62. Unique Paths

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`.

62. Unique Paths
``````struct Solution;

impl Solution {
fn unique_paths(m: i32, n: i32) -> i32 {
let m = m as usize;
let n = n as usize;
let mut a = vec![vec![0; m + 1]; n + 1];
for i in 1..=n {
for j in 1..=m {
if i == 1 && j == 1 {
a[i][j] = 1;
} else {
a[i][j] = a[i - 1][j] + a[i][j - 1];
}
}
}
a[n][m]
}
}

#[test]
fn test() {
let m = 3;
let n = 2;
let res = 3;
assert_eq!(Solution::unique_paths(m, n), res);
let m = 7;
let n = 3;
let res = 28;
assert_eq!(Solution::unique_paths(m, n), res);
}
``````