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curriculum/challenges/italian/10-coding-interview-prep/rosetta-code/ackermann-function.md

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+---
+id: 594810f028c0303b75339acf
+title: Ackermann function
+challengeType: 5
+forumTopicId: 302223
+dashedName: ackermann-function
+---
+
+# --description--
+
+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` should be a function.
+
+```js
+assert(typeof ack === 'function');
+```
+
+`ack(0, 0)` should return 1.
+
+```js
+assert(ack(0, 0) === 1);
+```
+
+`ack(1, 1)` should return 3.
+
+```js
+assert(ack(1, 1) === 3);
+```
+
+`ack(2, 5)` should return 13.
+
+```js
+assert(ack(2, 5) === 13);
+```
+
+`ack(3, 3)` should return 61.
+
+```js
+assert(ack(3, 3) === 61);
+```
+
+# --seed--
+
+## --seed-contents--
+
+```js
+function ack(m, n) {
+
+}
+```
+
+# --solutions--
+
+```js
+function ack(m, n) {
+  return m === 0 ? n + 1 : ack(m - 1, n === 0 ? 1 : ack(m, n - 1));
+}
+```