---
id: 5900f3931000cf542c50fea6
title: 问题39：整数直角三角形
challengeType: 5
videoUrl: ''
dashedName: problem-39-integer-right-triangles
---

# --description--

如果p是具有整数长度边的直角三角形的周长{a，b，c}，则对于p = 120，恰好有三个解。{20,48,52}，{24,45,51}，{ 30,40,50}对于p≤n的值，最大化解的数量是多少？

# --hints--

`intRightTriangles(500)`应该返回420。

```js
assert(intRightTriangles(500) == 420);
```

`intRightTriangles(800)`应该返回420。

```js
assert(intRightTriangles(800) == 720);
```

`intRightTriangles(900)`应该返回840。

```js
assert(intRightTriangles(900) == 840);
```

`intRightTriangles(1000)`应该返回840。

```js
assert(intRightTriangles(1000) == 840);
```

# --seed--

## --seed-contents--

```js
function intRightTriangles(n) {

  return n;
}

intRightTriangles(500);
```

# --solutions--

```js
// Original idea for this solution came from
// https://www.xarg.org/puzzle/project-euler/problem-39/

function intRightTriangles(n) {
  // store the number of triangles with a given perimeter
  let triangles = {};
  // a is the shortest side
  for (let a = 3; a < n / 3; a++)
  // o is the opposite side and is at least as long as a
    for (let o = a; o < n / 2; o++) {
      let h = Math.sqrt(a * a + o * o); // hypotenuse
      let p = a + o + h;  // perimeter
      if ((h % 1) === 0 && p <= n) {
        triangles[p] = (triangles[p] || 0) + 1;
      }
    }

  let max = 0, maxp = null;
  for (let p in triangles) {
    if (max < triangles[p]) {
      max = triangles[p];
      maxp = parseInt(p);
    }
  }
  return maxp;
}
```