I am trying to write the Karatsuba algorithm using C. I tried my code using small numbers for example 9999 * 9999 and it is working fine however I am noticing when I increase the size of the number above 7 digits (I tried on 9999999 * 9999999 and it working fine). I realized my problem is with the pointers (after debugging). but I don't know what is the exact solution for it.
Could you please help me to find out the problem?
#include <stdio.h>
#include <stdlib.h>
#include <malloc.h>
int length (char *);
char *multiply (char *, char *);
char *add (char *, char *, int);
char *sub (char *, char *, int);
char *addzerosl (char *, int, int);
void reallocaddzerosl (char **, int, int);
char *addzerosr (char *, int);
char *karamult (char *, char *);
void removezero (char *);
int
main ()
{
char a[] =
"3141592653589793238462643383279502884197169399375105820974944592";
char b[] =
"2718281828459045235360287471352662497757247093699959574966967627";
char *c = karamult (a, b);
int d = length (c);
printf ("%s %d", c, d);
FILE * F = NULL;
F = fopen ("test_1.txt", "w");
fprintf (F, "%s", c);
fclose (F);
free (F);
free (c);
return 0;
}
// Length of array
int
length (char *c)
{
int l = 0;
while ((*c++) != '\0')
l++;
return l;
}
// multiply two integers
char *
multiply (char *a, char *b)
{
char *f = (char *) calloc ((3), sizeof (char));
if (f == NULL)
{
printf ("error in multiply\n");
exit (EXIT_FAILURE);
}
int e = (*a - '0') * (*b - '0');
f[0] = (e / 10) + '0';
f[1] = (e % 10) + '0';
f[2] = '\0';
removezero (f);
return f;
}
// add two integers
char *
add (char *a, char *b, int n)
{
char *f = NULL;
f = (char *) calloc ((n + 2), sizeof (char));
if (f == NULL)
{
printf ("error in add\n");
exit (EXIT_FAILURE);
}
int car = 0;
for (int i = n; i > 0; i--)
{
int e1 = (a[i - 1] - '0') + (b[i - 1] - '0') + car;
if (e1 - 10 >= 0)
car = 1;
else
car = 0;
f[i] = (e1 % 10) + '0';
}
if (car)
{
f[0] = '1';
f[n + 1] = '\0';
}
else
{
f[0] = '0';
f[n + 1] = '\0';
char *g = (char *) calloc ((n + 1), sizeof (char));
for (int i = 0; i < n + 1; i++)
g[i] = f[i + 1];
free (f);
f = NULL;
return g;
}
return f;
}
// sub two integers
char *
sub (char *a, char *b, int n)
{
char *f = (char *) calloc ((n + 1), sizeof (char));
if (f == NULL)
{
printf ("error in sub\n");
exit (EXIT_FAILURE);
}
int car = 0;
for (int i = n - 1; i >= 0; i--)
{
int e1 = (a[i] - '0') - (b[i] - '0') - car;
if (e1 < 0)
{
car = 1;
e1 += 10;
f[i] = e1 + '0';
}
else
{
f[i] = e1 + '0';
car = 0;
}
}
f[n] = '\0';
return f;
}
// add zeros to left
char *
addzerosl (char *a, int a1, int b)
{
int r = b - a1;
char *f = (char *) calloc ((b + 1), sizeof (char));
if (f == NULL)
{
printf ("error in addzerosl\n");
exit (EXIT_FAILURE);
}
for (int i = 0; i < a1; i++)
{
f[b - 1 - i] = a[a1 - 1 - i];
}
for (int i = 0; i < r; i++)
{
f[i] = '0';
}
f[b] = '\0';
return f;
}
void
reallocaddzerosl (char **a, int a1, int b)
{
int r = b - a1;
*a = (char *) realloc ((*a), sizeof (char));
if (*a == NULL)
{
printf ("error in reallocaddzerosl\n");
exit (EXIT_FAILURE);
}
for (int i = 0; i < a1; i++)
{
(*a)[b - 1 - i] = (*a)[a1 - 1 - i];
}
for (int i = 0; i < r; i++)
{
(*a)[i] = '0';
}
(*a)[b] = '\0';
}
// remove zeros from left
void
removezero (char *a)
{
int n = length (a);
int i = 0;
if (a[0] != '0')
return;
else
{
while (a[i] == '0' && a[i] != '\0')
i++;
int j = 0;
if (i < n)
{
for (j = 0; j < (n - i); j++)
{
a[j] = a[i + j];
}
a[j] = '\0';
}
else
{
a[0] = '0';
a[1] = '\0';
}
}
}
// add zeros to right
char *
addzerosr (char *a, int c)
{
char *f = (char *) calloc ((length (a) + c + 1), sizeof (char));
if (a == NULL)
{
printf ("error in addzerosr\n");
exit (EXIT_FAILURE);
}
for (int i = 0; i < length (a); i++)
f[i] = a[i];
for (int i = length (a); i < (length (a) + c); i++)
{
f[i] = '0';
}
f[(length (a) + c)] = '\0';
return f;
}
// Karatsuba multiplication
char *
karamult (char *a, char *b)
{
static int de = 0;
int la = length (a);
int lb = length (b);
char *ca = NULL;
char *cb = NULL;
int n = 0;
char *f = NULL;
if (la <= 1 && lb <= 1)
{
f = multiply (a, b);
return f;
}
if (la > lb)
{
n = la;
cb = addzerosl (b, lb, la);
ca = addzerosl (a, la, la);
}
else if (la < lb)
{
n = lb;
ca = addzerosl (a, la, lb);
cb = addzerosl (b, lb, lb);
}
else
{
ca = addzerosl (a, la, la);
cb = addzerosl (b, lb, lb);
n = lb;
}
if (n % 2)
{
reallocaddzerosl (&ca, n, n + 1);
reallocaddzerosl (&cb, n, n + 1);
n = n + 1;
}
char *a1 = (char *) calloc ((n / 2 + 1), sizeof (char));
char *b1 = (char *) calloc ((n / 2 + 1), sizeof (char));
char *c1 = (char *) calloc ((n / 2 + 1), sizeof (char));
char *d1 = (char *) calloc ((n / 2 + 1), sizeof (char));
if (a1 == NULL || b1 == NULL || c1 == NULL || d1 == NULL)
{
printf ("error in a1\n");
exit (EXIT_FAILURE);
}
for (int i = 0; i < n / 2; i++)
{
a1[i] = ca[i];
b1[i] = ca[i + n / 2];
c1[i] = cb[i];
d1[i] = cb[i + n / 2];
}
a1[n / 2] = '\0';
b1[n / 2] = '\0';
c1[n / 2] = '\0';
d1[n / 2] = '\0';
free (ca);
free (cb);
ca = NULL;
cb = NULL;
char *apb = add (a1, b1, length (a1));
if (apb == NULL)
{
printf ("error in apb\n");
exit (EXIT_FAILURE);
}
char *cpb = add (c1, d1, length (c1));
if (cpb == NULL)
{
printf ("error in cpb\n");
exit (EXIT_FAILURE);
}
char *ac = karamult (a1, c1);
if (ac == NULL)
{
printf ("error in ac\n");
exit (EXIT_FAILURE);
}
char *bd = karamult (b1, d1);
if (bd == NULL)
{
printf ("error in bd\n");
exit (EXIT_FAILURE);
}
removezero (ac);
removezero (bd);
removezero (apb);
removezero (cpb);
free (a1);
free (b1);
free (c1);
free (d1);
a1 = NULL;
b1 = NULL;
c1 = NULL;
d1 = NULL;
char *sec = karamult (apb, cpb);
if (sec == NULL)
{
printf ("error in sec\n");
exit (EXIT_FAILURE);
}
removezero (sec);
free (apb);
free (cpb);
apb = NULL;
cpb = NULL;
int lsec = length (sec);
int lac = length (ac);
if (lsec > lac)
reallocaddzerosl (&ac, lac, lsec);
else if (lsec < lac)
reallocaddzerosl (&sec, lsec, lac);
lsec = length (sec);
char *sec1 = sub (sec, ac, lsec);
if (sec1 == NULL)
{
printf ("error in sec1\n");
exit (EXIT_FAILURE);
}
removezero (sec1);
free (sec);
sec = NULL;
int lsec1 = length (sec1);
int lbd = length (bd);
if (lsec1 > lbd)
reallocaddzerosl (&bd, lbd, lsec1);
else if (lsec1 < lbd)
reallocaddzerosl (&sec1, lsec1, lbd);
lsec1 = length (sec1);
char *sec2 = sub (sec1, bd, lsec1);
if (sec2 == NULL)
{
printf ("error in sec2\n");
exit (EXIT_FAILURE);
}
removezero (sec2);
free (sec1);
sec1 = NULL;
int i = 0;
int j = 0;
char *f1 = addzerosr (ac, n);
if (f1 == NULL)
{
printf ("error in f1\n");
exit (EXIT_FAILURE);
}
free (ac);
ac = NULL;
removezero (f1);
char *f2 = addzerosr (sec2, (n / 2));
if (f2 == NULL)
{
printf ("error in f2\n");
exit (EXIT_FAILURE);
}
free (sec2);
sec2 = NULL;
removezero (f2);
int lf1 = length (f1);
int lf2 = length (f2);
if (lf1 > lf2)
reallocaddzerosl (&f2, lf2, lf1);
else if (lf1 < lf2)
reallocaddzerosl (&f1, lf1, lf2);
lf1 = length (f1);
char *f3 = add (f1, f2, lf1);
if (f3 == NULL)
{
printf ("error in f3\n");
exit (EXIT_FAILURE);
}
free (f1);
free (f2);
f1 = NULL;
f2 = NULL;
int lf3 = length (f3);
removezero (f3);
removezero (bd);
lbd = length (bd);
if (lf3 > lbd)
reallocaddzerosl (&bd, lbd, lf3);
else if (lf3 < lbd)
reallocaddzerosl (&f3, lf3, lbd);
lf3 = length (f3);
f = add (f3, bd, lf3);
if (f == NULL)
{
printf ("error in f\n");
exit (EXIT_FAILURE);
}
removezero (f);
free (f3);
if (bd == NULL)
{
printf ("error in bd\n");
exit (EXIT_FAILURE);
}
free (bd);
f3 = NULL;
bd = NULL;
return f;
}
