43. Multiply Strings (String)

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.

思路：首先确定结果的位数，难点在于知道结果中的每一位，是乘数中的哪两位相乘贡献的：是num2中的i-len1+1到i中的数分别乘以num1中的i-j相加而得的，并且要注意不能超过num2的界限[0,len2-1]

class Solution {
public:
    string multiply(string num1, string num2) {
        reverse(num1.begin(), num1.end());
        reverse(num2.begin(), num2.end());
        int carry = , sum =;
        string result="";
        int len1 = num1.length();
        int len2 = num2.length();
        int resLen = len1+len2-;

        for(int i = ; i < resLen; i++){ //traverse the result digit
            for(int j = max(,i-len1+) ; j <= min(i,len2-); j++){ //traverse the num2 digit
                sum += (num2[j]-'')*(num1[i-j]-'');
            }
            sum += carry;
            carry = sum/;
            result += ((sum%) + '');
            sum=;a
        }

        if(carry) result += (carry+'');
        reverse(result.begin(),result.end());
        if(result[]=='') return ""; //全0的情况
        return result;
    }
};