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.

 1 class Solution {
 2 public:
 3     string multiply(string num1, string num2) {
 4         int N = num1.size();
 5         int M = num2.size();
 6         string res(N+M,'0');
 7         for(int i = N - 1; i >= 0; i--) {
 8             int carry = 0;
 9             for(int j = M - 1; j >= 0; j--) {
10                 int sum = carry + (res[i+j+1] - '0')
11                             + (num1[i] - '0')*(num2[j] - '0');
12                 res[i+j+1] = sum % 10 + '0';
13                 carry = sum / 10;
14             }
15             res[i] += carry;
16         }
17         while (res.size() > 1 && res[0] == '0')
18             res.erase(res.begin());
19         return res;
20     }
21 };