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
class Solution {
    public List<String> getWordsInLongestSubsequence(String[] words, int[] groups) {
        int n = groups.length;
        int[] f = new int[n];
        int[] g = new int[n];
        Arrays.fill(f, 1);
        Arrays.fill(g, -1);
        int mx = 1;
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < i; ++j) {
                if (groups[i] != groups[j] && f[i] < f[j] + 1 && check(words[i], words[j])) {
                    f[i] = f[j] + 1;
                    g[i] = j;
                    mx = Math.max(mx, f[i]);
                }
            }
        }
        List<String> ans = new ArrayList<>();
        for (int i = 0; i < n; ++i) {
            if (f[i] == mx) {
                for (int j = i; j >= 0; j = g[j]) {
                    ans.add(words[j]);
                }
                break;
            }
        }
        Collections.reverse(ans);
        return ans;
    }

    private boolean check(String s, String t) {
        if (s.length() != t.length()) {
            return false;
        }
        int cnt = 0;
        for (int i = 0; i < s.length(); ++i) {
            if (s.charAt(i) != t.charAt(i)) {
                ++cnt;
            }
        }
        return cnt == 1;
    }
}