Double run-length encoding

Everyone knows what run-length encoding is. It has been the subject of many code-golf challenges already. We'll be looking at a certain variation.

Example

Normal: 11222222222222222222233333111111111112333322
Run-length: 112(19)3(5)1(11)2333322

The number in parentheses specifies the number of times the previous symbol occurred. In the example, only runs of 5 or more characters were encoded. This is because encoding runs of 4 or less doesn't improve the character count.

Challenge

Write a function/program that implements this variation of run-length encoding, but can also encode runs of two symbols. The runs of two symbols must also be enclosed in parentheses. A group will also be enclosed in parentheses. Your program must accept a string as input, and output the modified string with modifications that shorten the string.

Example

Normal: 111244411144411144411167676767222222277777222222277777123123123123
Double run-length: 1112((444111)(3))67676767((2(7)7(5))(2))123123123123

Notes

111 was not encoded because encoding it (1(3)) is not shorter.
The string 444111 occurs 3 times so it is encoded.
676767 was not encoded because ((67)(4)) is longer than before.
222222277777222222277777 was not encoded as ((222222277777)(2)). Why? Because 222222277777 itself can be reduced to 2(7)7(5).
123123123123 isn't encoded because your program is supposed to handle runs of two symbols, not three.

This is code-golf so shortest code wins. Tie-breaker is early submission.

If I missed anything, or if you are unsure of anything please notify me in the comments.

ericw31415

Posted 2016-05-06T18:43:57.970

Reputation: 2 229

But there are 4 67s. – Leaky Nun – 2016-05-06T18:58:00.303

Will we have to handle 441444144414 -> ((4414)(3))? – Leaky Nun – 2016-05-06T18:58:58.887

I have fixed it. – ericw31415 – 2016-05-06T18:59:08.547

@KennyLau No, you will not. 4414 is technically a series of 4. My wording is just bad. – ericw31415 – 2016-05-06T18:59:56.880

Can 111111111 be encoded as (1)(9)? – CalculatorFeline – 2016-05-06T21:44:53.190

It should be encoded as 1(9), because it's shorter than (1)(9). – ericw31415 – 2016-05-06T22:14:28.573

((4(9)1)(2)) or 4(9)14(9)1? – Leaky Nun – 2016-05-07T02:26:18.983

The second one. Remember, pick whichever is shorter. – ericw31415 – 2016-05-07T10:22:24.487

You might want to add more testcases (hint: they are in my solution) – Leaky Nun – 2016-05-07T10:30:44.880

Um, (67(4)) [7 characters] is definitely shorter than 67676767 [8 characters]. – Dúthomhas – 2016-05-07T10:48:01.313

(67(4)) implies 67777. – ericw31415 – 2016-05-07T11:10:25.497

Yoinks! (I need sleep, apparently.) – Dúthomhas – 2016-05-07T11:15:21.883

@ppperry I believe that should be (4(1111)). – ericw31415 – 2017-08-22T21:26:14.473

If you input 10101010100100100100100, the output is ((10)(5))0((100)(4)), yet ((10)(4))((100)(5)) would be one character shorter. – Marv – 2016-05-08T01:38:35.337

Do you really have to use such marginal testcases.... – Leaky Nun – 2016-05-08T01:41:31.777

Yes, thats all the fun! :^) – Marv – 2016-05-08T01:46:49.090

It's funny how this is the only answer currently here. – ericw31415 – 2016-05-23T23:50:10.520