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?
Above is a 7 x 3 grid. How many possible unique paths are there?
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 -> Right -> Down 2. Right -> Down -> Right 3. Down -> Right -> Right
Input: m = 7, n = 3 Output: 28
1 <= m, n <= 100- It's guaranteed that the answer will be less than or equal to
2 * 10 ^ 9.
implSolution{pubfnunique_paths(m:i32,n:i32) -> i32{let m = m asusize;let n = n asusize;letmut dp = vec![vec![0; n]; m]; dp[m - 1][n - 1] = 1;for i in(0..m).rev(){for j in(0..n).rev(){if i < m - 1{ dp[i][j] += dp[i + 1][j];}if j < n - 1{ dp[i][j] += dp[i][j + 1];}}} dp[0][0]}}implSolution{pubfnunique_paths(m:i32,n:i32) -> i32{(1..(m asi64)).fold(1, |acc, x| acc *(n asi64 - 1 + x) / x)asi32}}