Great idea! It also works on the side of the board, I couldn't help building it out: https://onemillionchessboards.com/#4363,6
HN user
melonmouse
https://twitter.com/MelonMouseGames
The linked proof for that median of medians is O(n) feels counterintuitive to me. Here's a (simpler?) alternative.
T(0) = 0
T(1) = 1
T(n) = n + T(n/5) + T(7/10*n)
We want to prove that: T(n) ≤ C*n
It is intuitive that T(a+b) ≥ T(a) + T(b), or in other words, T is superadditive. That can be shown by induction:Induction base: it holds for all a+b < 1, the only case being a=0, b=0:
T(0+0) = 0 + T(0) + T(0) ≥ T(0) + T(0)
Induction step: suppose it holds for all a+b < k. Let a+b = k. T(a+b) = T(k)
= k + T(k/5) + T(7/10*k)
≥ k + T(a/5) + T(b/5) + T(7/10*a) + T(7/10*b)
= [a + T(a/5) + T(7/10*a)] + [b + T(b/5) + T(7/10*b)]
= T(a) + T(b)
Because T is superadditive: T(n) = n + T(n/5) + T(7/10*n)
≤ n + T(n/5 + 7/10*n)
= n + T(9/10*n)
Now we can apply the master theorem. Or to write out the proof (using a geometric series): T(n) ≤ n + T(9/10*n)
≤ n * ∑ᵢ₌₀ᶦⁿᶠᶦⁿᶦᵗʸ (9/10)^i
= n * 1/(1-9/10)
= 10*n
So, we have shown the algorithm is O(n) with C=10 (or less).As a joke, I made a webpage where you can do attribution to ALL GitHub repositories:
It scrolls past all the repos movie-credits-style. Doing it that way takes several days! It shows how abstract and absurd giving contribution to such a large body of works is.
Who should we thank for the code written by Copilot? In a way, we should thank everyone in the training data. That includes: everyone with a public Github repository.
Context: https://github.com/usewits/ThanksForTheCode
You can customize it like this: thanksforthecode.com?name=PROJECT_NAME
Another funemployed xoogler here! I've been making games for the last year, and one thing I would definitely love to explore is designing a deep but easy to learn game using learning techniques. We should talk!
You can reach me on: melonmousegames@gmail.com
This is factually wrong, looks at CO2 emissions per capita, USA has carbon footprint double that of France.
It's closer to 3x: USA 15.7 vs France 5.2 tonnes of CO2 per capita per year (2017, not accounting for other gasses that contribute to warming) [1]
[1] https://en.wikipedia.org/wiki/List_of_countries_by_carbon_di...
I made a game about polyominoes: https://melonmouse.itch.io/polyominoes
If you try it out, please let me know what you think :)
P.S. work on that led to a sequence on the Online Encyclopedia of Integer Sequences: https://oeis.org/A239658