You Won't Believe The Scientific Proofs Snoop Dogg Just Dropped

In this video, Snoop Dogg overengineers an algebraic explanation to a simple bioinformatics problem. In essence, he will teach us how we can compute the index value of a k-mer (basically a word of size k) in a nucleotide string in strictly O(n). That is, accessing every nucleotide only once! Moreover, he will prove why it is correct from an algebraic standpoint.
The code listing shown at the end is taken from github.com/refresh-bio/kmer-d....
Many other bioinformatics tools also make use of this trick.
Timestamps:
00:00:00 Introduction to comparative genomics
00:00:45 Simple example
00:02:44 General case proofs
00:03:53 Computational application
00:05:16 Real-world use of the trick
Well, I definitely sunk way more time than I anticipated on this one. But I had never seen a formal derivation for this, so there we go. Anyway if you liked this video, there is no chance you like my other videos, because they are completely unrelated. Yet you can check them out here:
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S, N, double O, P, D, O, double G? More like C, A, double G, T, A, G, double C...