931. Minimum Falling Path Sum

Given an `n x n` array of integers `matrix`, return the minimum sum of any falling path through `matrix`.

A falling path starts at any element in the first row and chooses the element in the next row that is either directly below or diagonally left/right. Specifically, the next element from position `(row, col)` will be `(row + 1, col - 1)`, `(row + 1, col)`, or `(row + 1, col + 1)`.

Example 1:

```Input: matrix = [[2,1,3],[6,5,4],[7,8,9]]
Output: 13
Explanation: There are two falling paths with a minimum sum underlined below:
[[2,1,3],      [[2,1,3],
[6,5,4],       [6,5,4],
[7,8,9]]       [7,8,9]]
```

Example 2:

```Input: matrix = [[-19,57],[-40,-5]]
Output: -59
Explanation: The falling path with a minimum sum is underlined below:
[[-19,57],
[-40,-5]]
```

Example 3:

```Input: matrix = [[-48]]
Output: -48
```

Constraints:

• `n == matrix.length`
• `n == matrix[i].length`
• `1 <= n <= 100`
• `-100 <= matrix[i][j] <= 100`

Rust Solution

``````struct Solution;

impl Solution {
fn min_falling_path_sum(a: Vec<Vec<i32>>) -> i32 {
let n = a.len();
let m = a[0].len();
let mut dp = vec![vec![0; m]; n];
for i in 0..n {
for j in 0..m {
let mut min = std::i32::MAX;
if i > 0 {
let l = 0.max(j as i32 - 1) as usize;
let r = (n - 1).min(j + 1);
for k in l..=r {
min = min.min(dp[i - 1][k]);
}
} else {
min = 0;
}
dp[i][j] = a[i][j] + min;
}
}
*dp[n - 1].iter().min().unwrap()
}
}

#[test]
fn test() {
let a = vec_vec_i32![[1, 2, 3], [4, 5, 6], [7, 8, 9]];
let res = 12;
assert_eq!(Solution::min_falling_path_sum(a), res);
}
``````

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