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：模拟竖乘的思路，跟大数计算一样，先将字符串倒置

class Solution {
public:
    string multiply(string num1, string num2) {
        reverse(num1.begin(), num1.end());
        reverse(num2.begin(), num2.end());
        int len1 = num1.size(), len2 = num2.size();

        string ans(len1+len2+1, '0');
        int tmp = 0;
        for (int i = 0; i < len1; i++) {
            int cur = num1[i] - '0';
            tmp = 0;
            for (int j = 0; j < len2; j++) {
                int a = tmp + cur * (num2[j]-'0') + (ans[i+j]-'0');
                tmp = a / 10;
                ans[i+j] = a % 10 + '0';
            }
            int idx = len2;
            while (tmp != 0) {
                int a = tmp + (ans[i+idx]-'0');
                tmp = a / 10;
                ans[i+idx] = a % 10 + '0';
                idx++;
            }
        }

        while (!ans.empty() && ans.back() == '0') 
            ans.pop_back();
        if (ans.empty()) return "0";
        reverse(ans.begin(), ans.end());
        return ans;
    }
};