How to check for division by 7 for big number in C++?

Question

I have to check, if given number is divisible by 7, which is usualy done just by doing something like n % 7 == 0, but the problem is, that given number can have up to 100000000, which doesn't fit even in long long.

Another constrain is, that I have only few kilobytes of memory available, so I can't use an array.

I'm expecting the number to be on stdin and output to be 1/0.

This is an example

34123461273648125348912534981264376128345812354821354127346821354982135418235489162345891724592183459321864592158
0

It should be possible to do using only about 7 integer variables and cin.get(). It should be also done using only standard libraries.

Answer 1

you can use a known rule about division by 7 that says: group each 3 digits together starting from the right and start subtracting and adding them alternativly, the divisibility of the result by 7 is the same as the original number:

ex.:

testing 341234612736481253489125349812643761283458123548213541273468213
        549821354182354891623458917245921834593218645921580

   (580-921+645-218+593-834+921-245+917-458+623-891+354-182
    +354-821+549-213+468-273+541-213+548-123+458-283+761-643
    +812-349+125-489+253-481+736-612+234-341 
    = 1882 )
    % 7 != 0 --> NOK!

there are other alternatives to this rule, all easy to implement.

Answer 2

Think about how you do division on paper. You look at the first digit or two, and write down the nearest multiple of seven, carry down the remainder, and so on. You can do that on any abritrary length number because you don't have to load the whole number into memory.