length of the longest possible string contains no repeated 3-mers

Question

I'm trying to find the length of the longest possible string of consecutive digits that contains no repeated 3-mers.

This is a bioinformatics question, and I'm sorting this for protein sequence.

basically, something like 0102340109 does not work because 010repeats.

But something like 0002223589765 works because you cannot find any repeated 3 digits.

I need to find the longest sequence and I'm kinda stuck and clueless.

Do you really have nine distinct digits in your actual application, or is the real number there considerably different? Would `701080109` contain a repeated `010` even though the string in between is not a multiple of three digits in length? How about overlapping repeats? Would `01010` be illegal because there are two occurrences of `010` even though they overlap? — MvG, Nov 02 '16 at 08:02
I think this is the reference you need https://en.wikipedia.org/wiki/De_Bruijn_sequence — Bill, Nov 02 '16 at 08:51
Thank you so much! I never thought about its actually de bruijin sequence — JY078, Nov 02 '16 at 17:49

Mulan · Answer 1 · 2016-11-07T07:12:34.217

The following codes are written in ES6. You can make a sliding procedure which takes a string input a returns an Iterable of substring "windows"

Array.from(sliding (3,1) ('012345'))
// [ '012', '123', '234', '345' ]

Array.from(sliding (2,2) ('012345'))
// [ '01', '23', '45' ]

Array.from(sliding (4,2) ('012345'))
// [ '0123', '1234', '2345' ]

Then, using this, you can define a seqIsRepeated procedure which iterates thru the sliding windows. Instead of pre-computing the entire list of windows, we will look at them 1-by-1, adding each result to a Set. If the window already exists in the Set, true will be returned immediately and iteration is stopped. If the procedure makes it thru all windows without finding a duplicate, false will be returned.

const sliding = (m,n) => function* (xs) {
  for (let i = 0; i + m <= xs.length; i += n)
    yield xs.substr(i, m);
};

const seqIsRepeated = n => xs => {
  let set = new Set();
  for (let seq of sliding (n,1) (xs))
    if (set.has(seq))
      return true;
    else
      set.add(seq);
  return false;
};

console.log (seqIsRepeated (3) ('0102340109'));    // true
console.log (seqIsRepeated (3) ('0002223589765')); // false

This doesn't find you the longest sequence, but hopefully it does give you a start. From here, you'd be looking at substrings of your input sequence and using seqIsRepeated(3) to eliminate substrings as possibilities

length of the longest possible string contains no repeated 3-mers

1 Answers1