43. Multiply Strings

Given two non-negative integers

num1

and

num2

represented as strings, return the product of

num1

and

num2

.

Note:

The length of both

num1

and

num2

is < 110.
Both

num1

and

num2

contains only digits

0-9

.
Both

num1

and

num2

does not contain any leading zero.
You must not use any built-in BigInteger library or
convert the inputs to integer directly.



求两个字符串表示的数相乘的结果，以字符串形式表示。和多项式的相乘类似，结果res的第n位是所有符合i+j=n的第i和j项相乘得到的，因为是十进制，所以取mod 10的结果，多出的部分进位。代码如下：

class Solution
{
public:
string multiply(string num1, string num2)
{
int m = num1.size(), n = num2.size();
if(m == 0 || n == 0) return 0;
string res(m + n, '0');

reverse(num1.begin(), num1.end());
reverse(num2.begin(), num2.end());

for(int i = 0; i < m; ++i)
{
int r = 0;
for(int j = 0; j < n; ++j)
{
int tmp = (res[i + j] - '0') + (num1[i] - '0') * (num2[j] - '0') + r;
res[i + j] = tmp % 10 + '0';
r = tmp / 10;
}
res[i + n] += r;
}

reverse(res.begin(), res.end());

size_t pos = res.find_first_not_of("0");
if(pos != string::npos)
{
return res.substr(pos);
}

return "0";
}
};