43. Multiply Strings 大数相乘 leetcode

题目：

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.
• Converting the input string to integer is NOT allowed.
• You should NOT use internal library such as BigInteger.

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思路：

首先将两个字符串翻转，那么mul[i + j] += (num1[i] - '0') * (num2[j] - '0');，然后转换为string输出。

代码：

class Solution {
public:
    string multiply(string num1, string num2) {
	reverse(num1.begin(), num1.end());
	reverse(num2.begin(), num2.end());
	int m = num1.size(), n = num2.size();
	vector<int> mul(m + n, 0);
	for (int i = 0; i < m; i++)
		for (int j = 0; j < n; j++)
			mul[i + j] += (num1[i] - '0') * (num2[j] - '0');
		
	for (int i = 0; i < m + n - 1; i++)
	{
		int remainder = mul[i] % 10, quotients = mul[i] / 10;
		mul[i] = remainder;
		mul[i + 1] += quotients;
	}
	string ans("");
	int i = m + n - 1;
	while ( i >= 0 && mul[i] == 0) i-- ;
	if (i == -1)return "0";
	else
		for (int k = i; k >= 0; k--)
				ans += mul[k] + '0';
	
	return ans;
    }
};

总结：很简单的一道题，考的是string的基础。