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
func getWordsInLongestSubsequence(words []string, groups []int) []string {
	check := func(s, t string) bool {
		if len(s) != len(t) {
			return false
		}
		cnt := 0
		for i := range s {
			if s[i] != t[i] {
				cnt++
			}
		}
		return cnt == 1
	}
	n := len(groups)
	f := make([]int, n)
	g := make([]int, n)
	for i := range f {
		f[i] = 1
		g[i] = -1
	}
	mx := 1
	for i, x := range groups {
		for j, y := range groups[:i] {
			if x != y && f[i] < f[j]+1 && check(words[i], words[j]) {
				f[i] = f[j] + 1
				g[i] = j
				if mx < f[i] {
					mx = f[i]
				}
			}
		}
	}
	ans := make([]string, 0, mx)
	for i, x := range f {
		if x == mx {
			for j := i; j >= 0; j = g[j] {
				ans = append(ans, words[j])
			}
			break
		}
	}
	slices.Reverse(ans)
	return ans
}