70 lines
1.6 KiB
Markdown
70 lines
1.6 KiB
Markdown
---
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title: Ackermann function
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id: 594810f028c0303b75339acf
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challengeType: 5
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forumTopicId: 302223
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---
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## Description
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<section id='description'>
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The Ackermann function is a classic example of a recursive function, notable especially because it is not a primitive recursive function. It grows very quickly in value, as does the size of its call tree.
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The Ackermann function is usually defined as follows:
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$A(m, n) = \begin{cases} n+1 & \mbox{if } m = 0 \\ A(m-1, 1) & \mbox{if } m > 0 \mbox{ and } n = 0 \\ A(m-1, A(m, n-1)) & \mbox{if } m > 0 \mbox{ and } n > 0. \end{cases}$
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Its arguments are never negative and it always terminates.
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</section>
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## Instructions
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<section id='instructions'>
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Write a function which returns the value of $A(m, n)$. Arbitrary precision is preferred (since the function grows so quickly), but not required.
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>ack</code> is a function.
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testString: assert(typeof ack === 'function');
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- text: <code>ack(0, 0)</code> should return 1.
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testString: assert(ack(0, 0) === 1);
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- text: <code>ack(1, 1)</code> should return 3.
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testString: assert(ack(1, 1) === 3);
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- text: <code>ack(2, 5)</code> should return 13.
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testString: assert(ack(2, 5) === 13);
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- text: <code>ack(3, 3)</code> should return 61.
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testString: assert(ack(3, 3) === 61);
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function ack(m, n) {
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// Good luck!
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}
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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function ack(m, n) {
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return m === 0 ? n + 1 : ack(m - 1, n === 0 ? 1 : ack(m, n - 1));
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}
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```
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</section>
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