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Problem40.html
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<html>
<head>
<title>
Project Euler, Problem 40: Champernowne's Constant
</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=x">
<text id="problemID" x="50%" y="50%" text-anchor="middle" dominant-baseline="middle">
Problem 40: Champernowne's Constant
</text>
</a>
</svg>
</header>
<nav>
<svg height="3rem" width="75vw">
<a href="https://dkallen78.github.io/Project-Euler-Files/Problem39.html">
<text x="0%" y="50%" text-anchor="start" dominant-baseline="middle">
Problem 39
</text>
</a>
<a href="https://dkallen78.github.io/Project-Euler-Files/Problem41.html">
<text x="100%" y="50%" text-anchor="end" dominant-baseline="middle">
Problem 41
</text>
</a>
</svg>
</nav>
<main>
<p>
An irrational decimal fraction is created by concatenating the positive integers:
<br /><br />
0.12345678910<span style="color:red">1</span>112131415161718192021...
<br /><br />
It can be seen that the 12<sup>th</sup> digit of the fractional part is 1.
<br /><br />
If d<sub>n</sub> represents the n<sup>th</sup> digit of the fractional part,
find the value of the following expression.
<br /><br />
d<sub>1</sub> × d<sub>10</sub> × d<sub>100</sub> × d<sub>1000</sub> ×
d<sub>10000</sub> × d<sub>100000</sub> × d<sub>1000000</sub>
</p>
<br />
<button id="problem" onclick="projectEuler()">
Find Product
</button>
<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>
The trick to this solution is finding the n<sup>th</sup> digit. The key
to that is figuring out which number is represented by each digit so you
need a slightly different process based on that. Once the awkward math is
worked out it's just a quick number crunch.
<br /><br />
79,882
</p>
</summary>
</main>
</body>
<script>
let population = [];
function projectEuler() {
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);
}
function findDigit(number) {
let fullNumber;
let numString;
//
//One digit numbers
if (number <= 9) {
return number;
//
//Two digit numbers
} else if (number <= 189) {
fullNumber = Math.ceil((number - 9) / 2) + 9;
numString = fullNumber.toString(10).split("");
return numString[(number - 10) % 2];
//
//Three digit numbers
} else if (number <= 2_889) {
fullNumber = Math.ceil((number - 189) / 3) + 99;
numString = fullNumber.toString(10).split("");
return numString[(number - 190) % 3];
//
//Four digit numbers
} else if (number <= 38_889) {
fullNumber = Math.ceil((number - 2_889) / 4) + 999;
numString = fullNumber.toString(10).split("");
return numString[(number - 2_890) % 4];
//
//Five digit numbers
} else if (number <= 488_889) {
fullNumber = Math.ceil((number - 38_889) / 5) + 9_999;
numString = fullNumber.toString(10).split("");
return numString[(number - 38_890) % 5];
//
//Six digit numbers
} else if (number <= 5_888_889) {
fullNumber = Math.ceil((number - 488_889) / 6) + 99_999;
numString = fullNumber.toString(10).split("");
return numString[(number - 488_890) % 6];
}
}
const startTime = performance.now();
let solution = 1;
for (let i = 0; i <= 6; i++) {
solution *= findDigit(10**i);
}
const endTime = performance.now();
const totalTime = parseFloat((endTime - startTime).toFixed(3), 10);
display(totalTime, solution);
}
</script>
</html>