sol1.c File Reference

Problem 401 solution - Sum of squares of divisors More...

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

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Macros
#define	__STDC_FORMAT_MACROS
#define	MOD_LIMIT   (uint64_t)1e9
	modulo limit
#define	MAX_LENGTH   5000
	chunk size of array allocation

Functions
char	is_in (uint64_t N, uint64_t *D, uint64_t L)
	Check if a number is present in given array.
uint64_t	get_divisors (uint64_t N, uint64_t *D)
	Get all integer divisors of a number.
uint64_t	sigma2 (uint64_t N)
	compute sum of squares of all integer factors of a number
uint64_t	sigma (uint64_t N)
	sum of squares of factors of numbers from 1 thru N
int	main (int argc, char **argv)
	Main function.

Detailed Description

Problem 401 solution - Sum of squares of divisors

Author

Krishna Vedala

Function Documentation

get_divisors()

uint64_t get_divisors	(	uint64_t	N,
		uint64_t *	D
	)

Get all integer divisors of a number.

Parameters

[in]	N	number to find divisors for
[out]	D	array to store divisors in

Returns

number of divisors found

{
    uint64_t q, r;
    int64_t i, num = 0;
 
    if (N == 1)
    {
        D[0] = 1;
        return 1;
    }
 
    // search till sqrt(N)
    // because after this, the pair of divisors will repeat themselves
    for (i = 1; i * i <= N + 1; i++)
    {
        r = N % i;  // get reminder
 
        // reminder = 0 if 'i' is a divisor of 'N'
        if (r == 0)
        {
            q = N / i;
            if (!is_in(i, D, num))  // if divisor was already stored
            {
                D[num] = i;
                num++;
            }
            if (!is_in(q, D, num))  // if divisor was already stored
            {
                D[num] = q;
                num++;
            }
        }
 
        if (num == MAX_LENGTH)
        {  // limit of array reached, allocate more space
            D = (uint64_t *)realloc(D, MAX_LENGTH * sizeof(uint64_t) << 1);
        }
    }
    return num;
}

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is_in()

char is_in	(	uint64_t	N,
		uint64_t *	D,
		uint64_t	L
	)

Check if a number is present in given array.

Parameters

[in]	N	number to check
[in]	D	array to check
[in]	L	length of array

Returns

1 if present

0 if absent

{
    uint64_t i;
    for (i = 0; i < L; i++)
    {
        if (D[i] == N)
        {
            return 1;
        }
    }
    return 0;
}

main()

int main	(	int	argc,
		char **	argv
	)

Main function.

{
    uint64_t N = 1000;
 
    if (argc == 2)
    {
        N = strtoll(argv[1], NULL, 10);
    }
    else if (argc > 2)
    {
        fprintf(stderr, "Wrong number of input arguments!\n");
        printf("Usage:\t ./sol1.c [N=1000]");
        return -1;
    }
 
    clock_t start_time = clock();
    uint64_t result = sigma(N);
    double dtime = clock() - start_time;
 
    printf("N = %" PRIu64 "\nSum: %" PRIu64 "\n", N, result);
    printf("Time taken: %.4gms\n", dtime * 1e3 / CLOCKS_PER_SEC);
 
    return 0;
}

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sigma()

uint64_t sigma

(

uint64_t

N

)

sum of squares of factors of numbers from 1 thru N

{
    uint64_t s, sum = 0;
    int64_t i;
 
#ifdef _OPENMP
// parallelize on threads
#pragma omp parallel for reduction(+ : sum)
#endif
    for (i = 0; i <= N; i++)
    {
        s = sigma2(i);
        sum += s;
    }
    return sum % MOD_LIMIT;
}

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sigma2()

uint64_t sigma2

(

uint64_t

N

)

compute sum of squares of all integer factors of a number

Parameters

[in]

N

Returns

sum of squares

{
    uint64_t sum = 0, L;
    int64_t i;
    uint64_t *D = (uint64_t *)malloc(MAX_LENGTH * sizeof(uint64_t));
 
    L = get_divisors(N, D);
    for (i = 1; i < L; i++)
    {
        uint64_t DD = (D[i] * D[i]) % MOD_LIMIT;
        sum += DD;
    }
 
    free(D);
    return sum % MOD_LIMIT;
}

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