Question

Basicaly when i run the code it works if i give it a large number (splitting it in prime numbers,but when i want to run it for low numbers it doesnt work) The problem i see is that if i give the program number 8 it doesnt print nothing on the screen.(i think its something to do with 2+2+2+2 ) and if i write 50 it shows all the posibilities WITHOUT repeating 1 prime number on a line

#include <math.h>
#include <stdio.h>
#include <stdlib.h>


#define is_sol  2
#define is_pos  4
#define impos  0

int n, *st;

int prim (int n)
{ 
    if ( n < 2 ) 
        return impos;
    else
        if ( n != 2 && (n % 2) == 0)
            return impos;
        else 
        { long i;
    for(i = 3; i <=sqrt(1.0*n); i +=2)
        if ( n % i == 0)
            return impos;
    }
    return is_pos;                   
}

int test(int h)
{  
    int i;
    if(!h) 
        return (st[h] < 2 ? impos : prim(st[h]));
    if(st[h] <= st[h-1]) 
        return impos;
    int p = st[h];
    if(!prim(p)) 
        return impos;
    int S = 0;
    for(i = 0 ; i <= h ; i++)
        S += st[i];
    if(S == n) 
        return is_sol;
    return (S < n ? is_pos : impos);
}

void print (int h)
{    
    int i;
    for(i = 0 ; i <= h; i++)
        printf("%d ", st[i]);
    printf("\n");
}

void back(int h) 
{ 
    int k;
    for(k = 2; k <= n/2; k++) 
    { 
        st[h] = k;
        int rez = test(h);
        if(rez == is_sol)
            print(h);
        else 
        { 
            if(rez == is_pos)
                back(h+1);
        }
    }
}

int main()
{ 
    printf( "Your number: ");
    scanf("%d",&n);
    st = (int*)malloc(sizeof(int)*(n/2));
    back(0);
}

Answer 1

The condition

for(k = 2; k <= n/2; k++)

is responsible. If you want to write a number as the sum of distinct primes, for small numbers, the only ways often include one prime larger than n/2 – e.g. the only way to write 8 as the sum of distinct primes is 8 = 3 + 5.

If you make it k <= n-2, it will work.

If you want to allow using the same prime several times, as in 8 = 2+2+2+2 or 8 = 2+3+3, you need to change

if(st[h] <= st[h-1])

to

if(st[h] < st[h-1])

in test.

And you should keep track of the sum you have so far to avoid the most blatant inefficiencies. (And store a list of primes instead of checking each number every time.)