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Contribute: Added algorithm and tests for Unique Paths DP problem #1118

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39 changes: 39 additions & 0 deletions Dynamic-Programming/UniquePaths.js
Original file line number Diff line number Diff line change
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/*
* A Dynamic Programming based solution for calculating the number ways to travel from Top-Left of the matrix to Bottom-Right of the matrix
* https://leetcode.com/problems/unique-paths/
* Problem Statement:
* There is a robot on an m x n grid. The robot is initially located at the top-left corner (i.e., grid[0][0]). The robot tries to move to the bottom-right corner (i.e., grid[m - 1][n - 1]). 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.
* Approach:
* As the given problem can be reduced to smaller and overlapping sub problems, we can use dynamic programming and memoization to solve this problem.
* Time complexity: O(M * N) (M->ROWS | N->COLS)
* Space complexity: O(M * N) (M->ROWS | N->COLS)
*/

/**
* @param {number} rows
* @param {number} cols
* @return {number}
*/

// Return the number of unique paths, given the dimensions of rows and columns

const uniquePaths = (rows, cols) => {
let dp = new Array(cols).fill(1)

for (let i = 1; i < rows; i++) {
const tmp = []

for (let j = 0; j < cols; j++) {
if (j === 0) {
tmp[j] = dp[j]
} else {
tmp[j] = tmp[j - 1] + dp[j]
}
}
dp = tmp
}
return dp.pop()
}

export { uniquePaths }
7 changes: 7 additions & 0 deletions Dynamic-Programming/tests/UniquePaths.test.js
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import { uniquePaths } from '../UniquePaths'

test('Test case for UniquePaths', () => {
expect(uniquePaths(3, 7)).toBe(28)
expect(uniquePaths(3, 2)).toBe(3)
expect(uniquePaths(8, 14)).toBe(77520)
})