According to the benchmark in the article it’s already way faster at n = 1000. I think you’re overestimating the cost of multiplication relative to just cutting down n logarithmically.
log_2(1000) = roughly a growth factor of 10. 2000 would be 11, and 4000 would be 12. Logs are crazy.
The article is comparing to the dynamic programming algorithm, which requires reading and writing to an array or hash table (the article uses a hash table, which is slower).
The naive algorithm is way faster than the DP algorithm.
According to the article the linear algebra algorithm has a running time of O(log n)
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According to the benchmark in the article it’s already way faster at n = 1000. I think you’re overestimating the cost of multiplication relative to just cutting down n logarithmically.
log_2(1000) = roughly a growth factor of 10. 2000 would be 11, and 4000 would be 12. Logs are crazy.
The article is comparing to the dynamic programming algorithm, which requires reading and writing to an array or hash table (the article uses a hash table, which is slower).
The naive algorithm is way faster than the DP algorithm.