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Problem14.html
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<html>
<head>
<title>
Project Euler, Problem 14: Longest Collatz Sequence
</title>
<link rel="stylesheet" type="text/css" href="eulerStyle.css" />
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
</head>
<body>
<header>
<svg height="5rem" width="90vw">
<a href="https://dkallen78.github.io/Project-Euler-Files/projectEulerIndex.html">
<text id="euler" x="50%" y="50%" text-anchor="middle" dominant-baseline="middle">
Project Euler
</text>
</a>
</svg>
<br />
<svg height="4rem" width="90vw">
<a href="https://projecteuler.net/problem=14">
<text id="problemID" x="50%" y="50%" text-anchor="middle" dominant-baseline="middle">
Problem 14: Longest Collatz Sequence
</text>
</a>
</svg>
</header>
<nav>
<svg height="3rem" width="75vw">
<a href="https://dkallen78.github.io/Project-Euler-Files/Problem13.html">
<text x="0%" y="50%" text-anchor="start" dominant-baseline="middle">
Problem 13
</text>
</a>
<a href="https://dkallen78.github.io/Project-Euler-Files/Problem14.1.html">
<text x="100%" y="50%" text-anchor="end" dominant-baseline="middle">
Problem 14 (Stored Values)
</text>
</a>
</svg>
</nav>
<main>
<p>
The following iterative sequence is defined for the set of positive integers:
<br />
<div class="inset">
<math>
<mi>n</mi>
<mo> → </mo>
<mfrac>
<mrow>
<mi>n</mi>
</mrow>
<mn>2</mn>
</mfrac>
<mtext>
(n is even)
</mtext>
</math>
<br />
<math>
<mi>n</mi>
<mo> → </mo>
<mn>3</mn>
<mo>⁢</mo>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
<mtext>
(n is odd)
</mtext>
</math>
<br />
</div>
<br />
Using the rule above and starting with 13, we generate the following sequence:
<br /><br />
<div class="example">
<math>
<mn>13</mn>
<mo> → </mo>
<mn>40</mn>
<mo> → </mo>
<mn>20</mn>
<mo> → </mo>
<mn>10</mn>
<mo> → </mo>
<mn>5</mn>
<mo> → </mo>
<mn>16</mn>
<mo> → </mo>
<mn>8</mn>
<mo> → </mo>
<mn>4</mn>
<mo> → </mo>
<mn>2</mn>
<mo> → </mo>
<mn>1</mn>
</math>
<br />
</div>
<br />
It can be seen that this sequence (starting at 13 and finishing at 1) contains
10 terms. Although it has not been proved yet (Collatz Problem), it is thought
that all starting numbers finish at 1.
<br /><br />
Which starting number, under one million, produces the longest chain?
<br /><br />
<span class="bold">NOTE:</span> Once the chain starts the terms are allowed
to go above one million.
</p>
<button id="problem" onclick="projectEulerProblem14()">
Find Number
</button>
</br>
<summary id="notes">
<div id="totalTime"></div>
<p>
I take the straight-forward approach and calculate the sequence of each
number up to 1,000,000.
<br /><br />
I use a while loop to run through the sequence until I reach 1 and I
store the longest sequence and the number that produced it as I go along.
<br /><br />
###,###
</p>
</summary>
</main>
</body>
<script>
function projectEulerProblem14() {
let startTime = new Date();
let limit = 1000000;
let longestChain = 0;
let longestSeed = 0
let collatz = 0;
//
//Counts up to 1 million, calculating the
//Collatz length of the number
for (let x = 1; x < limit; x++) {
collatz = getCollatz(x);
if (collatz > longestChain) {
longestChain = collatz;
longestSeed = x;
}
}
let endTime = new Date();
let totalTime = endTime - startTime;
document.getElementById("totalTime").innerHTML = totalTime + " ms";
document.getElementById("notes").style.display = "block";
document.getElementById("problem").innerHTML = longestSeed;
console.log("Number with longest chain: " + longestSeed);
console.log("Chain length: " + longestChain);
}
function getCollatz(start) {
//----------------------------------------------------//
//Finds the Collatz length of a number //
//integer-> start: number to check //
//----------------------------------------------------//
let stepCounter = 1;
let originalStart = start;
//
//Runs through the Collatz algorithm, counting
//steps as it goes
while (start !== 1) {
if ((start % 2) === 0) {
start /= 2;
} else {
start = (start * 3) + 1;
}
stepCounter++;
}
return stepCounter;
}
</script>
</html>