/*----------------------------------------------------------
 *				HTBLA-Leonding / Class: 2IHIF
 * ---------------------------------------------------------
 * Exercise Number: 0
 * Title:			Pyramid of Numbers
 * Author:			Marc Tismonar
 * ----------------------------------------------------------
 * Description:
 * Calculates a pyramid of numbers, i.e., it multiplies a big
 * integer by the number 2, its result by 3, etc. and then
 * returns to the original value by subsequently dividing,
 * again starting by 2, 3, etc.
 * ----------------------------------------------------------
 */
#include <stdio.h>
#include <string.h>

/// The maximum number of digits allowed in a big int.
#define MAX_DIGITS 80

/** BigInt represents an integer number which can have MAX_DIGITS digits
*** @see MAX_DIGITS
*/
struct BigInt {
	/** number of digits of the big int. */
	int digits_count;

	/** array of digits of big int. */
	unsigned int the_int[MAX_DIGITS];
};

/** reset_big_int sets content to 0
*** @param *big_int The BigInt to be reset
*** @param startPos The start position where the reset shall begin
**/
void reset_big_int(struct BigInt *big_int, int startPos) {
	if (startPos < 0 || startPos > MAX_DIGITS) {
		startPos = 0;
	}

	startPos = MAX_DIGITS - startPos;
	for (int i = startPos; i >= 0; i--)
	{
		big_int->the_int[i] = 0;
	}
	big_int->digits_count = 0;
}

/** set_big_int_length determines the length and sets it
*** @param *big_int The BigInt to determine the length
**/
void set_big_int_length(struct BigInt *big_int)
{
	for (int i = 0; i < MAX_DIGITS; i++)
	{
		if(big_int->the_int[i] != 0)
		{
			big_int->digits_count = MAX_DIGITS - i;
			return;
		}
	}
}

/** strtobig_int converts a string into a BigInt. If strtobig_int runs
*** against a character not between '0' and '9' the conversion stops
*** at this point.
*** @param *str The string to be converted.
*** @param len Number of characters in string to be converted.
*** @param *big_int The converted string now as BigInt.
* @return The number of characters converted.
*/
int strtobig_int(const char* str, int len, struct BigInt* big_int) {
	reset_big_int(big_int, -1);
	int conversions = 0;
	int j = 0;
	for (int i = len - 1; i >= 0; i--)
	{
		int big_int_position = MAX_DIGITS - j - 1;
		int converted = str[i] - '0';
		if (converted >= 0 && converted <= 9)
		{
			big_int->the_int[big_int_position] = converted;
			conversions++;
		}
		else
		{
			big_int->digits_count = conversions;
			//reset_big_int(big_int, conversions);
			return conversions;
		}
		j++;
	}
	big_int->digits_count = conversions;
	//reset_big_int(big_int, conversions);
	return conversions;
}

/** print_big_int() prints a BigInt.
*** @param *big_int The BigInt to be printed.
*/
void print_big_int(const struct BigInt *big_int) {
	for (int i = MAX_DIGITS - big_int->digits_count; i < MAX_DIGITS; i++)
	{
		printf("%d", big_int->the_int[i]);
	}
}

/** multiply() multiplies a BigInt by an int.
*** @param big_int The BigInt to be multiplied.
*** @param factor The int value which is multiplied by BigInt.
*** @param *big_result The result of the multiplication.
*/
void multiply(const struct BigInt* big_int, int factor, struct BigInt* big_result) {
	//set everything in the result to 0
	reset_big_int(big_result, -1);

	//no global overflow needed as it automatically saves it in the next place
	//no need for '()' braces in the calculation, but used for a better view
	for (int i = MAX_DIGITS - 1; i >= MAX_DIGITS - big_int->digits_count; i--) {
		int result = (big_int->the_int[i] * factor) + big_result->the_int[i];
		int overflow = result / 10;
		int result_for_i = result - overflow * 10;

		big_result->the_int[i] = result_for_i;
		big_result->the_int[i - 1] = overflow;
	}
	set_big_int_length(big_result);
}

/** divide() multiplies a BigInt by an int.
*** @param big_int The BigInt to be divided.
*** @param divisor The int value by which we want to devide big_int.
*** @param *big_result The result of the division.
*/
void divide(const struct BigInt* big_int, int divisor, struct BigInt* big_result) {
	//set everything in the result to 0
	reset_big_int(big_result, -1);

	//no global remainder needed as the remainder is automatically saved in the big_result
	//no need for '()' braces in the calculation, but used for a better view
	for (int i = MAX_DIGITS - big_int->digits_count; i < MAX_DIGITS; i++) {
		int result = (big_int->the_int[i] + big_result->the_int[i]) / divisor;
		int remainder = big_int->the_int[i] + big_result->the_int[i] - (result * divisor);

		big_result->the_int[i + 1] = remainder * 10;
		big_result->the_int[i] = result;
	}
	set_big_int_length(big_result);
}

/** copy_big_int() copies a BigInt to another BigInt.
*** @param from The source where we want to copy from.
*** @param *to The target where we want to copy to.
*/
void copy_big_int(const struct BigInt* from, struct BigInt* to) {
	to->digits_count = from->digits_count;
	for (int i = 0; i < MAX_DIGITS; i++) {
		to->the_int[i] = from->the_int[i];
	}
}

/**
*** main() reads the base number from which the pyramid has to be calculated
*** into an array of char. The max. length of this number is MAX_DIGITS.
*** The number is checked to contain only digits. If not the program exits.
*** Then the inputted number is converted into a big int by calling the
*** function strtobig_int().
*** After the conversion the tower is calculated by calling the functions
*** multiply(), print_big_int(), and copy_big_int() consecutively from 2 to
*** 9 and then again with divide() instead of multiply() from 2 to 9.
***
*/
int main(int argc, char* argv[])
{
	printf("Pyramid of Numbers\n\n");

	printf("Please enter a number: ");
	char input_str[MAX_DIGITS];
	scanf("%s", input_str);

	struct BigInt original_big_int;
	int len = strlen(input_str);
	reset_big_int(&original_big_int, -1);
	strtobig_int(input_str, len, &original_big_int);

	struct BigInt changed_big_int;
	copy_big_int(&original_big_int, &changed_big_int);

	//multiply
	for (int i = 2; i < 10; i++)
	{
		//create temp BigInt & multiply
		struct BigInt temp;
		multiply(&changed_big_int, i, &temp);
		
		print_big_int(&changed_big_int);
		printf(" * %d = ", i);
		print_big_int(&temp);
		printf("\n");

		copy_big_int(&temp, &changed_big_int);
	}

	//divide
	for (int i = 9; i > 1; i--)
	{
		//create temp BigInt & divide
		struct BigInt temp;
		divide(&changed_big_int, i, &temp);
		
		print_big_int(&changed_big_int);
		printf(" / %d = ", i);
		print_big_int(&temp);
		printf("\n");

		copy_big_int(&temp, &changed_big_int);
	}

	return 0;
}