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Problem9.html
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<html>
<head>
<title>
Project Euler, Problem 9: Special Pythagorean Triplet
</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">
<script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
</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=9">
<text id="problemID" x="50%" y="50%" text-anchor="middle" dominant-baseline="middle">
Problem 9: Special Pythagorean Triplet
</text>
</a>
</svg>
</header>
<nav>
<svg height="3rem" width="75vw">
<a href="https://dkallen78.github.io/Project-Euler-Files/Problem8.html">
<text x="0%" y="50%" text-anchor="start" dominant-baseline="middle">
Problem 8
</text>
</a>
<a href="https://dkallen78.github.io/Project-Euler-Files/Problem10.html">
<text x="100%" y="50%" text-anchor="end" dominant-baseline="middle">
Problem 10 (Primality Test)
</text>
</a>
</svg>
</nav>
<main>
<p>
A Pythagorean triplet is a set of three natural numbers,
<math>
<mi>a</mi>
<mo><</mo>
<mi>b</mi>
<mo><</mo>
<mi>c</mi>
</math>
for which,<br />
<div class="example">
<math>
<msup>
<mi>a</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mi>b</mi>
<mn>2</mn>
</msup>
<mo>=</mo>
<msup>
<mi>c</mi>
<mn>2</mi>
</msup>
</math>
</div>
<br />
For example,
<math>
<msup>
<mn>3</mn>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mn>4</mn>
<mn>2</mn>
</msup>
<mo>=</mo>
<mn>9</mn>
<mo>+</mo>
<mn>16</mn>
<mo>=</mo>
<mn>25</mn>
<mo>=</mo>
<msup>
<mn>5</mn>
<mn>2</mn>
</msup>
</math>
<br /><br />
There exists exactly one Pythagorean triplet for which
<math>
<mi>a</mi>
<mo>+</mo>
<mi>b</mi>
<mo>+</mo>
<mi>c</mi>
<mo>=</mo>
<mn>1000</mn>
</math>.
<br /><br />
Find the product
<math>
<mi>a</mi>
<mo>⁢</mo>
<mi>b</mi>
<mo>⁢</mo>
<mi>c</mi>
</math>.
</p>
<button id="problem" onclick="projectEulerProblem9()">
Find Product
</button>
<br />
<summary id="notes">
<div>Runtime: <span id="totalTime">0</span></div>
<div>Average: <span id="avgTime">0</span> Runs: <span id="runs">0</span></div>
<div>SD: <span id="stdDev">0</span> ms</div>
<div class="red">Max: <span id="max">0</span></div>
<div class="green">Min: <span id="min">1000</span></div>
<p>
I use Euclid's formula for generating Pythagorean triples:<br />
<div class="example">
<math>
<mi>a</mi>
<mo>=</mo>
<msup>
<mi>m</mi>
<mn>2</mn>
</msup>
<mo>-</mo>
<msup>
<mi>n</mi>
<mn>2</mn>
</msup>
</math>,
<math>
<mi>b</mi>
<mo>=</mo>
<mn>2</mn>
<mo>⁢</mo>
<mi>m</mi>
<mo>⁢</mo>
<mi>n</mi>
</math>,
<math>
<mi>c</mi>
<mo>=</mo>
<msup>
<mi>m</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mi>n</mi>
<mn>2</mn>
</msup>
</math>
</div>
<br />
With this, I run a nested set of for loops, each counting up to 25 to test if the
sum of my three numbers is 1,000.
</p>
</summary>
</main>
</body>
<script>
let population = [];
function projectEulerProblem9() {
function display(totalTime, solution) {
//----------------------------------------------------//
//Displays the information to the window after the //
// program has run //
//float-> totalTime: time it took to run the program //
//----------------------------------------------------//
function getAvg(totalTime) {
//----------------------------------------------------//
//Calculates the average time to run the program //
//float-> totalTime: time it took to run the program //
//----------------------------------------------------//
let oldAvg = parseFloat(document.getElementById("avgTime").innerHTML, 10);
let oldIter = Number(document.getElementById("runs").innerHTML);
let newIter = oldIter + 1;
document.getElementById("runs").innerHTML = newIter;
let avgTime = ((oldAvg * oldIter) + totalTime) / newIter;
return avgTime.toFixed(3);
}
function getSD(average, population) {
//----------------------------------------------------//
//Calculates standard deviation of the runtimes //
//float-> average: average program runtime //
//array-> population: an array of runtimes //
//----------------------------------------------------//
average = Number(average);
let sum = 0;
for (let i = 0; i < population.length; i++) {
sum += (population[i] - average) ** 2;
}
sum /= population.length;
return Math.sqrt(sum).toFixed(3);;
}
population.push(totalTime);
//
//Display the solution
document.getElementById("problem").innerHTML = solution;
//
//Display the runtime
document.getElementById("totalTime").innerHTML = totalTime.toFixed(3) + " ms";
let average = getAvg(totalTime);
//
//Display the average
document.getElementById("avgTime").innerHTML = average + " ms";
//
//Display the standard deviation
document.getElementById("stdDev").innerHTML = getSD(average, population);
//
//Display the highest runtime
let max = parseFloat(document.getElementById("max").innerHTML, 10);
if (totalTime > max) {
document.getElementById("max").innerHTML = totalTime.toFixed(3) + " ms";
}
//
//Display the lowest runtime
let min = parseFloat(document.getElementById("min").innerHTML, 10);
if (totalTime < min) {
let minString = "";
if (totalTime === 0) {
minString = "< 0.020";
} else {
minString = totalTime.toFixed(3);
}
document.getElementById("min").innerHTML = minString + " ms";
}
//
//Display the explanatory notes
document.getElementById("notes").style.display = "block";
let summary = document.querySelector("summary").scrollHeight;
setTimeout(function() {
document.querySelector("summary").style.height = summary + "px";
}, 1);
}
const startTime = performance.now();
let a = 0;
let b = 0;
let c = 0;
//
//This is an implamentation of Euclid's formula for generating Pythagorean triples
//I picked 25 as an arbitrary bound because 625 seemed like a good limit
for (let n = 1; n < 25; n++) {
for (let m = 2; m < 25; m++) {
a = (m * m) - (n * n);
b = 2 * m * n;
c = (m * m) + (n * n);
if ((a + b + c) === 1000) {
break;
}
}
if ((a + b + c) === 1000) {
break;
}
}
if ((a + b + c) === 1000) {
let finalProduct = (a * b * c);
const endTime = performance.now();
const totalTime = parseFloat((endTime - startTime).toFixed(3), 10);
display(totalTime, finalProduct);
}
}
</script>
</html>