# 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

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](https://drscdn.500px.org/photo/130178585/m%3D2048/300d71f784f679d5e70fadda8ad7d68f)](https://drscdn.500px.org/photo/130178585/m%3D2048/300d71f784f679d5e70fadda8ad7d68f)

## Code

```java
public String multiply(String num1, String num2) {
    int m = num1.length(), 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 mul = (num1.charAt(i) - '0') * (num2.charAt(j) - '0'); 
            int p1 = i + j, p2 = i + j + 1;
            int sum = mul + pos[p2];

            pos[p1] += sum / 10;
            pos[p2] = (sum) % 10;
        }
    }  

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