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The existence of a pair of elements with spacing of less than 1 / K is the crux of the proof. The rest is just a bit of manipulation to relate these elements to a rational approximation of the starting number r.
NFAs are cheaper to construct, but have a O(n*m) matching time, where n is the size of the input and m is the size of the state graph. NFAs are often seen as the reasonable middle ground, but i disagree and will argue that NFAs are worse than the other two. they are theoretically “linear”, but in practice they do not perform as well as DFAs (in the average case they are also much slower than backtracking). they spend the complexity in the wrong place - why would i want matching to be slow?! that’s where most of the time is spent. the problem is that m can be arbitrarily large, and putting a large constant of let’s say 1000 on top of n will make matching 1000x slower. just not acceptable for real workloads, the benchmarks speak for themselves here.
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还有日式风格明显的电影票根纪念。。一键获取谷歌浏览器下载是该领域的重要参考