freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/rosetta-code/ackermann-function.english.md

title	id	challengeType
Ackermann function	594810f028c0303b75339acf	5

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. Write a function which returns the value of $A(m, n)$. Arbitrary precision is preferred (since the function grows so quickly), but not required.

Instructions

Tests

tests:
  - text: <code>ack</code> is a function.
    testString: assert(typeof ack === 'function', '<code>ack</code> is a function.');
  - text: <code>ack(0, 0)</code> should return 1.
    testString: assert(ack(0, 0) === 1, '<code>ack(0, 0)</code> should return 1.');
  - text: <code>ack(1, 1)</code> should return 3.
    testString: assert(ack(1, 1) === 3, '<code>ack(1, 1)</code> should return 3.');
  - text: <code>ack(2, 5)</code> should return 13.
    testString: assert(ack(2, 5) === 13, '<code>ack(2, 5)</code> should return 13.');
  - text: <code>ack(3, 3)</code> should return 61.
    testString: assert(ack(3, 3) === 61, '<code>ack(3, 3)</code> should return 61.');

Challenge Seed

function ack (m, n) {
  // Good luck!
}

Solution

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