C program which is finding "happy" nums recursively - c

Question

Hello guys i am trying to implement a program which is finding the happy numbers were between two numbers A and B.
Summing the squares of all the digits of the number, we replace the number with the outcome, and repeat the process. If after some steps the result is equal to 1 (and stay there), then we say that the number N is **<happy>**. Conversely, if the process is repeated indefinitely without ever showing the number 1, then we say that the number N is **<sad>**.
For example, the number 7 is happy because the procedure described above leads to the following steps: 7, 49, 97, 130, 10, 1, 1, 1 ... Conversely, the number 42 is sad because the process leads to a infinite sequence 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37 ...
I try this right down but i am getting either segm faults or no results.
Thanks in advance.
#include <stdio.h>
#include <math.h>
#include <string.h>
#include <stdlib.h>
void happy( char * A, int n);
int numPlaces (long n);
int main(void)
{
long A,B;
int npA;
char *Ap;
printf("Give 2 Numbers\n");
scanf("%li %li",&A,&B);
npA = numPlaces(A);
Ap = malloc(npA);
printf("%ld %d\n",A,npA);
//Search for happy numbers from A to B
do{
sprintf(Ap, "%ld", A);
happy(Ap,npA);
A++;
if ( npA < numPlaces(A) )
{
npA++;
Ap = realloc(Ap, npA);
}
}while( A <= B);
}
//Finds happy numbers
void happy( char * A, int n)
{
//Basic Condition
if ( n == 1)
{
if (A[0] == 1 || A[0] == 7)
printf("%c\n",A[0]);
printf("%s\n",A);
return;
}
long sum = 0 ;
char * sumA;
int nsum;
int Ai;
//Sum the squares of the current number
for(int i = 0 ; i < n;i++)
{
Ai = atoi(&A[i]);
sum = sum + (Ai*Ai);
}
nsum = numPlaces (sum);
sumA = malloc(nsum);
sprintf(sumA, "%li", sum);
happy(sumA,nsum);
free(sumA);
}
//Count digits of a number
int numPlaces (long n)
{
if (n < 0) return 0;
if (n < 10) return 1;
return 1 + numPlaces (n / 10);
}
Thanks for your time.

Answer 1

by the definition of your program sad numbers will cause your program to run forever
Conversely, if the process is repeated indefinitely
You need to add a stopping condition, like if I have looped for 1000 times, or if you hit a well known non terminating number (like 4) (is there a definite list of these? I dont know)

Answer 2

I find this solution tested and working..
Thanks for your time and I am sorry for my vagueness.
Every advice about this solution would be welcome
#include <stdio.h>
#include <math.h>
#include <string.h>
#include <stdlib.h>
void happy( char * A, int n);
int numPlaces (long n);
int happynum = 0;
int main(void)
{
long A,B;
int npA;
char *Ap;
printf("Give 2 Numbers\n");
scanf("%li %li",&A,&B);
npA = numPlaces(A);
Ap = malloc(npA);
//Search for happy numbers from A to B
do{
sprintf(Ap, "%ld", A);
happy(Ap,npA);
if (happynum ==1)
printf("%s\n",Ap);
A++;
if ( npA < numPlaces(A) )
{
npA++;
Ap = realloc(Ap, npA);
}
}while( A <= B);
}
//Finds happy numbers
void happy( char * A, int n)
{
//Basic Condition
if ( n == 1)
{
if (A[0] == '3' || A[0] == '6' || A[0] == '9')
{
happynum = 0;
}
else
{
happynum = 1;
}
return;
}
long sum = 0;
char * sumA;
int nsum;
int Ai;
//Sum the squares of the current number
for(int i = 0 ; i < n;i++)
{
Ai = (int)(A[i]-48);
sum = sum + (Ai*Ai);
}
nsum = numPlaces (sum);
sumA = malloc(nsum);
sprintf(sumA, "%li", sum);
happy(sumA,nsum);
free(sumA);
}
//Count digits of a number
int numPlaces (long n)
{
if (n < 0) return 0;
if (n < 10) return 1;
return 1 + numPlaces (n / 10);
}

Answer 3

Your code uses some questionable practices. Yoe may be misguided because you are concerned about performance and memory usage.
When you allocate memory for the string, you forget to allocate one character for the null terminator. But you shouldn't be allocating, re-allocating and freeing constantly anyway. Dynamic memory allocation is expensive compared to your other operations.
Your limits are long, which may be a 32-bit or 64-bit signed integer, depending on your platform. The maximum number that can be represented with e 64-bit signed integer is 9,223,372,036,854,775,807. This is a number with 19 digits. Add one for the null terminator and one for a possible minus sign, so that overflow won't hurt, you and use a buffer of 21 chars on the stack.
You probably shouldn't be using strings inthe first place. Use the basic code to extract the digits: Split off the digit by taking the remainder of a division by 10. Then divide by 10 until you get zero. (And if you use strings with a fixed buffer size, as described above, you don't have to calculate the difits separately: sprintf returns the number of characters written to the string.
Your functions shouldn't be recursive. A loop is enough. As pm100 has noted, you need a termination criterion: You must keep track of the numbers that you have already visited. Each recursive call creates a new state; it is easier to keep an array, that can be repeatedly looked at in a loop. When you see a number that you have already seen (other than 1, of course), your number is sad.
Happy and sad numbers have this property that when your sum of squares is a number with a known happiness, the original number has this happiness, too. If you visit a known das number, the original number is sad. If you visit a known happy number, the original number is happy.
The limits of your ranges may ba large, but the sum of square digits is not large; it can be at most the number of digits times 81. In particular:
type max. number number of max. square sum dss
int 2,147,483,647 1,999,999,999 730
uint 4,294,967,295 3,999,999,999 738
long 9,223,372,036,854,775,807 8,999,999,999,999,999,999 1522
ulong 18,446,744,073,709,55,1616 9,999,999,999,999,999,999 1539
That means that when you take the sum of digit squares of an unsigned long, you will get a number that is smaller than 1540. Create an array of 1540 entries and mark all known happy numbers with 1. Then you can reduce your problem to taking the sum of digit squares once and then looking up the happiness of the number in this array.
(You can do the precalculation of the array once when you start the program.)