2018-10-10 22:03:03 +00:00
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---
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id: 5900f37b1000cf542c50fe8e
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2020-12-16 07:37:30 +00:00
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title: 问题15:格子路径
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2018-10-10 22:03:03 +00:00
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challengeType: 5
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videoUrl: ''
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2021-01-13 02:31:00 +00:00
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dashedName: problem-15-lattice-paths
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2018-10-10 22:03:03 +00:00
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---
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2020-12-16 07:37:30 +00:00
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# --description--
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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从2×2网格的左上角开始,只能向右和向下移动,右下角有6条路线。 ![6 2乘2网格的图表显示了右下角的所有路线](https://cdn-media-1.freecodecamp.org/imgr/1Atixoj.gif)
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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通过给定的`gridSize`有多少这样的路由?
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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# --hints--
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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`latticePaths(4)`应该返回70。
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2018-10-10 22:03:03 +00:00
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```js
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2020-12-16 07:37:30 +00:00
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assert.strictEqual(latticePaths(4), 70);
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2018-10-10 22:03:03 +00:00
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```
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2020-12-16 07:37:30 +00:00
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`latticePaths(9)`应该返回48620。
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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```js
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assert.strictEqual(latticePaths(9), 48620);
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```
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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`latticePaths(20)`应该返回137846528820。
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2018-10-10 22:03:03 +00:00
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```js
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2020-12-16 07:37:30 +00:00
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assert.strictEqual(latticePaths(20), 137846528820);
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2018-10-10 22:03:03 +00:00
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```
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2020-08-13 15:24:35 +00:00
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2021-01-13 02:31:00 +00:00
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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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2020-12-16 07:37:30 +00:00
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# --solutions--
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2021-01-13 02:31:00 +00:00
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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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