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---
id: 594810f028c0303b75339acf
title: 阿克曼功能
title: Ackermann function
challengeType: 5
videoUrl: ''
forumTopicId: 302223
dashedName: ackermann-function
---
# --description--
<p> Ackermann函数是递归函数的典型示例,尤其值得注意的是它不是原始递归函数。它的值增长非常快,其调用树的大小也是如此。 </p><p> Ackermann函数通常定义如下 </p> $$ Amn= \\ begin {cases} n + 1\\ mbox {if} m = 0 \\\\ Am-1,1\\ mbox {if} m> 0 \\ mbox {和} n = 0 \\\\ Am-1Amn-1\\ mbox {if} m> 0 \\ mbox {和} n> 0. \\ end {cases} $$ <p>它的论点永远不会消极,它总是终止。编写一个返回$ Amn$的值的函数。任意精度是首选(因为函数增长如此之快),但不是必需的。 </p>
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.
The Ackermann function is usually defined as follows:
$A(m, n) = \\begin{cases} n+1 & \\mbox{if } m = 0 \\\\ A(m-1, 1) & \\mbox{if } m > 0 \\mbox{ and } n = 0 \\\\ A(m-1, A(m, n-1)) & \\mbox{if } m > 0 \\mbox{ and } n > 0. \\end{cases}$
Its arguments are never negative and it always terminates.
# --instructions--
Write a function which returns the value of $A(m, n)$. Arbitrary precision is preferred (since the function grows so quickly), but not required.
# --hints--
`ack`是一个功能。
`ack` should be a function.
```js
assert(typeof ack === 'function');
```
`ack(0, 0)`应该返回1。
`ack(0, 0)` should return 1.
```js
assert(ack(0, 0) === 1);
```
`ack(1, 1)`应该返回3。
`ack(1, 1)` should return 3.
```js
assert(ack(1, 1) === 3);
```
`ack(2, 5)`应该返回13
`ack(2, 5)` should return 13.
```js
assert(ack(2, 5) === 13);
```
`ack(3, 3)`应该返回61
`ack(3, 3)` should return 61.
```js
assert(ack(3, 3) === 61);