加法乘法模拟

题目 字符串相乘43. 字符串相乘 - 力扣（LeetCode） (leetcode-cn.com)

无论是模拟乘法还是加法，流程都可归纳为：

循环按位加法或者乘法运算得到tempres->curr(tempres/10)->进位carry(tempres%进制)

class Solution {
public:
    string multiply(string num1, string num2) {
        if (num1 == "0" || num2 == "0") {
            return "0";
        }
        string ans = "0";
        int m = num1.size(), n = num2.size();
        for (int i = n - 1; i >= 0; i--) {//num2每一位与num1相乘
            string curr;
            int add = 0;
            for (int j = n - 1; j > i; j--) {
                curr.push_back(0);
            }
            int y = num2.at(i) - '0';
            for (int j = m - 1; j >= 0; j--) {
                int x = num1.at(j) - '0';
                int product = x * y + add;
                curr.push_back(product % 10);
                add = product / 10;
            }
            while (add != 0) {
                curr.push_back(add % 10);
                add /= 10;
            }
            reverse(curr.begin(), curr.end());
            for (auto &c : curr) {
                c += '0';
            }
            ans = addStrings(ans, curr);
        }
        return ans;
    }
    //字符串相加
    string addStrings(string &num1, string &num2) {
        int i = num1.size() - 1, j = num2.size() - 1, add = 0;
        string ans;
        while (i >= 0 || j >= 0 || add != 0) {
            int x = i >= 0 ? num1.at(i) - '0' : 0;
            int y = j >= 0 ? num2.at(j) - '0' : 0;
            int result = x + y + add;
            ans.push_back(result % 10);
            add = result / 10;
            i--;
            j--;
        }
        reverse(ans.begin(), ans.end());
        for (auto &c: ans) {
            c += '0';
        }
        return ans;
    }
};