<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>

#include <vector>
#include <string>
#include <algorithm>
using namespace std;

class Solution {
public:
    static bool compare(const string &s1, const string &s2) {
        return s1.size() < s2.size();
    }

    int finddiff(int i, int j, const string &s, const string &a, vector<vector<int>>& dp) {
        if (i >= s.size() || j >= a.size()) {
            return 0;
        }

        if (dp[i][j] != -1) {
            return dp[i][j];
        }

        int ans = 0;

        if (s[i] == a[j]) {
            ans = 1 + finddiff(i + 1, j + 1, s, a, dp);
        } else {
            int s1 = finddiff(i + 1, j, s, a, dp);
            int s2 = finddiff(i, j + 1, s, a, dp);
            ans = max(s1, s2);
        }

        return dp[i][j] = ans;
    }

    int solve(int index, vector<string>& words, vector<int>& dp) {
        if (dp[index] != -1) {
            return dp[index];
        }

        int maxLength = 1;

        for (int i = index + 1; i < words.size(); ++i) {
            if (words[i].size() == words[index].size() + 1) {
                vector<vector<int>> memo(words[index].size(), vector<int>(words[i].size(), -1));
                if (finddiff(0, 0, words[index], words[i], memo) == words[index].size()) {
                    maxLength = max(maxLength, 1 + solve(i, words, dp));
                }
            }
        }

        return dp[index] = maxLength;
    }

    int longestStrChain(vector<string>& words) {
        sort(words.begin(), words.end(), compare);

        int n = words.size();
        vector<int> dp(n, -1);
        int ans = 0;

        for (int i = 0; i < n; i++) {
            ans = max(ans, solve(i, words, dp));
        }

        return ans;
    }
};

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