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[Solved]: What is the TAK function for?

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We covered this in class today. I understand the mechanics of it, but aside from being a nice example of recursion does it serve any purpose?

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Searching the web reveals lots of pages with the formula and it's implementation in code, some talk about the author, but nothing about it's purpose.

Asked By : bot_bot

Answered By : luigif

You might use it to evaluate the performance of programming languages:

since recursive methods are pretty useful for benchmarking. In particular, deep recursion tests the speed with which a language can make method calls. This is important because modern applications have a tendency to spend much of their time calling various API functions.

You will also need it to solve ballot problems like this one:

Suppose A and B are candidates for office and there are 2n voters, n voting for A and n for B. In how many ways can the ballots be counted so that B is never ahead of A?

or just to generate Takeuchi Numbers:

0, 1, 4, 14, 53, 223, 1034, 5221, 28437, ...  
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