Find a Median String solved by 1450

Given a k-mer Pattern and a longer string Text, we use d(Pattern, Text) to denote the minimum Hamming distance between Pattern and any k-mer in Text,

$d(\textit{Pattern}, \textit{Text}) = \min\limits_{\text{all k-mers Pattern' in Text}}{HammingDistance(Pattern, Pattern')}.$

Given a k-mer Pattern and a set of strings Dna = {Dna₁, … , Dna_t}, we define d(Pattern, Dna) as the sum of distances between Pattern and all strings in Dna,

$d(\textit{Pattern},\textit{Dna}) = \sum\limits_{i=1}^t d(\textit{Pattern},\textit{Dna}_i).$

Our goal is to find a k-mer Pattern that minimizes d(Pattern, Dna) over all k-mers Pattern, the same task that the Equivalent Motif Finding Problem is trying to achieve. We call such a k-mer a median string for Dna.

Median String Problem

Find a median string.

Given: An integer k and a collection of strings Dna.

Return: A k-mer Pattern that minimizes d(Pattern, Dna) over all k-mers Pattern. (If multiple answers exist, you may return any one.)

Sample Dataset

3
AAATTGACGCAT
GACGACCACGTT
CGTCAGCGCCTG
GCTGAGCACCGG
AGTACGGGACAG

Sample Output

GAC

Extra Datasets

Click for debug datasets