## 43. Multiply Strings

Given two non-negative integers`num1`and`num2`represented as strings, return the product of`num1`and`num2`, also represented as a string.

Example 1:

``````Input: num1 = "2", num2 = "3"

Output: "6"
``````

Example 2:

``````Input: num1 = "123", num2 = "456"

Output: "56088"
``````

Note:

1. The length of both `num1`and `num2`is < 110.
2. Both `num1`and `num2`contain only digits `0-9`.
3. Both `num1`and `num2`do not contain any leading zero, except the number 0 itself.
4. You must not use any built-in BigInteger library or convert the inputs to integer directly.

Thoughts:

Start from right to left, perform multiplication on every pair of digits, and add them together. Let's draw the process! From the following draft, we can immediately conclude:

`````` `num1[i] * num2[j]` will be placed at indices `[i + j`, `i + j + 1]`
`````` ``````class Solution {
public String multiply(String num1, String num2) {
int m = num1.length(), n = num2.length();
int [] pro = new int[m + n];
for(int i = m-1; i >= 0  ; i--){
for (int j = n-1; j >= 0; j-- ){
int mul = (num1.charAt(i) - '0')*(num2.charAt(j) - '0');
int p1 = i + j, p2 = i + j + 1;
int sum = pro[p2] + mul;

pro[p1] += sum / 10;
pro[p2] = sum % 10;
}
}

StringBuilder sb = new StringBuilder();
for(int p : pro) if(!(sb.length() == 0 && p == 0)) sb.append(p); // triming leading 0 zeros
return sb.length() == 0 ? "0": sb.toString();
}
}
``````