sol2.c File Reference

Problem 23 solution - optimization using look-up array More...

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

Include dependency graph for sol2.c:

Functions
char	get_perfect_number (unsigned long N)
char	is_abundant (unsigned long N)
	Is the given number an abundant number (1) or not (0)
unsigned long	get_next_abundant (unsigned long N)
	Find the next abundant number after N and not including N.
char	is_sum_of_abundant (unsigned long N)
	check if a given number can be represented as a sum of two abundant numbers. More...
int	main (int argc, char **argv)
	Main function.

Variables
char *	abundant_flags = NULL
	This is the global array to be used to store a flag to identify if a particular number is abundant (1) or not (0). More...

Detailed Description

Problem 23 solution - optimization using look-up array

Author

Krishna Vedala

Optimization applied - compute & store abundant numbers once into a look-up array.

Function Documentation

get_perfect_number()

char get_perfect_number

(

unsigned long

N

)

Returns

-1 if N is deficient

1 if N is abundant

0 if N is perfect

{
    unsigned long sum = 1;
    char ret = 0;
 
    for (unsigned long i = 2; i * i <= N; i++)
    {
        if (N % i == 0)
        {
            sum += i;
            unsigned long tmp = N / i;
            if (tmp != i)
            {
                sum += tmp;
            }
        }
    }
 
    ret = sum == N ? 0 : (sum > N ? 1 : -1);
#ifdef DEBUG
    printf("%5lu: %5lu : %d\n", N, sum, ret);
#endif
    return ret;
}

is_sum_of_abundant()

char is_sum_of_abundant

(

unsigned long

N

)

check if a given number can be represented as a sum of two abundant numbers.

Returns

1 - if yes

0 - if not

{
    /* optimized logic:
     * i + j = N   where both i and j should be abundant
     * hence we can simply check for j = N - i as we loop through i
     */
    for (unsigned long i = get_next_abundant(1); i <= (N >> 1);
         i = get_next_abundant(i))
    {
        if (is_abundant(N - i))
        {
#ifdef DEBUG
            printf("\t%4lu + %4lu = %4lu\n", i, N - i, N);
#endif
            return 1;
        }
    }
    return 0;
}

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Variable Documentation

abundant_flags

char* abundant_flags = NULL

This is the global array to be used to store a flag to identify if a particular number is abundant (1) or not (0).

Using a whole byte to store a binary info would be redundant. We will use each byte to represent 8 numbers by relying on bits. This saves memory required by 1/8