<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>

#include <bits/stdc++.h>
#define ss second
#define ff first
#define pii pair<int,int>
#define pb push_back
#define ll long long
#define vi vector<int>
#define vvi vector<vi>
#define vll vector<ll>	
#define pll pair<ll,ll>
#define vpll vector<pll>
#define vvll vector<vll>
#define ld long double
#define um unordered_map
#define all(x) x.begin(),x.end()c

class Solution {
public:
    string s1,s2;
    ll n1,n2;
    struct h_{
        size_t operator()(const pll& key) const {
            ll h1= hash<ll>()(key.ff);
            ll h2= hash<ll>()(key.ss);
            return h1 ^ (h2<<1);
        }
    };

    unordered_map<pll,ll,h_> memo;
    ll foo(ll i, ll j){

        if(i>=n1 && j>=n2)return 0;
        if(i>=n1)return n2-j;
        if(j>=n2)return n1-i;

        if(memo.count({i,j}))return memo[{i,j}];
        if(s1[i]==s2[j])return memo[{i,j}] = foo(i+1,j+1);
        else {//replace, insert, delete
           return memo[{i,j}] = min(1+foo(i+1,j+1),min(1+foo(i,j+1),1+foo(i+1,j)));  
        }
    }   
    int minDistance(string word1, string word2) {
        s1=word1;
        s2=word2;

        n1=s1.size();
        n2=s2.size();

        return foo(0,0);


    }
};
22448