algorithm: unique paths (TheAlgorithms#1211)

* dp problem * update Directory.md * suggested changes

Author: hiitesh1127

DIRECTORY.md

@@ -105,6 +105,7 @@
  * [RodCutting](Dynamic-Programming/RodCutting.js)
  * [Shuf](Dynamic-Programming/Shuf.js)
  * [SieveOfEratosthenes](Dynamic-Programming/SieveOfEratosthenes.js)
+ * [UniquePaths](Dynamic-Programming/UniquePaths.js)
  * **Sliding-Window**
  * [LongestSubstringWithoutRepeatingCharacters](Dynamic-Programming/Sliding-Window/LongestSubstringWithoutRepeatingCharacters.js)
  * [PermutationinString](Dynamic-Programming/Sliding-Window/PermutationinString.js)

Dynamic-Programming/UniquePaths.js

@@ -0,0 +1,41 @@
+
+/*
+ *
+ * Unique Paths
+ *
+ * There is a robot on an `m x n` grid.
+ * The robot is initially located at the top-left corner.
+ * The robot tries to move to the bottom-right corner.
+ * The robot can only move either down or right at any point in time.
+ *
+ * Given the two integers `m` and `n`,
+ * return the number of possible unique paths that the robot can take to reach the bottom-right corner.
+ * More info: https://leetcode.com/problems/unique-paths/
+ */
+
+/*
+ * @param {number} m
+ * @param {number} n
+ * @return {number}
+ */
+
+const uniquePaths = (m, n) => {
+ // only one way to reach end
+ if (m === 1 || n === 1) return 1
+
+ // build a linear grid of size m
+ // base case, position 1 has only 1 move
+ const paths = new Array(m).fill(1)
+
+ for (let i = 1; i < n; i++) {
+ for (let j = 1; j < m; j++) {
+ // paths[j] in RHS represents the cell value stored above the current cell
+ // paths[j-1] in RHS represents the cell value stored to the left of the current cell
+ // paths [j] on the LHS represents the number of distinct pathways to the cell (i,j)
+ paths[j] = paths[j - 1] + paths[j]
+ }
+ }
+ return paths[m - 1]
+}
+
+export { uniquePaths }

Dynamic-Programming/tests/UniquePaths.test.js

@@ -0,0 +1,11 @@
+import { uniquePaths } from '../UniquePaths'
+
+describe('Unique Paths', () => {
+ it('should return 28 when m is 3 and n is 7', () => {
+ expect(uniquePaths(3, 7)).toBe(28)
+ })
+
+ it('should return 48620 when m is 10 and n is 10', () => {
+ expect(uniquePaths(10, 10)).toBe(48620)
+ })
+})