## INDEX

### Division of large numbers in c

1. C code for division of very big numbers.
2. How to get division of two very large numbers larger or beyond than long int in c programming language.

#include<stdio.h>
#include<string.h>
#define MAX 10000

int validate(char []);
char * division(char[],long);
long int remainder;

int main(){

char dividend[MAX],*quotient;
long int divisor;

printf("Enter dividend: ");
scanf("%s",dividend);
if(validate(dividend))
return 0;

printf("Enter divisor: ");
scanf("%ld",&divisor);

quotient = division(dividend,divisor);

while(*quotient)
if(*quotient ==48)
quotient++;
else
break;

printf("Quotient: %s / %ld  =  %s",dividend,divisor,quotient);
printf ("\nRemainder: %ld",remainder);
return 0;
}

int validate(char num[]){
int i=0;

while(num[i]){
if(num[i] < 48 || num[i]> 57){
printf("Invalid positive integer: %s",num);
return 1;
}
i++;
}

return 0;
}

char * division(char dividend[],long divisor){

static char quotient[MAX];
long temp=0;
int i=0,j=0;

while(dividend[i]){

temp = temp*10 + (dividend[i] -48);
if(temp<divisor){

quotient[j++] = 48;

}
else{
quotient[j++] = (temp / divisor) + 48;;
temp = temp % divisor;

}
i++;
}

quotient[j] = '\0';
remainder = temp;
return quotient;
}

Sample output:
Enter dividend: 543109237823560187
Enter divisor: 456
Quotient: 543109237823560187 / 456 = 1191029030314824
Remainder: 443

Other program (source code):

#include<stdio.h>
#include<math.h>
#include<stdlib.h>
#include<string.h>
#define MAX 10000

char * division(char [],unsigned long);
int main(){
char a[MAX];
unsigned long b;
char *c;
printf("Enter the divdend : ");
scanf("%s",a);
printf("Enter the divisor : ");
scanf("%lu",&b);
c = division(a,b);
printf("\nQuotient of the division : ");
printf("%s",c);
return 0;
}

char * division(char a[],unsigned long b){
static char c[MAX];
int la;
int i,k=0,flag=0;
unsigned long temp=1,reminder;
la=strlen(a);

for(i=0;i<=la;i++){
a[i] = a[i] - 48;
}

temp = a;
reminder = a;
for(i=1;i<=la;i++){
if(b<=temp){
c[k++] = temp/b;
temp = temp % b;
reminder = temp;
temp =temp*10 + a[i];
flag=1;

}
else{
reminder = temp;
temp =temp*10 + a[i];
if(flag==1)
c[k++] = 0;
}
}

for(i=0;i<k;i++){
c[i]=c[i]+48;
}
c[i]= '\0';

printf("Reminder of division:  %lu  ",reminder);
return c;
}

Sample output:
Enter the divdend:
55555555555555555555555555555555555555555
Enter the divisor: 5
Reminder of division:  0
Quotient of the division:
11111111111111111111111111111111111111111

### Logic of the program Division of large numbers

Algorithm:

As we know in c there are not any such data types which can store a very large numbers.  For example we want to solve the expression:

4928351200966342333331289107/34269

Number 4928351200966342333331289107 is beyond the range of even long int or long double.  Then question is how to store such a big numbers in c?

Solution is very simple i.e. using array. Above program has used same logic that is we are using as usual logic to solve the expression except instead of storing the data in the normal variables we are storing into the array. Anonymous said...

very good algorithm!
but what happens when the divisor has MAX digits too?? Anonymous said...

Not bad, but "bignum / normal integer" is the easy part... the basic algorithm...

you should bugfix the part with division by too large numbers...
(MAX LONG + 1) / (MAX LONG) would not work I guess, because there would be an overflow before the division occurs...

next step would be
-not using human read-able ascii --> use of binary numbers (less space needed and faster)
- +/- numbers
- bignum div by bignum or (even if not needed:)
- floating support

Unknown said...

why to store as string first and then to integer array?
why don't you directly store in integer array?