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algorithm: unique paths (TheAlgorithms#1211)

* dp problem * update Directory.md * suggested changes

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`105`	`105`	`* [RodCutting](Dynamic-Programming/RodCutting.js)`
`106`	`106`	`* [Shuf](Dynamic-Programming/Shuf.js)`
`107`	`107`	`* [SieveOfEratosthenes](Dynamic-Programming/SieveOfEratosthenes.js)`
	`108`	`+ * [UniquePaths](Dynamic-Programming/UniquePaths.js)`
`108`	`109`	`* Sliding-Window`
`109`	`110`	`* [LongestSubstringWithoutRepeatingCharacters](Dynamic-Programming/Sliding-Window/LongestSubstringWithoutRepeatingCharacters.js)`
`110`	`111`	`* [PermutationinString](Dynamic-Programming/Sliding-Window/PermutationinString.js)`

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	`1`	`+`
	`2`	`+/*`
	`3`	`+ *`
	`4`	`+ * Unique Paths`
	`5`	`+ *`
	`6`	+ * There is a robot on an `m x n` grid.
	`7`	`+ * The robot is initially located at the top-left corner.`
	`8`	`+ * The robot tries to move to the bottom-right corner.`
	`9`	`+ * The robot can only move either down or right at any point in time.`
	`10`	`+ *`
	`11`	+ * Given the two integers `m` and `n`,
	`12`	`+ * return the number of possible unique paths that the robot can take to reach the bottom-right corner.`
	`13`	`+ * More info: https://leetcode.com/problems/unique-paths/`
	`14`	`+ */`
	`15`	`+`
	`16`	`+/*`
	`17`	`+ * @param {number} m`
	`18`	`+ * @param {number} n`
	`19`	`+ * @return {number}`
	`20`	`+ */`
	`21`	`+`
	`22`	`+const uniquePaths = (m, n) => {`
	`23`	`+ // only one way to reach end`
	`24`	`+ if (m === 1 \|\| n === 1) return 1`
	`25`	`+`
	`26`	`+ // build a linear grid of size m`
	`27`	`+ // base case, position 1 has only 1 move`
	`28`	`+ const paths = new Array(m).fill(1)`
	`29`	`+`
	`30`	`+ for (let i = 1; i < n; i++) {`
	`31`	`+ for (let j = 1; j < m; j++) {`
	`32`	`+ // paths[j] in RHS represents the cell value stored above the current cell`
	`33`	`+ // paths[j-1] in RHS represents the cell value stored to the left of the current cell`
	`34`	`+ // paths [j] on the LHS represents the number of distinct pathways to the cell (i,j)`
	`35`	`+ paths[j] = paths[j - 1] + paths[j]`
	`36`	`+ }`
	`37`	`+ }`
	`38`	`+ return paths[m - 1]`
	`39`	`+}`
	`40`	`+`
	`41`	`+export { uniquePaths }`

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	`1`	`+import { uniquePaths } from '../UniquePaths'`
	`2`	`+`
	`3`	`+describe('Unique Paths', () => {`
	`4`	`+ it('should return 28 when m is 3 and n is 7', () => {`
	`5`	`+ expect(uniquePaths(3, 7)).toBe(28)`
	`6`	`+ })`
	`7`	`+`
	`8`	`+ it('should return 48620 when m is 10 and n is 10', () => {`
	`9`	`+ expect(uniquePaths(10, 10)).toBe(48620)`
	`10`	`+ })`
	`11`	`+})`

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