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

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
594810f028c0303b75339acf	Ackermann function	5	302223	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.

assert(typeof ack === 'function');

ack(0, 0) should return 1.

assert(ack(0, 0) === 1);

ack(1, 1) should return 3.

assert(ack(1, 1) === 3);

ack(2, 5) should return 13.

assert(ack(2, 5) === 13);

ack(3, 3) should return 61.

assert(ack(3, 3) === 61);

--seed--

--seed-contents--

function ack(m, n) {

}

--solutions--

function ack(m, n) {
  return m === 0 ? n + 1 : ack(m - 1, n === 0 ? 1 : ack(m, n - 1));
}