Delete Columns to Make Sorted III
<p>You are given an array of <code>n</code> strings <code>strs</code>, all of the same length.</p>

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

<p>For example, if we have <code>strs = [&quot;abcdef&quot;,&quot;uvwxyz&quot;]</code> and deletion indices <code>{0, 2, 3}</code>, then the final array after deletions is <code>[&quot;bef&quot;, &quot;vyz&quot;]</code>.</p>

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

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

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

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> strs = [&quot;edcba&quot;]
<strong>Output:</strong> 4
<strong>Explanation:</strong> If we delete less than 4 columns, the only row will not be lexicographically sorted.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> strs = [&quot;ghi&quot;,&quot;def&quot;,&quot;abc&quot;]
<strong>Output:</strong> 0
<strong>Explanation:</strong> All rows are already lexicographically sorted.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == strs.length</code></li>
	<li><code>1 &lt;= n &lt;= 100</code></li>
	<li><code>1 &lt;= strs[i].length &lt;= 100</code></li>
	<li><code>strs[i]</code> consists of lowercase English letters.</li>
</ul>

<ul>
	<li>&nbsp;</li>
</ul>
Array; String; Dynamic Programming
impl Solution {
    pub fn min_deletion_size(strs: Vec<String>) -> i32 {
        let n = strs[0].len();
        let mut f = vec![1; n];

        for i in 1..n {
            for j in 0..i {
                if strs.iter().all(|s| s.as_bytes()[j] <= s.as_bytes()[i]) {
                    f[i] = f[i].max(f[j] + 1);
                }
            }
        }

        (n - *f.iter().max().unwrap()) as i32
    }
}
