curriculum/challenges/english/blocks/project-euler-problems-1-to-100/5900f3c71000cf542c50feda.md
The points ${P}(x_1, y_1)$ and ${Q}(x_2, y_2)$ are plotted at integer coordinates and are joined to the origin, ${O}(0, 0)$, to form ${\Delta}OPQ$.
There are exactly fourteen triangles containing a right angle that can be formed when each coordinate lies between 0 and 2 inclusive; that is, $0 ≤ x_1, y_1, x_2, y_2 ≤ 2$.
Given that $0 ≤ x_1, y_1, x_2, y_2 ≤ limit$, how many right triangles can be formed?
rightTrianglesIntCoords(2) should return a number.
assert(typeof rightTrianglesIntCoords(2) === 'number');
rightTrianglesIntCoords(2) should return 14.
assert.strictEqual(rightTrianglesIntCoords(2), 14);
rightTrianglesIntCoords(10) should return 448.
assert.strictEqual(rightTrianglesIntCoords(10), 448);
rightTrianglesIntCoords(25) should return 3207.
assert.strictEqual(rightTrianglesIntCoords(25), 3207);
rightTrianglesIntCoords(50) should return 14234.
assert.strictEqual(rightTrianglesIntCoords(50), 14234);
function rightTrianglesIntCoords(limit) {
return true;
}
rightTrianglesIntCoords(2);
function rightTrianglesIntCoords(limit) {
function isRightTriangle(points) {
for (let i = 0; i < points.length; i++) {
const pointA = points[i];
const pointB = points[(i + 1) % 3];
const pointC = points[(i + 2) % 3];
const vectorAB = [pointB[0] - pointA[0], pointB[1] - pointA[1]];
const vectorAC = [pointC[0] - pointA[0], pointC[1] - pointA[1]];
if (isRightAngleBetween(vectorAB, vectorAC)) {
return true;
}
}
return false;
}
function isRightAngleBetween(vector1, vector2) {
return vector1[0] * vector2[0] + vector1[1] * vector2[1] === 0;
}
function getSetKey(points) {
return (
'0.0,' +
points
.sort((a, b) => a[0] - b[0])
.map(point => point.join('.'))
.join(',')
);
}
const pointO = [0, 0];
const rightTriangles = new Set();
for (let x1 = 1; x1 <= limit; x1++) {
for (let y1 = 0; y1 <= limit; y1++) {
const pointP = [x1, y1];
for (let x2 = 0; x2 <= limit; x2++) {
for (let y2 = 1; y2 <= limit; y2++) {
const pointQ = [x2, y2];
if (pointP[0] === pointQ[0] && pointP[1] === pointQ[1]) {
continue;
}
if (isRightTriangle([pointO, pointP, pointQ])) {
rightTriangles.add(getSetKey([pointP, pointQ]));
}
}
}
}
}
return rightTriangles.size;
}