<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:
    //all possible ways, kind of inclusion exclusion
    int usingRecursion(string &word1,string &word2, int i, int j){
        if(i>=word1.size()){
            return word2.size() - j;
        }
        if(j>=word2.size()){
            return word1.size() - i;
        }
        int ans=0;
        if(word1[i]==word2[j]){
            ans= 0+ usingRecursion(word1,word2,i+1,j+1);
        }
        else{
            int replace= 1+ usingRecursion(word1,word2,i+1,j+1);
            int deletion=1 + usingRecursion(word1,word2, i+1,j);
            int insertion= 1+ usingRecursion(word1,word2,i,j+1);
            ans=min(insertion,min(deletion,replace));
        }
        return ans;
    }
    int usingMemoisation(string &word1,string &word2, int i, int j,vector<vector<int>>&dp){
        if(i==word1.size()){
            return word2.size() - j;
        }
        if(j==word2.size()){
            return word1.size() - i;
        }
        if(dp[i][j] != -1)return dp[i][j];
        int ans=0;
        if(word1[i]==word2[j]){
            ans= 0+ usingMemoisation(word1,word2,i+1,j+1,dp);
        }
        else{
            int replace= 1+ usingMemoisation(word1,word2,i+1,j+1,dp);
            int deletion=1 + usingMemoisation(word1,word2, i+1,j,dp);
            int insertion= 1+ usingMemoisation(word1,word2,i,j+1,dp);
            ans=min(insertion,min(deletion,replace));
        }
        dp[i][j]=ans;
        return dp[i][j];
    }
    int usingTabulation(string &word1,string &word2){
        vector<vector<int>>dp(word1.size()+1,vector<int>(word2.size()+1,0));
        for(int col =0;col <=word2.size();col++){
            dp[word1.size()][col]=word2.size()-col;    
        }
        for(int row=0;row<=word1.size();row++){
            dp[row][word2.size()]=word1.size()-row;
        }
        for(int row=word1.size()-1;row>=0;row--){
            for(int col=word2.size()-1;col>=0;col--){
                int ans=0;
                if(word1[row]==word2[col]){
                    ans= 0+ dp[row+1][col+1];
                }
                else{
                    int replace= 1+ dp[row+1][col+1];
                    int deletion=1 + dp[row+1][col];
                    int insertion= 1+ dp[row][col+1];
                    ans=min(insertion,min(deletion,replace));
                }
                dp[row][col]=ans;
            }
        }
        return dp[0][0];
    }
    int minDistance(string word1, string word2) {
        vector<vector<int>>dp(word1.size()+1,vector<int>(word2.size()+1,-1));
        return usingTabulation(word1,word2);
    }
};
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