LeetCode 62. Unique Paths (javascript)

A robot is located at the top-left corner of a m x n grid (marked ‘Start’ in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked ‘Finish’ in the diagram below).

How many possible unique paths are there?

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

Example 3:

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

Example 4:

Input: m = 3, n = 3
Output: 6

Constraints:

1 <= m, n <= 100
It’s guaranteed that the answer will be less than or equal to 2 * 10⁹.

Idea:

Dynamic Programing

dp[m][n] = unique paths of m x n grid
// base case:
dp[1][1] = 1; 
// dp[i][j] = top(unique paths) + left(unique paths)
dp[i][j] = dp[i - 1][j] + dp[i][j - 1];

Solution:

/**
 * @param {number} m
 * @param {number} n
 * @return {number}
 */
var uniquePaths = function(m, n) {
    // one row or one column dp[i][1] = dp[1][j] = 1; Let's fill them all 1
    let dp = Array.from(new Array(m), () => new Array(n).fill(1));
    for (let i = 0; i < m; i++) {
        for (let j = 0; j < n; j++) {
            // dp[i][j] = top(unique paths) + left(unique paths)
            dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
        }
    }
    return dp[m - 1][n - 1];
}