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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