92 lines
1.9 KiB
Markdown
92 lines
1.9 KiB
Markdown
---
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id: 5900f3931000cf542c50fea6
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title: '問題 39: 整数辺を持つ直角三角形'
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challengeType: 5
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forumTopicId: 302054
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dashedName: problem-39-integer-right-triangles
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---
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# --description--
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長さが整数である辺 {a,b,c} を持つ直角三角形の周長を `p` とします。p = 120 のとき、ちょうど 3 つの解があります。
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{20,48,52}, {24,45,51}, {30,40,50}
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`p` ≤ `n` のとき、解の個数が最大になる `p` を求めなさい。
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# --hints--
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`intRightTriangles(500)` は数値を返す必要があります。
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```js
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assert(typeof intRightTriangles(500) === 'number');
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```
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`intRightTriangles(500)` は 420 を返す必要があります。
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```js
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assert(intRightTriangles(500) == 420);
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```
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`intRightTriangles(800)` は 720 を返す必要があります。
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```js
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assert(intRightTriangles(800) == 720);
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```
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`intRightTriangles(900)` は 840 を返す必要があります。
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```js
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assert(intRightTriangles(900) == 840);
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```
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`intRightTriangles(1000)` は 840 を返す必要があります。
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```js
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assert(intRightTriangles(1000) == 840);
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```
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# --seed--
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## --seed-contents--
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```js
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function intRightTriangles(n) {
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return n;
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}
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intRightTriangles(500);
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```
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# --solutions--
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```js
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// Original idea for this solution came from
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// https://www.xarg.org/puzzle/project-euler/problem-39/
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function intRightTriangles(n) {
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// store the number of triangles with a given perimeter
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let triangles = {};
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// a is the shortest side
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for (let a = 3; a < n / 3; a++)
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// o is the opposite side and is at least as long as a
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for (let o = a; o < n / 2; o++) {
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let h = Math.sqrt(a * a + o * o); // hypotenuse
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let p = a + o + h; // perimeter
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if ((h % 1) === 0 && p <= n) {
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triangles[p] = (triangles[p] || 0) + 1;
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}
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}
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let max = 0, maxp = null;
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for (let p in triangles) {
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if (max < triangles[p]) {
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max = triangles[p];
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maxp = parseInt(p);
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}
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}
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return maxp;
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}
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```
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