<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:
    vector<vector<int>>dp;
    int helper(int i,int j,string &word1,string &word2){
        int n1 = word1.size();
        int n2 = word2.size();
        if (dp[i][j]!=-1)return dp[i][j];
        if (i==n1 && j == n2){
            return 0;
        }
        if (i==n1){
            return  dp[i][j] =  1+helper(i,j+1,word1,word2);
        }
        else if(j==n2){
            return dp[i][j] = 1+helper(i+1,j,word1,word2);
        }

        if (dp[i][j]!=-1)return dp[i][j];
        int ans = 1e9;
        if (word1[i]==word2[j]){
            ans = helper(i+1,j+1,word1,word2);
        }
        ans = min(ans,helper(i+1,j+1,word1,word2)+1);
        int a1 = helper(i+1,j,word1,word2)+1;
        int a2 = helper(i,j+1,word1,word2)+1;
        ans = min(ans,a1);
        ans = min(ans,a2);
        cout<<"i "<<i<<" j "<<j<<" ands "<<ans<<endl;
        return dp[i][j] =ans;


    }
    int minDistance(string word1, string word2) {
        dp = vector<vector<int>>(word1.length()+5,vector<int>(word2.length()+5,-1));
        return helper(0,0,word1,word2);
    }
};
14101