<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 {
    void display(vector<vector<int>> dp){
        for(int i=0;i<dp.size();++i){
            for(int j=0;j<dp[0].size();++j){
                cout<<dp[i][j]<<" ";
            }
            cout<<endl;
        }
        cout<<endl;
    }
    int solve(string &w1,string &w2){
        vector<vector<int>> dp(w1.size()+1,vector<int> (w2.size()+1,0));

        int ans;

        for(int i=0;i<w1.length();++i){
            dp[i][w2.length()] = w1.length() - i;
        }

        for(int j=0;j<w2.length();++j){
            dp[w1.length()][j] = w2.length() - j;
        }
        display(dp);
        for(int i = w1.length()-1;i >= 0;--i){
            for(int j = w2.length()-1;j >= 0;--j){
                if(w1[i] == w2[j]){
                    ans = dp[i+1][j+1];
                }
                else{
                    int insert = dp[i][j+1];
                    int replace = dp[i+1][j+1];
                    int dlt = dp[i+1][j];
                    ans = (min(insert,min(replace,dlt)) + 1);
                }
                dp[i][j] = ans;
            }
        }
        display(dp);
        return dp[0][0];
    }
public:
    int minDistance(string word1, string word2) {
        int ans = solve(word1,word2);
        return ans;
    }
};
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