<p>Given two strings <code>word1</code> and <code>word2</code>, return <em>the minimum number of operations required to convert <code>word1</code> to <code>word2</code></em>.</p>

<p>You have the following three operations permitted on a word:</p>

<ul>
	<li>Insert a character</li>
	<li>Delete a character</li>
	<li>Replace a character</li>
</ul>

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

<pre>
<strong>Input:</strong> word1 = &quot;horse&quot;, word2 = &quot;ros&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong> 
horse -&gt; rorse (replace &#39;h&#39; with &#39;r&#39;)
rorse -&gt; rose (remove &#39;r&#39;)
rose -&gt; ros (remove &#39;e&#39;)
</pre>

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

<pre>
<strong>Input:</strong> word1 = &quot;intention&quot;, word2 = &quot;execution&quot;
<strong>Output:</strong> 5
<strong>Explanation:</strong> 
intention -&gt; inention (remove &#39;t&#39;)
inention -&gt; enention (replace &#39;i&#39; with &#39;e&#39;)
enention -&gt; exention (replace &#39;n&#39; with &#39;x&#39;)
exention -&gt; exection (replace &#39;n&#39; with &#39;c&#39;)
exection -&gt; execution (insert &#39;u&#39;)
</pre>

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

<ul>
	<li><code>0 &lt;= word1.length, word2.length &lt;= 500</code></li>
	<li><code>word1</code> and <code>word2</code> consist of lowercase English letters.</li>
</ul>

class Solution {
public:
    int mini = INT_MAX;
    int helper(string &a ,string &b, int i,int j,int cnt,vector<vector<int>>&dp,string s){
        // if(s == b){
        //     mini = min(mini,cnt);
        //     return 0;
        // }
        // if(i >= a.size() || j >= b.size()) return 0;
        if(i == a.size())return dp[i][j] = b.size() - j;
        if(j == b.size())return dp[i][j] = a.size() - i;
        if(dp[i][j] != -1) return dp[i][j];
        int p=0,q=0,r=0;
        if(a[i] == b[j])dp[i][j] = helper(a,b,i+1,j+1,cnt,dp,s+b[j]);
        else{
            p = 1 + helper(a,b,i,j+1,cnt+1,dp,s+b[j]);
            q = 1 + helper(a,b,i+1,j,cnt+1,dp,s);
            r = 1 + helper(a,b,i+1,j+1,cnt+1,dp,s+b[j]);
            return dp[i][j] = min({p,q,r});
        }
        return dp[i][j];
    }
    int minDistance(string word1, string word2) {
        vector<vector<int>>dp(word1.size()+1,vector<int>(word2.size()+1,-1));
        int gg = helper(word1,word2,0,0,0,dp,"");
        return gg;
    }
};
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