This weeks assignment deals with an old fashioned primary school problem. Most of you will know the "Turmrechnen" as a pain of your former school days. How it works is shown in the following example
Pyramid of Numbers
Please enter a number: 3453454359654646756757434 3453454359654646756757434 * 2 = 6906908719309293513514868 6906908719309293513514868 * 3 = 20720726157927880540544604 20720726157927880540544604 * 4 = 82882904631711522162178416 82882904631711522162178416 * 5 = 414414523158557610810892080 414414523158557610810892080 * 6 = 2486487138951345664865352480 2486487138951345664865352480 * 7 = 17405409972659419654057467360 17405409972659419654057467360 * 8 = 139243279781275357232459738880 139243279781275357232459738880 * 9 = 1253189518031478215092137649920 1253189518031478215092137649920 / 2 = 626594759015739107546068824960 626594759015739107546068824960 / 3 = 208864919671913035848689608320 208864919671913035848689608320 / 4 = 52216229917978258962172402080 52216229917978258962172402080 / 5 = 10443245983595651792434480416 10443245983595651792434480416 / 6 = 1740540997265941965405746736 1740540997265941965405746736 / 7 = 248648713895134566486535248 248648713895134566486535248 / 8 = 31081089236891820810816906 31081089236891820810816906 / 9 = 3453454359654646756757434
To see more about it's internal structure browse through this documentation. A good starting point is, of course, the function main() and, furthermore, the struct BigInt.
When browsing through this documentation you might stumble over the keyword const in the argument list of several functions. This shows you that the argument must not be altered by the function, i.e., you may be sure that, even if a pointer is passed to the function the content of the argument is not changed in the function.
We have to read in the number via a string. Check, whether the entered number does exceed the maximum length of MAX_DIGITS. In this case print an error message and leave the program with error code -1.
The string has than to be converted into a BigInt. Implement a function strtobig_int() as specified. The conversion of one single character c containing a digit to an int can be done via c - '0'. Also think of the correct way to fill the array. Is for the number 123456 the array element a[0] == 1 or is a[0] == 6? Finally do not forget to set BigInt.digits to the right value. After calling strtobig_int() check whether the function was able to convert the entire string. If not an invalid character occured in your string and the program should give an error message and should return with error code -2.
Should be straight forward.
Do a few multiplications and division by hand (yes as you learned this in primary school :-)). Write down the tiny steps and transform these then into C source code. Keep stuck to the interface multiply() and divide() as given in this documentation. An Engish word you might need for naming a variable: "Uebertrag": carry
Take care that simply assigning a BigInt from one variable to another will fail, because the array BigInt.the_int won't be copied but only its pointer. Therefore, you have to write a function copy_big_int(), which copies the array element by element.
1.7.0
