diff --git a/DIRECTORY.md b/DIRECTORY.md index e1bbd7700..b5cf0077a 100644 --- a/DIRECTORY.md +++ b/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) diff --git a/Dynamic-Programming/UniquePaths.js b/Dynamic-Programming/UniquePaths.js new file mode 100644 index 000000000..4b3d67a1a --- /dev/null +++ b/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 } diff --git a/Dynamic-Programming/tests/UniquePaths.test.js b/Dynamic-Programming/tests/UniquePaths.test.js new file mode 100644 index 000000000..eb6f8c74d --- /dev/null +++ b/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) + }) +})