Longest Unequal Adjacent Groups Subsequence II
<p>You are given a string array <code>words</code>, and an array <code>groups</code>, both arrays having length <code>n</code>.</p>

<p>The <strong>hamming distance</strong> between two strings of equal length is the number of positions at which the corresponding characters are <strong>different</strong>.</p>

<p>You need to select the <strong>longest</strong> <span data-keyword="subsequence-array">subsequence</span> from an array of indices <code>[0, 1, ..., n - 1]</code>, such that for the subsequence denoted as <code>[i<sub>0</sub>, i<sub>1</sub>, ..., i<sub>k-1</sub>]</code> having length <code>k</code>, the following holds:</p>

<ul>
	<li>For <strong>adjacent</strong> indices in the subsequence, their corresponding groups are <strong>unequal</strong>, i.e., <code>groups[i<sub>j</sub>] != groups[i<sub>j+1</sub>]</code>, for each <code>j</code> where <code>0 &lt; j + 1 &lt; k</code>.</li>
	<li><code>words[i<sub>j</sub>]</code> and <code>words[i<sub>j+1</sub>]</code> are <strong>equal</strong> in length, and the <strong>hamming distance</strong> between them is <code>1</code>, where <code>0 &lt; j + 1 &lt; k</code>, for all indices in the subsequence.</li>
</ul>

<p>Return <em>a string array containing the words corresponding to the indices <strong>(in order)</strong> in the selected subsequence</em>. If there are multiple answers, return <em>any of them</em>.</p>

<p><strong>Note:</strong> strings in <code>words</code> may be <strong>unequal</strong> in length.</p>

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

<div class="example-block" style="border-color: var(--border-tertiary); border-left-width: 2px; color: var(--text-secondary); font-size: .875rem; margin-bottom: 1rem; margin-top: 1rem; overflow: visible; padding-left: 1rem;">
<p><strong>Input: </strong><span class="example-io" style="font-family: Menlo,sans-serif; font-size: 0.85rem;">words = [&quot;bab&quot;,&quot;dab&quot;,&quot;cab&quot;], groups = [1,2,2]</span></p>

<p><strong>Output: </strong><span class="example-io" style="font-family: Menlo,sans-serif; font-size: 0.85rem;">[&quot;bab&quot;,&quot;cab&quot;]</span></p>

<p><strong>Explanation: </strong>A subsequence that can be selected is <code>[0,2]</code>.</p>

<ul>
	<li><code>groups[0] != groups[2]</code></li>
	<li><code>words[0].length == words[2].length</code>, and the hamming distance between them is 1.</li>
</ul>

<p>So, a valid answer is <code>[words[0],words[2]] = [&quot;bab&quot;,&quot;cab&quot;]</code>.</p>

<p>Another subsequence that can be selected is <code>[0,1]</code>.</p>

<ul>
	<li><code>groups[0] != groups[1]</code></li>
	<li><code>words[0].length == words[1].length</code>, and the hamming distance between them is <code>1</code>.</li>
</ul>

<p>So, another valid answer is <code>[words[0],words[1]] = [&quot;bab&quot;,&quot;dab&quot;]</code>.</p>

<p>It can be shown that the length of the longest subsequence of indices that satisfies the conditions is <code>2</code>.</p>
</div>

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

<div class="example-block" style="border-color: var(--border-tertiary); border-left-width: 2px; color: var(--text-secondary); font-size: .875rem; margin-bottom: 1rem; margin-top: 1rem; overflow: visible; padding-left: 1rem;">
<p><strong>Input: </strong><span class="example-io" style="font-family: Menlo,sans-serif; font-size: 0.85rem;">words = [&quot;a&quot;,&quot;b&quot;,&quot;c&quot;,&quot;d&quot;], groups = [1,2,3,4]</span></p>

<p><strong>Output: </strong><span class="example-io" style="font-family: Menlo,sans-serif; font-size: 0.85rem;">[&quot;a&quot;,&quot;b&quot;,&quot;c&quot;,&quot;d&quot;]</span></p>

<p><strong>Explanation: </strong>We can select the subsequence <code>[0,1,2,3]</code>.</p>

<p>It satisfies both conditions.</p>

<p>Hence, the answer is <code>[words[0],words[1],words[2],words[3]] = [&quot;a&quot;,&quot;b&quot;,&quot;c&quot;,&quot;d&quot;]</code>.</p>

<p>It has the longest length among all subsequences of indices that satisfy the conditions.</p>

<p>Hence, it is the only answer.</p>
</div>

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

<ul>
	<li><code>1 &lt;= n == words.length == groups.length &lt;= 1000</code></li>
	<li><code>1 &lt;= words[i].length &lt;= 10</code></li>
	<li><code>1 &lt;= groups[i] &lt;= n</code></li>
	<li><code>words</code> consists of <strong>distinct</strong> strings.</li>
	<li><code>words[i]</code> consists of lowercase English letters.</li>
</ul>
Array; String; Dynamic Programming
impl Solution {
    pub fn get_words_in_longest_subsequence(words: Vec<String>, groups: Vec<i32>) -> Vec<String> {
        fn check(s: &str, t: &str) -> bool {
            s.len() == t.len() && s.chars().zip(t.chars()).filter(|(a, b)| a != b).count() == 1
        }

        let n = groups.len();

        let mut f = vec![1; n];
        let mut g = vec![-1; n];

        let mut mx = 1;

        for i in 0..n {
            let x = groups[i] as usize;
            for j in 0..i {
                let y = groups[j] as usize;
                if x != y && f[i] < f[j] + 1 && check(&words[i], &words[j]) {
                    f[i] = f[j] + 1;
                    g[i] = j as i32;
                    mx = mx.max(f[i]);
                }
            }
        }

        let mut ans = vec![];
        let mut i = n - 1;

        while f[i] != mx {
            i -= 1;
        }

        let mut j = i as i32;
        while j >= 0 {
            ans.push(words[j as usize].clone());
            j = g[j as usize];
        }

        ans.reverse();
        ans
    }
}
