69 lines
1.3 KiB
Markdown
69 lines
1.3 KiB
Markdown
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---
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id: 5900f37b1000cf542c50fe8e
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title: 'Problem 15: Lattice paths'
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challengeType: 5
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forumTopicId: 301780
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dashedName: problem-15-lattice-paths
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---
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# --description--
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Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.
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<img class="img-responsive center-block" alt="a diagram of 6 2 by 2 grids showing all the routes to the bottom right corner" src="https://cdn-media-1.freecodecamp.org/project-euler/1Atixoj.gif" style="background-color: white; padding: 10px;" />
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How many such routes are there through a given `gridSize`?
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# --hints--
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`latticePaths(4)` should return a number.
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```js
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assert(typeof latticePaths(4) === 'number');
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```
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`latticePaths(4)` should return 70.
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```js
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assert.strictEqual(latticePaths(4), 70);
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```
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`latticePaths(9)` should return 48620.
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```js
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assert.strictEqual(latticePaths(9), 48620);
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```
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`latticePaths(20)` should return 137846528820.
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```js
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assert.strictEqual(latticePaths(20), 137846528820);
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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 latticePaths(gridSize) {
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return true;
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}
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latticePaths(4);
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```
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# --solutions--
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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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