6.8 KiB
6.8 KiB
| title | id | challengeType |
|---|---|---|
| Heronian triangles | 595b98f8b5a2245e243aa831 | 5 |
Description
Hero's formula for the area of a triangle given the length of its three sides a, b, and c is given by:
$$A = \sqrt{s(s-a)(s-b)(s-c)},$$
where s is half the perimeter of the triangle; that is,
$$s=\frac{a+b+c}{2}.$$
Heronian triangles are triangles whose sides and area are all integers.
An example is the triangle with sides 3, 4, 5 whose area is 6 (and whose perimeter is 12).
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.
Define a Primitive Heronian triangle as a Heronian triangle where the greatest common divisor
of all three sides is 1 (unity).
This will exclude, for example, triangle 6, 8, 10.
Task:Implement a function based on Hero's formula that returns the first nth ordered triangles in an array of arrays.
Instructions
Tests
tests:
- text: <code>heronianTriangle</code> is a function.
testString: assert(typeof heronianTriangle === 'function', '<code>heronianTriangle</code> is a function.');
- 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>
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>');
- 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>
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>');
- 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>
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>');
- 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>
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>');
Challenge Seed
// noprotect
function heronianTriangle (n) {
// Good luck!
return [];
}
After Test
const testCases = [10, 15, 20, 25];
const res = [
[[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]],
[[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]],
[[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]],
[[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]]
];
Solution
// noprotect
function heronianTriangle (n) {
const list = [];
const result = [];
let j = 0;
for (let c = 1; c <= 200; c++) {
for (let b = 1; b <= c; b++) {
for (let a = 1; a <= b; a++) {
if (gcd(gcd(a, b), c) === 1 && isHeron(heronArea(a, b, c))) {
list[j++] = new Array(a, b, c, heronArea(a, b, c));
}
}
}
}
sort(list);
for (let i = 0; i < n; i++) {
result[i] = [list[i][0], list[i][1], list[i][2]];
}
return result;
function heronArea(a, b, c) {
const s = (a + b + c) / 2;
return Math.sqrt(s * (s - a) * (s - b) * (s - c));
}
function isHeron(h) { return h % 1 === 0 && h > 0; }
function gcd(a, b) {
let leftover = 1;
let dividend = a > b ? a : b;
let divisor = a > b ? b : a;
while (leftover !== 0) {
leftover = dividend % divisor;
if (leftover > 0) {
dividend = divisor;
divisor = leftover;
}
}
return divisor;
}
function sort(arg) {
let swapped = true;
let temp = [];
while (swapped) {
swapped = false;
for (let i = 1; i < arg.length; i++) {
if (arg[i][4] < arg[i - 1][4] || arg[i][4] === arg[i - 1][4] && arg[i][3] < arg[i - 1][3]) {
temp = arg[i];
arg[i] = arg[i - 1];
arg[i - 1] = temp;
swapped = true;
}
}
}
}
}