# Calculating Factorial (Recursively & Iteratively)

Discussion in 'C' started by pradeep, Oct 30, 2006.

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Calculating the factorial of a number is a basic excercise while learning to program in C, many of us have done it iteratively, it can also be done recursively. I am posting both iterative and recursive versions below.

Code:
``` /* Recursive Version */
unsigned int recursive_factorial(int n)
{
return n>=1 ? n * recr_factorial(n-1) : 1;
}

/* Iterative Version */
unsigned int iter_factorial(int n)
{
int f = 1;
int i;
for(i = 1; i <= n; i++)
{
f *= i;
}
return f;
}```

2. ### bothieNew Member

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3. ### deepak.mobisyNew Member

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Thanks for this kind of efoorts.

4. ### oleberNew Member

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Good work but one small comment :p:

Why having int and unsigned int?

Just for coherence, and avoiding compilers work:

Code:
```[color=#808080][i]/* Recursive Version */[/i][/color]
[color=#993333]unsigned[/color] [color=#993333]int[/color] recursive_factorial[color=#66CC66]([/color][color=#993333]unsigned[/color] [color=#993333]int[/color] n[color=#66CC66])[/color]
[color=#66CC66]{[/color]
[color=#B1B100]return[/color] n >= [color=#CC66CC]1[/color] ? n * recr_factorial[color=#66CC66]([/color]n-[color=#CC66CC]1[/color][color=#66CC66])[/color] : [color=#CC66CC]1[/color];
[color=#66CC66]}[/color]```
Code:
```[color=#808080][i]/* Iterative Version */[/i][/color]
[color=#993333]unsigned[/color] [color=#993333]int[/color] iter_factorial[color=#66CC66]([/color][color=#993333]unsigned[/color] [color=#993333]int[/color] n[color=#66CC66])[/color]
[color=#66CC66]{[/color]
[color=#993333]unsigned[/color] [color=#993333]int[/color] f = [color=#CC66CC]1[/color];
[color=#B1B100]for[/color][color=#66CC66]([/color][color=#993333]unsigned[/color] [color=#993333]int[/color] i = [color=#CC66CC]1[/color]; i <= n; i++[color=#66CC66])[/color]
[color=#66CC66]{[/color]
f *= i;
[color=#66CC66]}[/color]
[color=#B1B100]return[/color] f;
[color=#66CC66]}

[/color]```

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6. ### pr1nc3k1dNew Member

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Everything looks good and nice but what's if you want to calculate " 1000! " or the factorial of greater values ? The " unsigned int " type can memorize a value between 0 and +4,294,967,295 but " 1000! " is more much greater than the dimension of " long double " which is the greatest data type in C/C++. I think this is a good question. I'm waiting suggestions and ideas.

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The greatest has also the limitation for large numbers and I think you are with the greatest "long double"

8. ### pr1nc3k1dNew Member

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Yes, it has, but i'm thinking on an algorithm which not calculates the result,but it generates it into a vector or a list. For example you can get a number with more than 1000 digits as result But if I put every digit of the number into a list I could view it and print it on the screen or into a file. So I think it could be a possible solution for this problem because there is no other data types which could memorize such a number. Opinions ?

9. ### pr1nc3k1dNew Member

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I made it but I don't really like it cuz` it's slow. It took about 6-7 minutes waiting for the result of " 1000! ".

Code:
```#include <iostream.h>
#include <conio.h>
#include <time.h>
void main ()
{
long int v,i,n;
double start;
clrscr();
v=1;
for(i=1;i<259000;i++) v[i]=0;
cout<<"Enter the number: "; cin>>n;
if(n==0 || n==1 ) cout<<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;
}
}
cout<<i<<"!=";
for(j=c;j>=0;j--)
cout<<v[j];
cout<<endl;
}
start=clock()-start;
cout<<"It took "<<start<<" seconds to complete. ";
}
getch();
}```

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Goodness gracious! 6-7 mins?? Try to rethink your logic!

11. ### pr1nc3k1dNew Member

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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;
int i,n;
double start;
ofstream fp_out;
fp_out.open("result.txt", ios::out);
v=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();
}```

12. ### pr1nc3k1dNew Member

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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;
int i,n;
double start=0.0;
v=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 ();
}```

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For big number, You can use Srerling's Approximate Formula>>>>

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

14. ### pr1nc3k1dNew Member

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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
```

15. ### pr1nc3k1dNew Member

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And Sterling's approximation is : n! ~ e^(-n)*n^n*Sqrt(2*PI*n)

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Just i am giving hing hint for Sterling Approximate Formula

> No Algorithm came uptill now except applying some AI .

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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

18. ### pr1nc3k1dNew Member

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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.

19. ### pr1nc3k1dNew Member

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the approximation above was for 1000!

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