freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/rosetta-code/hofstadter-q-sequence.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
59637c4d89f6786115efd814	Hofstadter Q sequence	5	302287	hofstadter-q-sequence

--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.

--instructions--

Implement the Hofstadter Q Sequence equation as a function. The function should accept number, n, and return an integer.

--hints--

hofstadterQ should be a function.

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

hofstadterQ() should return integer

assert(Number.isInteger(hofstadterQ(1000)));

hofstadterQ(1000) should return 502

assert.equal(hofstadterQ(testCase[0]), res[0]);

hofstadterQ(1500) should return 755

assert.equal(hofstadterQ(testCase[1]), res[1]);

hofstadterQ(2000) should return 1005

assert.equal(hofstadterQ(testCase[2]), res[2]);

hofstadterQ(2500) should return 1261

assert.equal(hofstadterQ(testCase[3]), res[3]);

--seed--

--after-user-code--

const testCase = [1000, 1500, 2000, 2500];
const res = [502, 755, 1005, 1261];

--seed-contents--

function hofstadterQ(n) {

  return n;
}

--solutions--

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);
}