93 lines
2.0 KiB
Markdown
93 lines
2.0 KiB
Markdown
---
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id: 59637c4d89f6786115efd814
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title: Hofstadter Q sequence
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challengeType: 5
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forumTopicId: 302287
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dashedName: hofstadter-q-sequence
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---
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# --description--
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The [Hofstadter Q sequence](https://en.wikipedia.org/wiki/Hofstadter_sequence#Hofstadter_Q_sequence "wp: Hofstadter_sequence#Hofstadter_Q_sequence") is defined as:
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$Q(1)=Q(2)=1, \\\\ Q(n)=Q\\big(n-Q(n-1)\\big)+Q\\big(n-Q(n-2)), \\quad n>2.$
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It is defined like the [Fibonacci sequence](https://rosettacode.org/wiki/Fibonacci sequence "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.
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# --instructions--
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Implement the Hofstadter Q Sequence equation as a function. The function should accept number, `n`, and return an integer.
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# --hints--
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`hofstadterQ` should be a function.
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```js
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assert(typeof hofstadterQ === 'function');
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```
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`hofstadterQ()` should return `integer`
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```js
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assert(Number.isInteger(hofstadterQ(1000)));
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```
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`hofstadterQ(1000)` should return `502`
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```js
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assert.equal(hofstadterQ(testCase[0]), res[0]);
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```
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`hofstadterQ(1500)` should return `755`
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```js
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assert.equal(hofstadterQ(testCase[1]), res[1]);
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```
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`hofstadterQ(2000)` should return `1005`
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```js
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assert.equal(hofstadterQ(testCase[2]), res[2]);
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```
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`hofstadterQ(2500)` should return `1261`
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```js
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assert.equal(hofstadterQ(testCase[3]), res[3]);
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```
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# --seed--
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## --after-user-code--
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```js
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const testCase = [1000, 1500, 2000, 2500];
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const res = [502, 755, 1005, 1261];
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```
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## --seed-contents--
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```js
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function hofstadterQ(n) {
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return n;
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}
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```
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# --solutions--
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```js
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function hofstadterQ (n) {
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const memo = [1, 1, 1];
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const Q = function (i) {
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let result = memo[i];
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if (typeof result !== 'number') {
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result = Q(i - Q(i - 1)) + Q(i - Q(i - 2));
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memo[i] = result;
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}
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return result;
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};
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return Q(n);
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}
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```
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