sol1.c File Reference

Problem 25 solution implemented using arbitrarily large numbers represented as arrays More...

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

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Macros
#define	MAX_DIGITS   1000

Functions
unsigned int	add_numbers (unsigned char *a, unsigned char *b, unsigned char *c, int N)
int	print_number (unsigned char *number, int N)
unsigned int	get_digits (unsigned char *number)
int	main (int argc, char *argv[])

Detailed Description

Problem 25 solution implemented using arbitrarily large numbers represented as arrays

Author

Krishna Vedala

Macro Definition Documentation

MAX_DIGITS

#define MAX_DIGITS   1000

maximum number of digits

Function Documentation

add_numbers()

unsigned int add_numbers	(	unsigned char *	a,
		unsigned char *	b,
		unsigned char *	c,
		int	N
	)

Function to add arbitraty length decimal integers stored in an array.
a + b = c = new b

{
    unsigned char carry = 0;
    unsigned int i;
 
    for (i = 0; i < N; i++)
    {
        // printf("\t%d + %d + %d ", a[i], b[i], carry);
        c[i] = carry + a[i] + b[i];
        if (c[i] > 9) /* check for carry */
        {
            carry = 1;
            c[i] -= 10;
        }
        else
            carry = 0;
        // printf("= %d, %d\n", carry, c[i]);
    }
 
    while (carry != 0)
    {
        // printf("\t\t...adding new digit\n");
        // printf("\t0 + %d + %d ", b[i], carry);
        c[i] = carry + c[i];
        if (c[i] > 9)
        {
            carry = 1;
            c[i] -= 10;
        }
        else
            carry = 0;
        // printf("= %d, %d\n", carry, c[i]);
        i++;
    }
    return i;
}

get_digits()

unsigned int get_digits

(

unsigned char *

number

)

Get number of digits in a large number

{
    unsigned int digits = MAX_DIGITS;
    while (number[digits] == 0) digits--;
    return digits;
}

main()

int main	(	int	argc,
		char *	argv[]
	)

Main function

{
    unsigned char
        fn[MAX_DIGITS + 1]; /* array to store digits of a large number */
    unsigned char fn1[MAX_DIGITS + 1];
    unsigned char sum[MAX_DIGITS + 1];
 
    memset(fn, 0, MAX_DIGITS);
    memset(fn1, 0, MAX_DIGITS);
    memset(sum, 0, MAX_DIGITS);
 
    fn[0] = 1;
    fn1[1] = 1;
 
    unsigned int index = 1, digit_count = 1;
 
    clock_t start_time = clock();
    do
    {
        digit_count = add_numbers(fn, fn1, sum, digit_count);
        // digit_count = get_digits(sum);
 
        // printf("%5u (%u) (%u) ", index, digit_count, get_digits(sum));
        // print_number(sum, digit_count);
        // putchar('\n');
 
        if (digit_count == MAX_DIGITS)
            break;
        memcpy(fn, fn1, MAX_DIGITS);
        memcpy(fn1, sum, MAX_DIGITS);
        index++;
    } while (digit_count < MAX_DIGITS);
    clock_t end_time = clock();
 
    printf("Time taken: %.4g ms\n",
           1e3 * (end_time - start_time) / CLOCKS_PER_SEC);
    printf("The nth term for %d digits: %u \n", MAX_DIGITS, index--);
    print_number(sum, digit_count);
 
    return 0;
}

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print_number()

int print_number	(	unsigned char *	number,
		int	N
	)

Print a large number

{
    int start_pos = N - 1;
 
    /* skip all initial zeros */
    while (number[start_pos] == 0) start_pos--;
 
    for (int i = start_pos; i >= 0; i--) putchar(number[i] + 0x30);
 
    return 0;
}