<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 t[501][501];
    int solve(int i,int j,string a,string b){
        if(i==a.size() || j==b.size()) {
            if(i==a.size()) return b.size()-j+1;
            else return a.size()-i+1;
        }

        if(t[i][j]!=-1) return t[i][j];

        int skip=INT_MAX,take=INT_MAX,temp=0;
        if(a[i]==b[j]) skip = solve(i+1,j+1,a,b);
        else {
            take=min(1+solve(i+1,j+1,a,b),min(1+solve(i+1,j,a,b),1+solve(i,j+1,a,b)));
        }

        return t[i][j]=min(skip,take);
    }
    int minDistance(string word1, string word2) {
        int n=word1.size();
        int m=word2.size();
        memset(t,-1,sizeof(t));
        return solve(0,0,word1,word2)-1;
        vector<vector<int>> dp(n+1,vector<int>(m+1,0));
        for(int i=0;i<=n;i++) dp[i][0]=i+1;
        //cout<<dp[n][0];
        for(int i=0;i<=m;i++) dp[0][i]=i+1;
        //cout<<dp[0][m];
        for(int i=1;i<=n;i++){
            for(int j=1;j<=m;j++){
                if(word1[i-1]==word2[j-1]) dp[i][j]=0+dp[i-1][j-1];
                else{
                    int mini=min(dp[i-1][j],dp[i][j-1]);
                    cout<<mini;
                    dp[i][j]=1+min(mini,dp[i-1][j-1]);
                }
                cout<<dp[i][j];
            }
            cout<<endl;
        }
        return dp[n][m]-1;
        
        
    }
};
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