<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>

// // ATTEMPT 1
// class Solution {
//     map<string,int> dp; 
// public:
//     int minDistance(string x, string y) {
//         if(dp.find(x+"#"+y) != dp.end()){
//             return dp[x+"#"+y];
//         }

//         if(x.length() == 0) return y.length();
//         if(y.length() == 0) return x.length();

//         int ans = min(1 + minDistance(x.substr(1), y),
//         1 + minDistance(x, y.substr(1)));
//         if(x[0] == y[0]){
//             ans = min(ans, minDistance(x.substr(1), y.substr(1)));
//         } else{
//             ans = min(ans, 1 + minDistance(x.substr(1), y.substr(1)));
//         }
//         dp[x+"#"+y] = ans;
//         return ans;
//     }
// };

// ATTEMPT 2
class Solution {
    map<pair<int,int>,int> dp; 
    string x,y;
public:
    int minDistance(string x1, string y1) {
        x = x1; y = y1;
        return solve(0,0); 
    }

    int solve(int i, int j){
        if(dp.find({i,j}) != dp.end()){
            return dp[{i,j}];
        }

        if(i == x.length()) return y.length()-j;
        if(y.length() == j) return x.length()-i;

        int ans = min(1 + solve(i+1,j),
        1 + solve(i,j+1));
        if(x[i] == y[j]){
            ans = min(ans, solve(i+1,j+1));
        } else{
            ans = min(ans, 1 + solve(i+1, j+1));
        }
        dp[{i,j}] = ans;
        return ans;
    }
};
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