# 1337. The K Weakest Rows in a Matrix

<https://leetcode.com/problems/the-k-weakest-rows-in-a-matrix>

## Description

You are given an `m x n` binary matrix `mat` of `1`'s (representing soldiers) and `0`'s (representing civilians). The soldiers are positioned **in front** of the civilians. That is, all the `1`'s will appear to the **left** of all the `0`'s in each row.

A row `i` is **weaker** than a row `j` if one of the following is true:

* The number of soldiers in row `i` is less than the number of soldiers in row `j`.
* Both rows have the same number of soldiers and `i < j`.

Return *the indices of the* `k` ***weakest** rows in the matrix ordered from weakest to strongest*.

**Example 1:**

```
**Input:** mat = 
[[1,1,0,0,0],
 [1,1,1,1,0],
 [1,0,0,0,0],
 [1,1,0,0,0],
 [1,1,1,1,1]], 
k = 3
**Output:** [2,0,3]
**Explanation:** 
The number of soldiers in each row is: 
- Row 0: 2 
- Row 1: 4 
- Row 2: 1 
- Row 3: 2 
- Row 4: 5 
The rows ordered from weakest to strongest are [2,0,3,1,4].
```

**Example 2:**

```
**Input:** mat = 
[[1,0,0,0],
 [1,1,1,1],
 [1,0,0,0],
 [1,0,0,0]], 
k = 2
**Output:** [0,2]
**Explanation:** 
The number of soldiers in each row is: 
- Row 0: 1 
- Row 1: 4 
- Row 2: 1 
- Row 3: 1 
The rows ordered from weakest to strongest are [0,2,3,1].
```

**Constraints:**

* `m == mat.length`
* `n == mat[i].length`
* `2 <= n, m <= 100`
* `1 <= k <= m`
* `matrix[i][j]` is either 0 or 1.

## ac

```java
```