43. Multiply Strings

Given two non-negative integersnum1andnum2represented as strings, return the product ofnum1andnum2, 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 num1and num2is < 110.
2. Both num1and num2contain only digits 0-9.
3. Both num1and num2do 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();
    }
}