75 lines
1.7 KiB
Markdown
75 lines
1.7 KiB
Markdown
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---
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id: 5
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localeTitle: 5900f37b1000cf542c50fe8e
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challengeType: 5
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title: 'Problem 15: Lattice paths'
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---
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## Description
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<section id='description'>
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Comenzando en la esquina superior izquierda de una cuadrícula de 2 × 2, y solo pudiendo moverse hacia la derecha y hacia abajo, hay exactamente 6 rutas hacia la esquina inferior derecha.
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<img class="img-responsive center-block" alt="un diagrama de 6 cuadrículas de 2 por 2 que muestra todas las rutas hacia la esquina inferior derecha" src="https://i.imgur.com/1Atixoj.gif">
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¿Cuántas de estas rutas hay a través de un <code>gridSize</code> dado?
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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>latticePaths(4)</code> debe devolver 70.
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testString: 'assert.strictEqual(latticePaths(4), 70, "<code>latticePaths(4)</code> should return 70.");'
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- text: <code>latticePaths(9)</code> debe devolver 48620.
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testString: 'assert.strictEqual(latticePaths(9), 48620, "<code>latticePaths(9)</code> should return 48620.");'
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- text: <code>latticePaths(20)</code> debe devolver 137846528820.
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testString: 'assert.strictEqual(latticePaths(20), 137846528820, "<code>latticePaths(20)</code> should return 137846528820.");'
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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 latticePaths(gridSize) {
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// Good luck!
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return true;
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}
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latticePaths(4);
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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 latticePaths(gridSize) {
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let paths = 1;
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for (let i = 0; i < gridSize; i++) {
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paths *= (2 * gridSize) - i;
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paths /= i + 1;
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}
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return paths;
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}
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```
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</section>
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