<p>Given two strings <code>word1</code> and <code>word2</code>, return <em>the minimum number of <strong>steps</strong> required to make</em> <code>word1</code> <em>and</em> <code>word2</code> <em>the same</em>.</p>

<p>In one <strong>step</strong>, you can delete exactly one character in either string.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> word1 = &quot;sea&quot;, word2 = &quot;eat&quot;
<strong>Output:</strong> 2
<strong>Explanation:</strong> You need one step to make &quot;sea&quot; to &quot;ea&quot; and another step to make &quot;eat&quot; to &quot;ea&quot;.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> word1 = &quot;leetcode&quot;, word2 = &quot;etco&quot;
<strong>Output:</strong> 4
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= word1.length, word2.length &lt;= 500</code></li>
	<li><code>word1</code> and <code>word2</code> consist of only lowercase English letters.</li>
</ul>

class Solution:
    """
        xxx
        yyy

        moving backwards
        If s1[-1] == s2[-1]
            Then we don't have to delete either
            So

        sea eat

        se eat or sea ea
        
    """
    def minDistance(self, word1: str, word2: str) -> int:       
        memo = {}
        return self.deleteDistance(word1, word2, len(word1) - 1, len(word2) - 1, memo)

    def deleteDistance(self, word1, word2, i, j, memo):
        if (i,j) in memo:
            return memo[(i, j)]

        if i < 0:
            return j + 1
        
        if j < 0:
            return i + 1

        # Nothing needs to be deleted
        if word1[i] == word2[j]:
            return self.deleteDistance(word1, word2, i-1, j-1, memo)
        
        # We either need to delete word1[i] or delete word2[j]
        distance = 1 + min(
            self.deleteDistance(word1, word2, i - 1, j, memo),
            self.deleteDistance(word1, word2, i, j - 1, memo))
        memo[(i,j)]= distance
        return distance
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