<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:
    class comparator{
        public:
            bool operator()(string &a,string &b){
                if(a.size()<b.size()){
                    return true;
                }
                return false;
            }
    };
    bool isValidMatch(string &a,string &b){
        int m=a.size();
        int n=b.size();
        if(n==m || n-m>1){
            return false;
        }
        vector<vector<int>> dp(m+1,vector<int>(n+1,0));
        for(int i=0;i<m;i++){
            dp[i][0]=0;
        }
        for(int i=0;i<n;i++){
            dp[0][i]=0;
        }
        dp[0][0]=0;
        for(int i=1;i<=m;i++){
            for(int j=1;j<=n;j++){
                if(a[i-1]==b[j-1]){
                    dp[i][j]=dp[i-1][j-1]+1;
                }
                else{
                    dp[i][j]=max(dp[i-1][j],dp[i][j-1]);
                }
            }
        }
        // if(a=="x" && b=="eo"){
        //     for(int i=0;i<=m;i++){
        //         for(int j=0;j<=n;j++){
        //             cout<<dp[i][j]<<" ";
        //         }
        //         cout<<endl;
        //     }
        // }
        return dp[m][n]==a.size();
    }
    int findLargestPath(string &str,unordered_map<string,vector<string>> &adj,unordered_map<string,int> &dp){
        if(adj.find(str)==adj.end()){
            return 1;
        }
        if(dp.find(str)!=dp.end()){
            return dp[str];
        }
        int res=0;
        for(int i=0;i<adj[str].size();i++){
            int curPathSize=findLargestPath(adj[str][i],adj,dp);
            res=max(res,curPathSize+1);
        }
        dp[str]=res;
        return res;
    }
    int longestStrChain(vector<string>& words) {
        sort(words.begin(),words.end(),comparator());
        unordered_map<string,vector<string>> adj;
        unordered_map<string,int> dp;
        for(int i=0;i<words.size();i++){
            for(int j=i+1;j<words.size();j++){
                if(isValidMatch(words[i],words[j])){
                    adj[words[i]].push_back(words[j]);
                }
            }
        }

        // for(auto it=adj.begin();it!=adj.end();it++){
        //     cout<<it->first<<"->";
        //     for(int i=0;i<it->second.size();i++){
        //         cout<<it->second[i]<<", ";
        //     }
        //     cout<<endl;
        // }

        int res=0;
        for(int i=words.size()-1;i>=0;i--){
            res=max(res,findLargestPath(words[i],adj,dp));
        }
        return res;
        return 0;
    }
};
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