2.9 KiB
2.9 KiB
title | id | challengeType |
---|---|---|
Hailstone sequence | 595608ff8bcd7a50bd490181 | 5 |
Description
- If n is 1 then the sequence ends.
- If n is even then the next n of the sequence
= n/2
- If n is odd then the next n of the sequence
= (3 * n) + 1
Instructions
- Create a routine to generate the hailstone sequence for a number.
- Use the routine to show that the hailstone sequence for the number 27 has 112 elements starting with
27, 82, 41, 124
and ending with8, 4, 2, 1
- Show the number less than 100,000 which has the longest hailstone sequence together with that sequence's length. (But don't show the actual sequence!)
- xkcd (humourous).
Tests
tests:
- text: <code>hailstoneSequence</code> is a function.
testString: assert(typeof hailstoneSequence === 'function', '<code>hailstoneSequence</code> is a function.');
- text: <code>hailstoneSequence()</code> should return <code>[[27,82,41,124,8,4,2,1], [351, 77031]]</code>
testString: assert.deepEqual(hailstoneSequence(), res, '<code>hailstoneSequence()</code> should return <code>[[27,82,41,124,8,4,2,1], [351, 77031]]</code>');
Challenge Seed
// noprotect
function hailstoneSequence() {
const res = [];
// Good luck!
return res;
}
After Test
const res = [[27, 82, 41, 124, 8, 4, 2, 1], [351, 77031]];
Solution
// noprotect
function hailstoneSequence () {
const res = [];
function hailstone(n) {
const seq = [n];
while (n > 1) {
n = n % 2 ? 3 * n + 1 : n / 2;
seq.push(n);
}
return seq;
}
const h = hailstone(27);
const hLen = h.length;
res.push([...h.slice(0, 4), ...h.slice(hLen - 4, hLen)]);
let n = 0;
let max = 0;
for (let i = 100000; --i;) {
const seq = hailstone(i);
const sLen = seq.length;
if (sLen > max) {
n = i;
max = sLen;
}
}
res.push([max, n]);
return res;
}