61 lines
1.0 KiB
Markdown
61 lines
1.0 KiB
Markdown
---
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id: 5900f37b1000cf542c50fe8e
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title: 问题15：格子路径
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challengeType: 5
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videoUrl: ''
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dashedName: problem-15-lattice-paths
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---
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# --description--
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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。 
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通过给定的`gridSize`有多少这样的路由？
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# --hints--
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`latticePaths(4)`应该返回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)`应该返回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)`应该返回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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