<p>You are given an array of <code>words</code> where each word consists of lowercase English letters.</p>

<p><code>word<sub>A</sub></code> is a <strong>predecessor</strong> of <code>word<sub>B</sub></code> if and only if we can insert <strong>exactly one</strong> letter anywhere in <code>word<sub>A</sub></code> <strong>without changing the order of the other characters</strong> to make it equal to <code>word<sub>B</sub></code>.</p>

<ul>
	<li>For example, <code>&quot;abc&quot;</code> is a <strong>predecessor</strong> of <code>&quot;ab<u>a</u>c&quot;</code>, while <code>&quot;cba&quot;</code> is not a <strong>predecessor</strong> of <code>&quot;bcad&quot;</code>.</li>
</ul>

<p>A <strong>word chain</strong><em> </em>is a sequence of words <code>[word<sub>1</sub>, word<sub>2</sub>, ..., word<sub>k</sub>]</code> with <code>k &gt;= 1</code>, where <code>word<sub>1</sub></code> is a <strong>predecessor</strong> of <code>word<sub>2</sub></code>, <code>word<sub>2</sub></code> is a <strong>predecessor</strong> of <code>word<sub>3</sub></code>, and so on. A single word is trivially a <strong>word chain</strong> with <code>k == 1</code>.</p>

<p>Return <em>the <strong>length</strong> of the <strong>longest possible word chain</strong> with words chosen from the given list of </em><code>words</code>.</p>

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

<pre>
<strong>Input:</strong> words = [&quot;a&quot;,&quot;b&quot;,&quot;ba&quot;,&quot;bca&quot;,&quot;bda&quot;,&quot;bdca&quot;]
<strong>Output:</strong> 4
<strong>Explanation</strong>: One of the longest word chains is [&quot;a&quot;,&quot;<u>b</u>a&quot;,&quot;b<u>d</u>a&quot;,&quot;bd<u>c</u>a&quot;].
</pre>

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

<pre>
<strong>Input:</strong> words = [&quot;xbc&quot;,&quot;pcxbcf&quot;,&quot;xb&quot;,&quot;cxbc&quot;,&quot;pcxbc&quot;]
<strong>Output:</strong> 5
<strong>Explanation:</strong> All the words can be put in a word chain [&quot;xb&quot;, &quot;xb<u>c</u>&quot;, &quot;<u>c</u>xbc&quot;, &quot;<u>p</u>cxbc&quot;, &quot;pcxbc<u>f</u>&quot;].
</pre>

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

<pre>
<strong>Input:</strong> words = [&quot;abcd&quot;,&quot;dbqca&quot;]
<strong>Output:</strong> 1
<strong>Explanation:</strong> The trivial word chain [&quot;abcd&quot;] is one of the longest word chains.
[&quot;abcd&quot;,&quot;dbqca&quot;] is not a valid word chain because the ordering of the letters is changed.
</pre>

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

<ul>
	<li><code>1 &lt;= words.length &lt;= 1000</code></li>
	<li><code>1 &lt;= words[i].length &lt;= 16</code></li>
	<li><code>words[i]</code> only consists of lowercase English letters.</li>
</ul>

class Solution {
public:
    int lcs(string s, string t) {
        int m = s.length();
        int n = t.length();

        // Initialize dp with dimensions (m+1) x (n+1) to account for zero-based indexing.
        vector<vector<int>> dp(m + 1, vector<int>(n + 1, 0));

        // Loop through all characters of both strings
        for (int i = 1; i <= m; i++) {
            for (int j = 1; j <= n; j++) {
                if (s[i - 1] == t[j - 1]) {
                    dp[i][j] = 1 + dp[i - 1][j - 1];  // Characters match
                } else {
                    dp[i][j] = max(dp[i - 1][j], dp[i][j - 1]);  // Take the maximum of insertion/deletion
                }
            }
        }

        // Return the length of the longest common subsequence
        return dp[m][n];
    }

    int chain(int ind,int prev,vector<string>& words,vector<vector<int>>& dp)
    {   
        int n = words.size();
        if(ind==n) return 0;

        if(dp[ind][prev+1]!=-1) return dp[ind][prev+1];

        int not_take = chain(ind+1,prev,words,dp);
        int take = INT_MIN;
        if(prev==-1 || words[prev].length()+1==words[ind].length())
        {
            if(prev==-1 || lcs(words[prev],words[ind])==words[prev].length())
            take= 1+chain(ind+1,ind,words,dp);
        }


        return dp[ind][prev+1]=max(take,not_take);
    }
    bool static comp(const string& w1,const string& w2)
    {
        return w1.length()<w2.length();
    }
    int longestStrChain(vector<string>& words) {
        int n = words.size();
        sort(words.begin(),words.end(),comp);
        for(int i=0;i<n;i++) cout<<words[i]<<" ";
        vector<vector<int>> dp(n,vector<int>(n+1,-1));
        return chain(0,-1,words,dp);
    }
};

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