1.8 KiB
1.8 KiB
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));
}