Creating a Character Table from Genetic Strings solved by 432

Phylogeny from Genetic Characters

In “Creating a Character Table”, we introduced the character table as a way of representing a number of characters simultaneously. In that problem, we found a character table representing an unrooted binary tree on a collection of taxa.

Of course, in practice, the problem operates in reverse. We first need to generate a character table before we can model a phylogeny on this table. In modern genetics, a reliable way to obtain a large number of characters is by using SNPs. As mentioned in “Counting Subsets”, for a given SNP, we can divide taxa into two sets depending on which of two bases is present at the nucleotide, thus defining the split of a character.

Problem

A collection of strings is characterizable if there are at most two possible choices for the symbol at each position of the strings.

Given: A collection of at most 100 characterizable DNA strings, each of length at most 300 bp.

Return: A character table for which each nontrivial character encodes the symbol choice at a single position of the strings. (Note: the choice of assigning '1' and '0' to the two states of each SNP in the strings is arbitrary.)

Sample Dataset

ATGCTACC
CGTTTACC
ATTCGACC
AGTCTCCC
CGTCTATC

Sample Output

10110
10100

Note

Recall that the character table does not encode trivial characters.