longest-common-subsequence.md

<p>Given two strings <code>text1</code> and <code>text2</code>, return the length of their longest common subsequence.</p>

<p>A <em>subsequence</em> 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. (eg, &quot;ace&quot; is a subsequence of &quot;abcde&quot; while &quot;aec&quot; is not).&nbsp;A <em>common subsequence</em>&nbsp;of two strings is a subsequence that is common to both strings.</p>

<p>&nbsp;</p>

<p>If there is no common subsequence, return 0.</p>

<p>&nbsp;</p>
<p><strong>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>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>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 &lt;= 1000</code></li>
	<li><code>1 &lt;= text2.length &lt;= 1000</code></li>
	<li>The input strings consist of lowercase English characters only.</li>
</ul>