43. Multiply Strings

Given two non-negative integers num1 and num2 represented as strings, return the product of num1 and num2.

Note:

1. The length of both num1 and num2 is < 110.
2. Both num1 and num2 contains only digits 0-9.
3. Both num1 and num2 does not contain any leading zero.
4. You must not use any built-in BigInteger library or convert the inputs to integer directly.

 1 class Solution
 2 {
 3 public:
 4     string multiply(string num1, string num2)
 5     {
 6         vector<int> vi(num1.size() + num2.size(), 0);
 7         for(int i = 0; i < num1.size(); ++ i)
 8             for(int j = 0; j < num2.size(); ++ j)
 9                 vi[i + j] += (num1[num1.size() - i - 1] - '0') * (num2[num2.size() - j- 1] - '0');
10 
11         for(int i = 0, c = 0; i < vi.size(); ++ i)
12         {
13             int num = vi[i] + c;
14             vi[i] = num % 10;
15             c = num / 10;
16         }
17 
18         string s = "";
19         int i = vi.size();
20         while(-- i >= 0 && vi[i] == 0);
21         if(i < 0)
22             s = "0";
23         else
24             for( ; i >= 0; -- i)
25                 s += vi[i] + '0';
26 
27         return s;
28     }
29 };