freeCodeCamp/curriculum/challenges/en/08-coding-interview-prep/rosetta-code/hofstadter-q-sequence.en.md

title, id, challengeType

title	id	challengeType
Hofstadter Q sequence	59637c4d89f6786115efd814	5

Description

The Hofstadter Q sequence is defined as:

$Q(1)=Q(2)=1, \\ Q(n)=Q\big(n-Q(n-1)\big)+Q\big(n-Q(n-2)), \quad n>2.$

It is defined like the Fibonacci sequence, 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.

Task: Implement the Hofstadter Q Sequence equation into JavaScript

Instructions

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>'');'

Challenge Seed

function hofstadterQ (n) {
  // Good luck!
  return n;
}

After Test

console.info('after the test');

Solution

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);
}