103 lines
3.4 KiB
Markdown
103 lines
3.4 KiB
Markdown
---
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title: 9 billion names of God the integer
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id: 5949b579404977fbaefcd736
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challengeType: 5
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---
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## Description
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<section id='description'>
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<p>This task is a variation of the <a href="https://en.wikipedia.org/wiki/The Nine Billion Names of God#Plot_summary" title="wp: The Nine Billion Names of God#Plot_summary">short story by Arthur C. Clarke</a>.</p>
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<p>(Solvers should be aware of the consequences of completing this task.)</p>
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<p>In detail, to specify what is meant by a “name”:</p>
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<p>The integer 1 has 1 name “1”.</p>
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<p>The integer 2 has 2 names “1+1”, and “2”.</p>
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<p>The integer 3 has 3 names “1+1+1”, “2+1”, and “3”.</p>
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<p>The integer 4 has 5 names “1+1+1+1”, “2+1+1”, “2+2”, “3+1”, “4”.</p>
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<p>The integer 5 has 7 names “1+1+1+1+1”, “2+1+1+1”, “2+2+1”, “3+1+1”, “3+2”, “4+1”, “5”.</p>
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<p>This can be visualized in the following form:</p>
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<pre>
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1
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1 1
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1 1 1
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1 2 1 1
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1 2 2 1 1
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1 3 3 2 1 1
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</pre>
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<p>Where row $n$ corresponds to integer $n$, and each column $C$ in row $m$ from left to right corresponds to the number of names beginning with $C$.</p>
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<p>Optionally note that the sum of the $n$-th row $P(n)$ is the <a href="http://mathworld.wolfram.com/PartitionFunctionP.html" title="link: http://mathworld.wolfram.com/PartitionFunctionP.html">integer partition function</a>.</p>
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Task
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<p>Implement a function that returns the sum of the $n$-th row.</p>
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>numberOfNames</code> is a function.
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testString: assert(typeof numberOfNames === 'function', '<code>numberOfNames</code> is a function.');
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- text: <code>numberOfNames(5)</code> should equal 7.
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testString: assert.equal(numberOfNames(5), 7, '<code>numberOfNames(5)</code> should equal 7.');
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- text: <code>numberOfNames(12)</code> should equal 77.
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testString: assert.equal(numberOfNames(12), 77, '<code>numberOfNames(12)</code> should equal 77.');
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- text: <code>numberOfNames(18)</code> should equal 385.
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testString: assert.equal(numberOfNames(18), 385, '<code>numberOfNames(18)</code> should equal 385.');
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- text: <code>numberOfNames(23)</code> should equal 1255.
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testString: assert.equal(numberOfNames(23), 1255, '<code>numberOfNames(23)</code> should equal 1255.');
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- text: <code>numberOfNames(42)</code> should equal 53174.
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testString: assert.equal(numberOfNames(42), 53174, '<code>numberOfNames(42)</code> should equal 53174.');
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- text: <code>numberOfNames(123)</code> should equal 2552338241.
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testString: assert.equal(numberOfNames(123), 2552338241, '<code>numberOfNames(123)</code> should equal 2552338241.');
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function numberOfNames (num) {
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// Good luck!
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return true;
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}
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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function numberOfNames (num) {
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const cache = [
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[1]
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];
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for (let l = cache.length; l < num + 1; l++) {
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let Aa;
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let Mi;
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const r = [0];
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for (let x = 1; x < l + 1; x++) {
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r.push(r[r.length - 1] + (Aa = cache[l - x < 0 ? cache.length - (l - x) : l - x])[(Mi = Math.min(x, l - x)) < 0 ? Aa.length - Mi : Mi]);
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}
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cache.push(r);
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}
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return cache[num][cache[num].length - 1];
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}
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```
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</section>
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