## 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:3Explanation: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:4Explanation:If we delete less than 4 columns, the only row will not be lexicographically sorted.

**Example 3:**

Input:strs = ["ghi","def","abc"]Output:0Explanation: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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