Leetcode•Mar 28, 2025
62. Unique Paths
Hazrat Ali
Leetcode
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.
The test cases are generated so that the answer will be less than or equal to 2 * 109.
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
Solution :
/**
* @param {number} m
* @param {number} n
* @return {number}
*/
const uniquePaths = (m, n) => {
const dp = Array(m);
for (let i = 0; i < m; i++) {
dp[i] = Array(n).fill(0);
}
for (let j = 0; j < n; j++) {
dp[0][j] = 1;
}
for (let i = 0; i < m; i++) {
dp[i][0] = 1;
}
for (let i = 1; i < m; i++) {
for (let j = 1; j < n; j++) {
dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
}
}
return dp[m - 1][n - 1];
};