/*

*

* 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 }