Game of Codes (mind game)

[Kevin]

In this game you will need to create a code to change the 'given' numbers into the 'target' numbers. The 'given' numbers will be processed based on your code.

Codes part 1:

Spoiler (Click to View)

PART 1 - AS-DH
Here are the terms:
A - Addition. This adds a number by one. If the number is nine, it will become zero instead of ten.
S - Subtraction. This is the reverse of addition, decreasing the number by one, and become nine if the number if zero.

D - Double. This doubles a number. Two becomes four, three becomes six. If the result is greater than nine, then only the last digit will be used. For example, if we double a '6', 6x2 = 12, and the last digit is '2'. So six will become two if doubled.
H - Half. This halves a number. Any decimals will be discarded. So, both six and seven will become three if halved.


An example of a problem.
Given numbers: 6543
Target numbers: 3456

The first digit of the given number is six and it needs to be converted into three, so we need to half it. The code to half a number is 'H'. So the first letter in our code should be 'H'.

Then, the five needs a subtraction to become four, while the four needs an addition to become five. So we will use 'S' and then 'A'.

The last digit needs to be doubles so we use a 'D'.

So our code is: HSAD. The problem is solved .

Codes part 2:

Spoiler (Click to View)

Easy isn't it? But to solve some problems, we need the connector.
The connector's symbol is 'AA'. So if we write the code 'SAAD', the A's in the code does not mean an addition, but a connector.

Now what does a connector do? It connects the code before and after it. Connected code will work on the same digit. Take a look at this example.
Given Number: 2
Target Number: 8

None of our AS-DH code can solve this problem. We need to double the number twice. How to do this? We use the connector.
Code: DAAD

This is a perfect answer. The first 'D' is connected by the connector 'AA' to the second 'D'. This makes both 'D' code works for the same digit. So after being doubled by the first 'D', the number will again be doubled by the second 'D'.
DAAD: 2 --> 4 --> 8

Another example
Given Number: 37
Target Number: 73

Code: DAAAH

Explanation: The 'AA' connects the 'D' with the third 'A'. So this process happens to the first digit:
3 DOUBLE --> 6 ADDITION --> 7

Meanwhile, the code 'H' is just a normal Half. It halves the number seven.
7 HALF --> 3.5 <rounded down> --> 3


You can also connect three or more operations. Example:
Given number: 7
Target number: 0

There are two effective answers to this problem:
Code #1: AAAAAAA
Code #2:HAAHAAH

Explanation:
Code #1:
let's divide it into parts to understand the code:
A-AA-A-AA-A
Translated into words, it becomes: Addition Connector Addition Connector Addition Subtraction Connector Addition.
So the two first connectors connects the three additions. The first digit will be added three times: 7 ADDITION --> 8 ADDITION --> 9 ADDITION --> 0

Code #2:
Similar to Code #1, except we use three 'Half's instead of additions.
7 HALF --> 3.5 <rounded down> --> 3 HALF --> 1.5 <rounded down> --> 1 HALF --> 0.5 <rounded down> --> 0

Part 3:

Spoiler (Click to View)

Numbers in code shows how many times a code will be used. For example:
Given Number: 246
Target Number: 357

Since each number needs an 'A', you can say this:
Code: A3
Which means: AAA.
This can greatly shorten the code in certain cases.

Additionally, brackets may be used to groups codes. Brackets are not counted when counting the code's length.
For example:
Given Number: 244772
Target number: 385484

The code, instead of: ADADAD, (length=6)
can be written as: (AD)3 (length = 3)

Using brackets in brackets is allowed. For example:
Given Number: 0122654850
Target Number: 1234568909
Code: ((AD)2S)2
Explanation: (AD)2 equals to ADAD, so the long code is: ADADSADADS. Then, it is a normal code.

We have already three parts above. I will be adding more rules to make everything more complicated, but let's start with a simpler one. I hope my sentences are understandable xD .

Problem #1
Given Number: 13895
Target Number: 24680

Code = ???

If you answered this problem, you may post another problem too - just don't make it too long xD . If you feel like it's too easy, I'll add more rules to the codes.