43. Multiply Strings

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.

num1[i] * num2[j]` will be placed at indices `[i + j`, `i + j + 1]`  //参考大神的code https://discuss.leetcode.com/topic/30508/easiest-java-solution-with-graph-explanation 

public class Solution {
    public String multiply(String num1, String num2) {
        int m = num1.length(); 
        int n = num2.length();
        int[] pos = new int[m+n];
        for(int i = m -1 ; i>= 0; i--){
            for(int j = n-1; j >= 0; j--){
                int pos1 = i + j;
                int pos2 = i+j+1;
                int mul = (num1.charAt(i) - '0') * (num2.charAt(j) - '0');
                int sum = mul + pos[pos2];
                pos[pos2] = sum % 10;
                pos[pos1] += sum /10;
            }
        }
        
        StringBuilder sb = new StringBuilder();
        for(int p : pos) {
            if(!(sb.toString().length() == 0 && p == 0))  //"0" * "0" = "00"
                sb.append(p);
        }
        return sb.toString().length() == 0? "0":sb.toString() ;
    }
}