LeetCode-in-All

62. Unique Paths

Medium

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

Constraints:

Solution

impl Solution {
    pub fn unique_paths(m: i32, n: i32) -> i32 {
        let m = m as usize;
        let n = n as usize;
        let mut dp = vec![vec![0; n]; m];

        // Initialize the first row and first column
        for i in 0..m {
            dp[i][0] = 1;
        }
        for j in 0..n {
            dp[0][j] = 1;
        }

        // Fill the DP table
        for i in 1..m {
            for j in 1..n {
                dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
            }
        }

        dp[m - 1][n - 1]
    }
}