<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 f(int ind1, int ind2, string s1, string s2, vector<vector<int>>& dp) {
        if (ind1 == 0)
            return ind2;
        if (ind2 == 0)
            return ind1;
        if (dp[ind1][ind2] != -1)
            return dp[ind1][ind2];
        if (s1[ind1 - 1] == s2[ind2 - 1])
            return dp[ind1][ind2] = f(ind1 - 1, ind2 - 1, s1, s2, dp);

        int insert = f(ind1, ind2 - 1, s1, s2, dp);
        int replace = f(ind1 - 1, ind2 - 1, s1, s2, dp);
        int del = f(ind1 - 1, ind2, s1, s2, dp);
        return dp[ind1][ind2] = 1 + min(insert, min(del, replace));
    }
    int minDistance(string s1, string s2) {
        int n = s1.length();
        int m = s2.length();
        vector<vector<int>> dp(n + 1, vector<int>(m + 1, 0));
        for (int i = 0; i <= n; i++) {
            dp[i][0] = i;
           
        }
        for(int i=0;i<=m;i++)
        {
            dp[0][i]=i;
        }
        for (int ind1 = 1; ind1 <= n; ind1++) {
            for (int ind2 = 1; ind2 <= m; ind2++) {
                if (s1[ind1 - 1] == s2[ind2 - 1])
                     dp[ind1][ind2] = f(ind1 - 1, ind2 - 1, s1, s2, dp);
                     else

                {
                int insert = dp[ind1][ind2-1];
                int replace = dp[ind1-1][ind2-1];
                int del = dp[ind1-1][ind2];
                 dp[ind1][ind2] = 1 + min(insert, min(del, replace));
                 }
            }
        }
        return dp[n][m];
    }
};
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