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Comment · 1 year ago
Comment · 1 year ago
If you have "3 1 5" and you burst 1, you gain 3x1x5 points and the state becomes "3 5", with the two remaining balloons being adjacent to each other.

The "1x3x1=1" part for the earlier example is a typo indeed, it should be 3.

Comment · 1 year ago
> I wouldn't say there's a ton to connect.

What's the point of your rude post? OP already knows this. In fact, they learned it from Tom Lehrer.

Comment · 1 year ago
Parent's point is that sometimes (but not always) the store is perfectly fine selling you a car for $1 less than what the "price tag" of Delta(G)+1 dollars asks for, so "need" is a bit inaccurate.
Comment · 1 year ago
For the edge-coloring problem, the optimal number of colors needed to properly color the edges of G is always either Delta(G) (the maximum degree of G) or Delta(G) + 1, but deciding which one is the true optimum is an NP-complete problem.

Nevertheless, you can always properly edge-color a graph with Delta(G) + 1 colors. Finding such a coloring could in principle be slow, though: the original proof that Delta(G) + 1 colors is always doable amounted to a O(e(G) * v(G)) algorithm, where e(G) and v(G) denote the number of edges and vertices of G, respectively. This is polynomial, but nowhere near linear. What the paper in question shows is how, given any graph G, to find an edge coloring using Delta(G) + 1 colors in O(e(G) * log(Delta(G))) time, which is linear time if the maximum degree is a constant.

Comment · 1 year ago
As you point out, 'icônes' is French for 'icons'; the name is probably related to the fact that the site is built using Vite. Was NES capitalized in the title earlier?
Comment · 1 year ago
Comment · 1 year ago
Comment · 1 year ago
Comment · 1 year ago
Volume 4, Fascicle 7 was officially released this week! The latest draft ("prefascicle", dated December 2024) is available at https://www-cs-faculty.stanford.edu/~knuth/fasc7a.ps.gz. As Knuth says, the contents "agree fairly well with the contents of the first paperback printing of Volume 4, Fascicle 7, except for parts of the index. As usual, the prefascicle is 'frozen' and will not be maintained, while the paperback will gradually improve with time."

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