uniquePaths.js

/*
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.

Example 1:
Input: m = 3, n = 7
Output: 28

Example 2:
Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
1. Right -> Down -> Down
2. Down -> Down -> Right
3. Down -> Right -> Down

Constraints:
    1 <= m, n <= 100
*/

/**
 * @param {number} m
 * @param {number} n
 * @return {number}
 */
function uniquePaths(m, n) {
    const dp = new Array(n).fill(1);

    for (let i = 1; i < m; i++) {
        for (let j = 1; j < n; j++) {
            dp[j] += dp[j - 1];
        }
    }
    return dp[n - 1];
}

// Example usage:
console.log(uniquePaths(3, 7)); // Output: 28
console.log(uniquePaths(3, 2)); // Output: 3