79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
148 lines
6.8 KiB
Markdown
148 lines
6.8 KiB
Markdown
---
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title: Heronian triangles
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id: 595b98f8b5a2245e243aa831
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challengeType: 5
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---
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## Description
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<section id='description'>
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<p><a href="https://en.wikipedia.org/wiki/Heron's formula" title="wp: Heron's formula">Hero's formula</a> for the area of a triangle given the length of its three sides <big> a,</big> <big>b,</big> and <big>c</big> is given by:</p><p><big>$$A = \sqrt{s(s-a)(s-b)(s-c)},$$</big></p><p>where <big>s</big> is half the perimeter of the triangle; that is,</p><p><big>$$s=\frac{a+b+c}{2}.$$</big></p>
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<p><a href="http://www.had2know.com/academics/heronian-triangles-generator-calculator.html" title="link: http://www.had2know.com/academics/heronian-triangles-generator-calculator.html">Heronian triangles</a> are triangles whose sides and area are all integers.</p>
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<p> An example is the triangle with sides 3, 4, 5 whose area is 6 (and whose perimeter is 12). </p>
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<p>Note that any triangle whose sides are all an integer multiple of 3, 4, 5; such as 6, 8, 10, will also be a Heronian triangle.</p><p>Define a Primitive Heronian triangle as a Heronian triangle where the greatest common divisor</p>
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<p>of all three sides is 1 (unity).</p><p>This will exclude, for example, triangle 6, 8, 10.</p>
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Task:
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<p>Implement a function based on Hero's formula that returns the first <code>n<sub>th</sub></code> ordered triangles in an array of arrays.</p>
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>heronianTriangle</code> is a function.
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testString: assert(typeof heronianTriangle === 'function', '<code>heronianTriangle</code> is a function.');
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- text: <code>heronianTriangle()</code> should return <code>[[3, 4, 5], [5, 5, 6], [5, 5, 8], [4, 13, 15], [5, 12, 13], [9, 10, 17], [3, 25, 26], [7, 15, 20], [10, 13, 13], [8, 15, 17]]</code>
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testString: assert.deepEqual(heronianTriangle(testCases[0]), res[0], '<code>heronianTriangle()</code> should return <code>[[3, 4, 5], [5, 5, 6], [5, 5, 8], [4, 13, 15], [5, 12, 13], [9, 10, 17], [3, 25, 26], [7, 15, 20], [10, 13, 13], [8, 15, 17]]</code>');
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- text: <code>heronianTriangle()</code> should return <code>[[3, 4, 5], [5, 5, 6], [5, 5, 8], [4, 13, 15], [5, 12, 13], [9, 10, 17], [3, 25, 26], [7, 15, 20], [10, 13, 13], [8, 15, 17], [13, 13, 24], [6, 25, 29], [11, 13, 20], [5, 29, 30], [13, 14, 15]],</code>
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testString: assert.deepEqual(heronianTriangle(testCases[1]), res[1], '<code>heronianTriangle()</code> should return <code>[[3, 4, 5], [5, 5, 6], [5, 5, 8], [4, 13, 15], [5, 12, 13], [9, 10, 17], [3, 25, 26], [7, 15, 20], [10, 13, 13], [8, 15, 17], [13, 13, 24], [6, 25, 29], [11, 13, 20], [5, 29, 30], [13, 14, 15]],</code>');
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- text: <code>heronianTriangle()</code> should return <code>[[3, 4, 5], [5, 5, 6], [5, 5, 8], [4, 13, 15], [5, 12, 13], [9, 10, 17], [3, 25, 26], [7, 15, 20], [10, 13, 13], [8, 15, 17], [13, 13, 24], [6, 25, 29], [11, 13, 20], [5, 29, 30], [13, 14, 15], [10, 17, 21], [7, 24, 25], [8, 29, 35], [12, 17, 25], [4, 51, 53]],</code>
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testString: assert.deepEqual(heronianTriangle(testCases[2]), res[2], '<code>heronianTriangle()</code> should return <code>[[3, 4, 5], [5, 5, 6], [5, 5, 8], [4, 13, 15], [5, 12, 13], [9, 10, 17], [3, 25, 26], [7, 15, 20], [10, 13, 13], [8, 15, 17], [13, 13, 24], [6, 25, 29], [11, 13, 20], [5, 29, 30], [13, 14, 15], [10, 17, 21], [7, 24, 25], [8, 29, 35], [12, 17, 25], [4, 51, 53]],</code>');
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- text: <code>heronianTriangle()</code> should return <code>[[3, 4, 5], [5, 5, 6], [5, 5, 8], [4, 13, 15], [5, 12, 13], [9, 10, 17], [3, 25, 26], [7, 15, 20], [10, 13, 13], [8, 15, 17], [13, 13, 24], [6, 25, 29], [11, 13, 20], [5, 29, 30], [13, 14, 15], [10, 17, 21], [7, 24, 25], [8, 29, 35], [12, 17, 25], [4, 51, 53], [19, 20, 37],[16, 17, 17], [17, 17, 30], [16, 25, 39], [13, 20, 21]]</code>
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testString: assert.deepEqual(heronianTriangle(testCases[3]), res[3], '<code>heronianTriangle()</code> should return <code>[[3, 4, 5], [5, 5, 6], [5, 5, 8], [4, 13, 15], [5, 12, 13], [9, 10, 17], [3, 25, 26], [7, 15, 20], [10, 13, 13], [8, 15, 17], [13, 13, 24], [6, 25, 29], [11, 13, 20], [5, 29, 30], [13, 14, 15], [10, 17, 21], [7, 24, 25], [8, 29, 35], [12, 17, 25], [4, 51, 53], [19, 20, 37],[16, 17, 17], [17, 17, 30], [16, 25, 39], [13, 20, 21]]</code>');
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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// noprotect
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function heronianTriangle (n) {
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// Good luck!
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return [];
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}
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```
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</div>
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### After Test
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<div id='js-teardown'>
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```js
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const testCases = [10, 15, 20, 25];
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const res = [
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[[3, 4, 5], [5, 5, 6], [5, 5, 8], [4, 13, 15], [5, 12, 13], [9, 10, 17], [3, 25, 26], [7, 15, 20], [10, 13, 13], [8, 15, 17]],
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[[3, 4, 5], [5, 5, 6], [5, 5, 8], [4, 13, 15], [5, 12, 13], [9, 10, 17], [3, 25, 26], [7, 15, 20], [10, 13, 13], [8, 15, 17], [13, 13, 24], [6, 25, 29], [11, 13, 20], [5, 29, 30], [13, 14, 15]],
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[[3, 4, 5], [5, 5, 6], [5, 5, 8], [4, 13, 15], [5, 12, 13], [9, 10, 17], [3, 25, 26], [7, 15, 20], [10, 13, 13], [8, 15, 17], [13, 13, 24], [6, 25, 29], [11, 13, 20], [5, 29, 30], [13, 14, 15], [10, 17, 21], [7, 24, 25], [8, 29, 35], [12, 17, 25], [4, 51, 53]],
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[[3, 4, 5], [5, 5, 6], [5, 5, 8], [4, 13, 15], [5, 12, 13], [9, 10, 17], [3, 25, 26], [7, 15, 20], [10, 13, 13], [8, 15, 17], [13, 13, 24], [6, 25, 29], [11, 13, 20], [5, 29, 30], [13, 14, 15], [10, 17, 21], [7, 24, 25], [8, 29, 35], [12, 17, 25], [4, 51, 53], [19, 20, 37], [16, 17, 17], [17, 17, 30], [16, 25, 39], [13, 20, 21]]
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];
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// noprotect
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function heronianTriangle (n) {
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const list = [];
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const result = [];
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let j = 0;
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for (let c = 1; c <= 200; c++) {
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for (let b = 1; b <= c; b++) {
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for (let a = 1; a <= b; a++) {
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if (gcd(gcd(a, b), c) === 1 && isHeron(heronArea(a, b, c))) {
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list[j++] = new Array(a, b, c, heronArea(a, b, c));
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}
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}
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}
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}
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sort(list);
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for (let i = 0; i < n; i++) {
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result[i] = [list[i][0], list[i][1], list[i][2]];
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}
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return result;
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function heronArea(a, b, c) {
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const s = (a + b + c) / 2;
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return Math.sqrt(s * (s - a) * (s - b) * (s - c));
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}
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function isHeron(h) { return h % 1 === 0 && h > 0; }
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function gcd(a, b) {
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let leftover = 1;
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let dividend = a > b ? a : b;
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let divisor = a > b ? b : a;
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while (leftover !== 0) {
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leftover = dividend % divisor;
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if (leftover > 0) {
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dividend = divisor;
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divisor = leftover;
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}
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}
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return divisor;
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}
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function sort(arg) {
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let swapped = true;
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let temp = [];
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while (swapped) {
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swapped = false;
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for (let i = 1; i < arg.length; i++) {
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if (arg[i][4] < arg[i - 1][4] || arg[i][4] === arg[i - 1][4] && arg[i][3] < arg[i - 1][3]) {
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temp = arg[i];
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arg[i] = arg[i - 1];
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arg[i - 1] = temp;
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swapped = true;
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}
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}
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}
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}
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}
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```
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</section>
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