<p>Given two strings <code>text1</code> and <code>text2</code>, return <em>the length of their longest <strong>common subsequence</strong>. </em>If there is no <strong>common subsequence</strong>, return <code>0</code>.</p>

<p>A <strong>subsequence</strong> of a string is a new string generated from the original string with some characters (can be none) deleted without changing the relative order of the remaining characters.</p>

<ul>
	<li>For example, <code>&quot;ace&quot;</code> is a subsequence of <code>&quot;abcde&quot;</code>.</li>
</ul>

<p>A <strong>common subsequence</strong> of two strings is a subsequence that is common to both strings.</p>

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

<pre>
<strong>Input:</strong> text1 = &quot;abcde&quot;, text2 = &quot;ace&quot; 
<strong>Output:</strong> 3  
<strong>Explanation:</strong> The longest common subsequence is &quot;ace&quot; and its length is 3.
</pre>

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

<pre>
<strong>Input:</strong> text1 = &quot;abc&quot;, text2 = &quot;abc&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong> The longest common subsequence is &quot;abc&quot; and its length is 3.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> text1 = &quot;abc&quot;, text2 = &quot;def&quot;
<strong>Output:</strong> 0
<strong>Explanation:</strong> There is no such common subsequence, so the result is 0.
</pre>

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

<ul>
	<li><code>1 &lt;= text1.length, text2.length &lt;= 1000</code></li>
	<li><code>text1</code> and <code>text2</code> consist of only lowercase English characters.</li>
</ul>

class Solution:
    def _longest_common_subsequence(self, text1: str, text2: str, index_1: int, index_2: int, memo: dict):
        text1_slice = text1[0:(index_1 + 1)]
        text2_slice = text2[0:(index_2 + 1)]
        if (index_1, index_2) in memo:
            return memo[(index_1, index_2)]
        if text1_slice == text2_slice:
            return len(text1_slice)
        if index_1 < 0 or index_2 < 0:
            return 0

        # Add base cases later...
        if text1[index_1] == text2[index_2]:
            result = self._longest_common_subsequence(text1, text2, index_1 - 1, index_2 - 1, memo) + 1
        else:
            result1 = self._longest_common_subsequence(text1, text2, index_1 - 1, index_2, memo)
            result2 = self._longest_common_subsequence(text1, text2, index_1, index_2 -1, memo)
            result =  max(result1, result2)
    
        memo[(index_1, index_2)] = result
        return result

    def longestCommonSubsequence(self, text1: str, text2: str) -> int:
        return self._longest_common_subsequence(text1, text2, len(text1) - 1, len(text2) - 1, memo ={})
187203