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class Solution(object):
    def multiply(self, num1, num2):
        """
        :type num1: str
        :type num2: str
        :rtype: str
        """
        m = len(num1);
        n = len(num2);
        
        res = [ 0 for i in xrange(m + n)];
        
        for i in xrange(m - 1, -1, -1):
            for j in xrange(n - 1, -1, -1):
                temp = int(num1[i]) * int(num2[j]) + res[i + j + 1];
                res[i + j] += temp / 10;
                res[i + j + 1] = temp % 10;
        
        resString = "";
        for i in res:
            if len(resString) == 0 and i == 0:
                continue;
            resString += str(i);
        
        return '0' if len(resString) == 0 else resString;
      
      
      
"""
TESTCASES:
Input:
"0"
"0"
"999"
"99"

Output:
"0"
"98901"

"""
"""
##########
#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]` 
#Multiplication

    1 2 3
      4 5
    ------
      1 5
    1 0
  0 5
    1 2
  0 8
0 4 
--------------
0 1 2 3 4   [index]

"""
                

public class Solution {
    public String multiply(String num1, String num2) {
        int len1 = num1.length();
        int len2 = num2.length();
        
        int[] res = new int[ len1 + len2];
        
        for(int i = len1 - 1; i >= 0; i-- ){
            for(int j = len2 - 1; j >=0; j-- ){
                int temp = (num1.charAt(i) - '0') * (num2.charAt(j) - '0') + res[i + j + 1];
                res[i + j] += temp / 10;
                res[i + j + 1] = temp % 10;
            }
        }
        
        StringBuilder resString = new StringBuilder();
        
        for(int i = 0; i < res.length; i++){
            if( resString.length() == 0 && res[i] == 0){
                continue;
            }
            resString.append(res[i]);
        }
        
        return resString.length() == 0 ? "0" : resString.toString();
    }
}


/*
"0"
"0"
"999"
"99"
"100"
"100"


    1 2 3
      4 5
    ------
      1 5
    1 2
    1 0    //res[i + j] += temp / 10; 累加！！
  0 8 
  0 5
0 4 
--------------
0 5 5 3 5
0 1 2 3 4   [index]
*/