84 lines
1.4 KiB
Markdown
84 lines
1.4 KiB
Markdown
---
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id: 5900f3b81000cf542c50fecb
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title: 'Problem 76: Counting summations'
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challengeType: 5
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forumTopicId: 302189
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dashedName: problem-76-counting-summations
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---
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# --description--
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It is possible to write five as a sum in exactly six different ways:
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<div style='margin-left: 4em;'>
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4 + 1<br>
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3 + 2<br>
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3 + 1 + 1<br>
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2 + 2 + 1<br>
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2 + 1 + 1 + 1<br>
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1 + 1 + 1 + 1 + 1<br><br>
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</div>
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How many different ways can `n` be written as a sum of at least two positive integers?
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# --hints--
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`countingSummations(5)` should return a number.
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```js
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assert(typeof countingSummations(5) === 'number');
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```
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`countingSummations(5)` should return `6`.
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```js
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assert.strictEqual(countingSummations(5), 6);
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```
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`countingSummations(20)` should return `626`.
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```js
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assert.strictEqual(countingSummations(20), 626);
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```
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`countingSummations(50)` should return `204225`.
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```js
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assert.strictEqual(countingSummations(50), 204225);
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```
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`countingSummations(100)` should return `190569291`.
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```js
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assert.strictEqual(countingSummations(100), 190569291);
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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 countingSummations(n) {
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return true;
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}
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countingSummations(5);
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```
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# --solutions--
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```js
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function countingSummations(n) {
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const combinations = new Array(n + 1).fill(0);
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combinations[0] = 1;
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for (let i = 1; i < n; i++) {
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for (let j = i; j < n + 1; j++) {
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combinations[j] += combinations[j - i];
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}
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}
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return combinations[n];
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}
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```
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