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

Answer 1

You can compute the value of the number modulo 7.

That is, for each digit d and value n so far compute n = (10 * n + d) % 7.

This has the advantage of working independently of the divisor 7 or the base 10.

I solved this problem exactly the same way on one of programming contests. Here is the fragment of code you need:

int sum = 0;
while (true) {
  char ch;
  cin>>ch;
  if (ch<'0' || ch>'9') break; // Reached the end of stdin
  sum = sum*10; // The previous sum we had must be multiplied
  sum += (int) ch;
  sum -= (int) '0'; // Remove the code to get the value of the digit
  sum %= 7; 
}

if (sum==0) cout<<"1";
else cout<<"0";

This code is working thanks to simple rules of modular arithmetics. It also works not just for 7, but for any divisor actually.