<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 solve(string word1,string word2,int index1,int index2,vector<vector<int>>&dp)
{
    if(index1==word1.length())
    {
        return word2.length()-index2;
    }
    if(index2==word2.length())
    {
        return word1.length()-index1;
    }
    if(dp[index1][index2]!=-1)
    {
        return dp[index1][index2];
    }
    if(word1[index1]==word2[index2])
    {
        return dp[index1][index2]=solve(word1,word2,index1+1,index2+1,dp);
    }
    else{
        return dp[index1][index2]=min(1+solve(word1,word2,index1,index2+1,dp),min(1+solve(word1,word2,index1+1,index2,dp),1+solve(word1,word2,index1+1,index2+1,dp)));
    }
    return dp[index1][index2];
}
int spaceop(string word1,string word2)
{
    vector<int>curr(word2.length()+1,0);
    vector<int>next(word2.length()+1,0);
    for(int i=0;i<=word2.size();i++)
    {
        next[i]=word2.size()-i;
    }
    for(int index1=word1.size()-1;index1>=0;index1--)
    {
        curr[word2.size()]=word1.size()-index1;
        for(int index2=word2.size()-1;index2>=0;index2--)
        {
            if(word1[index1]==word2[index2])
            {
                curr[index2]=next[index2+1];
            }else{
                curr[index2]=min(1+curr[index2+1],min(1+next[index2],1+next[index2+1]));
            }
        }
        next=curr;
    }
    return next[0];
}
    int minDistance(string word1, string word2) {
        vector<vector<int>>dp(word1.size()+1,vector<int>(word2.size()+1,-1));
        return solve(word1,word2,0,0,dp);
    }
};
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