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Problem38.html
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<html>
<head>
<title>
Project Euler, Problem 38: Pandigital Multiples
</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 38: Pandigital Multiples
</text>
</a>
</svg>
</header>
<nav>
<svg height="3rem" width="75vw">
<a href="https://dkallen78.github.io/Project-Euler-Files/Problem37.html">
<text x="0%" y="50%" text-anchor="start" dominant-baseline="middle">
Problem 37
</text>
</a>
<a href="https://dkallen78.github.io/Project-Euler-Files/Problem39.html">
<text x="100%" y="50%" text-anchor="end" dominant-baseline="middle">
Problem 39
</text>
</a>
</svg>
</nav>
<main>
<p>
Take the number 192 and multiply it by each of 1, 2, and 3:
<br />
<div class="inset">
<math>
<mn> 192 </mn>
<mo> × </mo>
<mn> 1 </mn>
<mo> = </mo>
<mn> 192 </mn>
</math>
<br />
<math>
<mn> 192 </mn>
<mo> × </mo>
<mn> 2 </mn>
<mo> = </mo>
<mn> 384 </mn>
</math>
<br />
<math>
<mn> 192 </mn>
<mo> × </mo>
<mn> 3 </mn>
<mo> = </mo>
<mn> 576 </mn>
</math>
</div>
<br />
By concatenating each product we get the 1 to 9 pandigital, 192384576. We
will call 192384576 the concatenated product of 192 and (1,2,3)
<br /><br />
The same can be achieved by starting with 9 and multiplying by 1, 2, 3, 4,
and 5, giving the pandigital, 918273645, which is the concatenated product
of 9 and (1,2,3,4,5).
<br /><br />
What is the largest 1 to 9 pandigital 9-digit number that can be formed as
the concatenated product of an integer with (1,2, ... ,
<math>
<mi> n </mi>
</math>) where
<math>
<mi> n </mi>
<mo> > </mo>
<mn> 1 </mn>
</math>?
</p>
<button id="problem" onclick="projectEuler()">
Find Number
</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>
My insight was that the "seed" number had to start with a 9 and that the
maximum "seed" had to be 4 digits since a 5-digit number would always
produce a 10-digit number on its second iteration.
</br></br>
I used a little ﾶﾑｲん-ﾌuｲ丂u to append the 9 and then I cycled through a
for loop 998 times.
</br></br>
61,501
</p>
</summary>
</main>
</body>
<script>
let population = [];
function projectEuler() {
//61501st
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 greatestCatProd = 0;
let catProduct = "";
//
//This loops through numbers, searching for candidate numbers
for (let i = 1; i < 1000; i++) {
//
//Any candidate number must start with a 9, this adds the 9
catProduct = getCatProduct((9 * (10 ** countDigits(i))) + i);
//
//If it's 9 digits long, and all digits are unique...
if (catProduct.length === 9 && uniqueDigits(catProduct)) {
//
//and it's larger than the last number AND has no 0s,
//make it the new largest candidate
if (Number(catProduct) > greatestCatProd && !hasZero(catProduct)) {
greatestCatProd = Number(catProduct);
}
}
}
console.log(greatestCatProd);
const endTime = performance.now();
const totalTime = parseFloat((endTime - startTime).toFixed(3), 10);
display(totalTime, greatestCatProd);
}
function getCatProduct(number) {
//----------------------------------------------------//
//Calculates the concatenated product of a number //
// until it reaches 9 or more digits //
//integer-> number: number to process //
//----------------------------------------------------//
let count = 1;
let catProduct = "";
while (catProduct.length < 9) {
catProduct += number * count;
count++;
}
return catProduct;
}
function countDigits(number) {
//----------------------------------------------------//
//Quick digit counter //
//integer-> number: number to check //
//----------------------------------------------------//
number = number.toString(10);
return number.length;
}
function uniqueDigits(number) {
//----------------------------------------------------//
//Checks to see if the digits of a number are unique //
//integer/string-> number: number to check //
//----------------------------------------------------//
number = number.toString();
//
//Compares num1 with itself
for (let i = 0; i < number.length - 1; i++) {
for (let j = i + 1; j < number.length; j++) {
if (number[i] === number[j]) {
return false;
}
}
}
return true;
}
function hasZero(num) {
//----------------------------------------------------//
//Checks to see if a number has a 0 as one of //
// its digits //
//integer-> num: number to check //
//----------------------------------------------------//
num = num.toString();
for (let i = 0; i < num.length; i++) {
if (num[i] === "0") {
return true;
}
}
return false;
}
</script>
</html>