[LeetCode] Multiply Strings 字符串相乘

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.

这道题让我们求两个字符串数字的相乘，输入的两个数和返回的数都是以字符串格式储存的，这样做的原因可能是这样可以计算超大数相乘，可以不受int或long的数值范围的约束，那么我们该如何来计算乘法呢，我们小时候都学过多位数的乘法过程，都是每位相乘然后错位相加，那么这里就是用到这种方法，参见网友JustDoIt的博客，把错位相加后的结果保存到一个一维数组中，然后分别每位上算进位，最后每个数字都变成一位，然后要做的是去除掉首位0，最后把每位上的数字按顺序保存到结果中即可，代码如下：

class Solution {
public:
    string multiply(string num1, string num2) {
        string res;
        int n1 = num1.size(), n2 = num2.size();
        int k = n1 + n2 - 2, carry = 0;
        vector<int> v(n1 + n2, 0);
        for (int i = 0; i < n1; ++i) {
            for (int j = 0; j < n2; ++j) {
                v[k - i - j] += (num1[i] - ‘0‘) * (num2[j] - ‘0‘);
            }
        }
        for (int i = 0; i < n1 + n2; ++i) {
            v[i] += carry;
            carry = v[i] / 10;
            v[i] %= 10;
        }
        int i = n1 + n2 - 1;
        while (v[i] == 0) --i;
        if (i < 0) return "0";
        while (i >= 0) res.push_back(v[i--] + ‘0‘);
        return res;
    }
};