## 960. Delete Columns to Make Sorted III

You are given an array of `n` strings `strs`, all of the same length.

We may choose any deletion indices, and we delete all the characters in those indices for each string.

For example, if we have `strs = ["abcdef","uvwxyz"]` and deletion indices `{0, 2, 3}`, then the final array after deletions is `["bef", "vyz"]`.

Suppose we chose a set of deletion indices `answer` such that after deletions, the final array has every string (row) in lexicographic order. (i.e., `(strs[0][0] <= strs[0][1] <= ... <= strs[0][strs[0].length - 1])`, and `(strs[1][0] <= strs[1][1] <= ... <= strs[1][strs[1].length - 1])`, and so on). Return the minimum possible value of `answer.length`.

Example 1:

```Input: strs = ["babca","bbazb"]
Output: 3
Explanation: After deleting columns 0, 1, and 4, the final array is strs = ["bc", "az"].
Both these rows are individually in lexicographic order (ie. strs[0][0] <= strs[0][1] and strs[1][0] <= strs[1][1]).
Note that strs[0] > strs[1] - the array strs is not necessarily in lexicographic order.```

Example 2:

```Input: strs = ["edcba"]
Output: 4
Explanation: If we delete less than 4 columns, the only row will not be lexicographically sorted.
```

Example 3:

```Input: strs = ["ghi","def","abc"]
Output: 0
Explanation: All rows are already lexicographically sorted.
```

Constraints:

• `n == strs.length`
• `1 <= n <= 100`
• `1 <= strs[i].length <= 100`
• `strs[i]` consists of lowercase English letters.
•

## Rust Solution

``````struct Solution;

impl Solution {
fn min_deletion_size(a: Vec<String>) -> i32 {
let n = a.len();
let a: Vec<Vec<char>> = a.into_iter().map(|s| s.chars().collect()).collect();
let m = a[0].len();
let mut dp = vec![1; m];
for i in 1..m {
'outer: for j in 0..i {
for k in 0..n {
if a[k][j] > a[k][i] {
continue 'outer;
}
}
dp[i] = dp[i].max(dp[j] + 1);
}
}
(m - dp.into_iter().max().unwrap()) as i32
}
}

#[test]
fn test() {
let a = vec_string!["babca", "bbazb"];
let res = 3;
assert_eq!(Solution::min_deletion_size(a), res);
let a = vec_string!["edcba"];
let res = 4;
assert_eq!(Solution::min_deletion_size(a), res);
let a = vec_string!["ghi", "def", "abc"];
let res = 0;
assert_eq!(Solution::min_deletion_size(a), res);
let a = vec_string!["cbbdabc"];
let res = 3;
assert_eq!(Solution::min_deletion_size(a), res);
}
``````

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