Multiply Strings

Given two numbers represented as strings, return multiplication of the numbers as a string.
Note: The numbers can be arbitrarily large and are non-negative.

Solution: Just like what we do when multiplying integers.

class Solution {
public:
    string multiply(string num1, string num2) {
        int N = num1.size();
        int M = num2.size();
        string res(N+M,'0');
        for(int i = N - 1; i >= 0; i--) {
            int carry = 0;
            for(int j = M - 1; j >= 0; j--) {
                int sum = carry + (res[i+j+1] - '0')
                            + (num1[i] - '0')*(num2[j] - '0');
                res[i+j+1] = sum % 10 + '0';
                carry = sum / 10;
            }
            res[i] += carry;
        }
        while (res.size() > 1 && res[0] == '0')
            res.erase(res.begin());
        return res;
    }
};