90 lines
2.7 KiB
Markdown
90 lines
2.7 KiB
Markdown
---
|
|
title: Hofstadter Q sequence
|
|
id: 59637c4d89f6786115efd814
|
|
challengeType: 5
|
|
---
|
|
|
|
## Description
|
|
<section id='description'>
|
|
<p>The <a href="https://en.wikipedia.org/wiki/Hofstadter_sequence#Hofstadter_Q_sequence" title="wp: Hofstadter_sequence#Hofstadter_Q_sequence">Hofstadter Q sequence</a> is defined as:</p>
|
|
<p>$Q(1)=Q(2)=1, \\ Q(n)=Q\big(n-Q(n-1)\big)+Q\big(n-Q(n-2)), \quad n>2.$</p>
|
|
<p>It is defined like the <a href="http://rosettacode.org/wiki/Fibonacci sequence" title="Fibonacci sequence">Fibonacci sequence</a>, but whereas the next term in the Fibonacci sequence is the sum of the previous two terms, in the Q sequence the previous two terms tell you how far to go back in the Q sequence to find the two numbers to sum to make the next term of the sequence.</p>
|
|
Task:
|
|
Implement the Hofstadter Q Sequence equation into JavaScript
|
|
</section>
|
|
|
|
## Instructions
|
|
<section id='instructions'>
|
|
|
|
</section>
|
|
|
|
## Tests
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
tests:
|
|
- text: <code>hofstadterQ</code> is a function.
|
|
testString: 'assert(typeof hofstadterQ === "function", "<code>hofstadterQ</code> is a function.");'
|
|
- text: <code>hofstadterQ()</code> should return <code>integer</code>
|
|
testString: 'assert(Number.isInteger(hofstadterQ(1000)), "<code>hofstadterQ()</code> should return <code>integer</code>");'
|
|
- text: <code>hofstadterQ(1000)</code> should return <code>502</code>
|
|
testString: 'assert.equal(hofstadterQ(testCase[0]), res[0], "<code>hofstadterQ(1000)</code> should return <code>502</code>");'
|
|
- text: <code>hofstadterQ(1500)</code> should return <code>755</code>
|
|
testString: 'assert.equal(hofstadterQ(testCase[1]), res[1], "<code>hofstadterQ(1500)</code> should return <code>755</code>");'
|
|
- text: <code>hofstadterQ(2000)</code> should return <code>1005</code>
|
|
testString: 'assert.equal(hofstadterQ(testCase[2]), res[2], "<code>hofstadterQ(2000)</code> should return <code>1005</code>");'
|
|
- text: <code>hofstadterQ(2500)</code> should return <code>1261</code>
|
|
testString: 'assert.equal(hofstadterQ(testCase[3]), res[3], "<code>hofstadterQ(2500)</code> should return <code>1261</code>");'
|
|
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
<section id='challengeSeed'>
|
|
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function hofstadterQ (n) {
|
|
// Good luck!
|
|
return n;
|
|
}
|
|
```
|
|
|
|
</div>
|
|
|
|
|
|
### After Test
|
|
<div id='js-teardown'>
|
|
|
|
```js
|
|
console.info('after the test');
|
|
```
|
|
|
|
</div>
|
|
|
|
</section>
|
|
|
|
## Solution
|
|
<section id='solution'>
|
|
|
|
|
|
```js
|
|
function hofstadterQ (n) {
|
|
const memo = [1, 1, 1];
|
|
const Q = function (i) {
|
|
let result = memo[i];
|
|
if (typeof result !== 'number') {
|
|
result = Q(i - Q(i - 1)) + Q(i - Q(i - 2));
|
|
memo[i] = result;
|
|
}
|
|
return result;
|
|
};
|
|
return Q(n);
|
|
}
|
|
|
|
```
|
|
|
|
</section>
|