## 1329. Sort the Matrix Diagonally

A matrix diagonal is a diagonal line of cells starting from some cell in either the topmost row or leftmost column and going in the bottom-right direction until reaching the matrix's end. For example, the matrix diagonal starting from `mat[2][0]`, where `mat` is a `6 x 3` matrix, includes cells `mat[2][0]`, `mat[3][1]`, and `mat[4][2]`.

Given an `m x n` matrix `mat` of integers, sort each matrix diagonal in ascending order and return the resulting matrix.

Example 1:

```Input: mat = [[3,3,1,1],[2,2,1,2],[1,1,1,2]]
Output: [[1,1,1,1],[1,2,2,2],[1,2,3,3]]
```

Example 2:

```Input: mat = [[11,25,66,1,69,7],[23,55,17,45,15,52],[75,31,36,44,58,8],[22,27,33,25,68,4],[84,28,14,11,5,50]]
Output: [[5,17,4,1,52,7],[11,11,25,45,8,69],[14,23,25,44,58,15],[22,27,31,36,50,66],[84,28,75,33,55,68]]
```

Constraints:

• `m == mat.length`
• `n == mat[i].length`
• `1 <= m, n <= 100`
• `1 <= mat[i][j] <= 100`

## Rust Solution

``````struct Solution;
use std::cmp::Reverse;
use std::collections::BinaryHeap;
use std::collections::HashMap;

impl Solution {
fn diagonal_sort(mut mat: Vec<Vec<i32>>) -> Vec<Vec<i32>> {
let n = mat.len();
let m = mat[0].len();
let mut hs: HashMap<i32, BinaryHeap<Reverse<i32>>> = HashMap::new();
for i in 0..n {
for j in 0..m {
hs.entry(i as i32 - j as i32)
.or_default()
.push(Reverse(mat[i][j]));
}
}
for i in 0..n {
for j in 0..m {
mat[i][j] = hs.entry(i as i32 - j as i32).or_default().pop().unwrap().0;
}
}
mat
}
}

#[test]
fn test() {
let mat = vec_vec_i32![[3, 3, 1, 1], [2, 2, 1, 2], [1, 1, 1, 2]];
let res = vec_vec_i32![[1, 1, 1, 1], [1, 2, 2, 2], [1, 2, 3, 3]];
assert_eq!(Solution::diagonal_sort(mat), res);
}
``````

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