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.

题意：这是一道大数乘法问题，这类算法可能一开始，我们真的想不到，所以我在网上找到算法之后，在纸上画了画感觉就好很多了，大家也可以根据我的例子在纸上画一画。

大数乘法的例子

java代码：

public String multiply(String num1, String num2) {
        num1 = new StringBuilder(num1).reverse().toString();
        num2 = new StringBuilder(num2).reverse().toString();
        int[] d = new int[num1.length() + num2.length()];
        for (int i = 0; i < num1.length(); i++) {
            int a = num1.charAt(i) - '0';
            for (int j = 0; j < num2.length(); j++) {
                int b = num2.charAt(j) - '0';
                d[i + j] += a * b;
            }
        }
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < d.length; i++) {
            int digit = d[i] % 10;
            int carry = d[i] / 10;
            sb.insert(0, digit);
            if (i < d.length - 1)
                d[i + 1] += carry;
        }
        // trim starting zeros
        while (sb.length() > 0 && sb.charAt(0) == '0') {
            sb.deleteCharAt(0);
        }
        return sb.length() == 0 ? "0" : sb.toString();
    }