148843370594801145777575035630312885989779863888320759224882127141544366251503974910100721650673810303577074640154112833393047276025799811224571534249672518380758145683914398263952929391318702517417558325636082722982882372594816582486826728614633199726211273072775131325222240100140952842572490801822994224069971613534603487874996852498623584383106014533830650022411053668508165547838962087111297947300444414551980512439088964301520461155436870989509667681805149977993044444138428582065142787356455528681114392680950815418208072393532616122339434437034424287842119316058881129887474239992336556764337968538036861949918847009763612475872782742568849805927378373244946190707168428807837146267156243185213724364546701100557714520462335084082176431173346929330394071476071813598759588818954312394234331327700224455015871775476100371615031940945098788894828812648426365776746774528000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
999!=  402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
1000!=  402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000


pr1nc3k1d 11Jan2008 15:59

Re: Calculating Factorial (Recursively & Iteratively)
 
And Sterling's approximation is : n! ~ e^(-n)*n^n*Sqrt(2*PI*n)

asadullah.ansari 11Jan2008 16:53

Re: Calculating Factorial (Recursively & Iteratively)
 
Just i am giving hing hint for Sterling Approximate Formula

> No Algorithm came uptill now except applying some AI .

asadullah.ansari 11Jan2008 16:55

Re: Calculating Factorial (Recursively & Iteratively)
 
For big number, 32-bit or 64-bit machine still not computing after some bit. So on that instant we can easily use sterling aproximation formula

pr1nc3k1d 11Jan2008 17:23

Re: Calculating Factorial (Recursively & Iteratively)
 
Oh .. :) it's calculating ... as you can see .. :) but you need to put the result into some data type which can hold this large number. Usually data types can't hold them, you're absolutely right but if you generate the result into a vector or a list you can print it on the screen as you see. The result is correct. Just verify the first numbers of the result with the Calculator from your Windows.

4.02387260077093773543702433923e+2567 << Here it is your aproximation but I wanted the full result.

pr1nc3k1d 11Jan2008 17:25

Re: Calculating Factorial (Recursively & Iteratively)
 
the approximation above was for 1000!

asadullah.ansari 11Jan2008 17:35

Re: Calculating Factorial (Recursively & Iteratively)
 
You are right But Too much overhead will be on case of storing into vector or some file i.e. into some container. Too much check has to put where calculation is going overflow.


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