<p>Given two strings <code>str1</code> and <code>str2</code>, return <em>the shortest string that has both </em><code>str1</code><em> and </em><code>str2</code><em> as <strong>subsequences</strong></em>. If there are multiple valid strings, return <strong>any</strong> of them.</p>

<p>A string <code>s</code> is a <strong>subsequence</strong> of string <code>t</code> if deleting some number of characters from <code>t</code> (possibly <code>0</code>) results in the string <code>s</code>.</p>

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

<pre>
<strong>Input:</strong> str1 = &quot;abac&quot;, str2 = &quot;cab&quot;
<strong>Output:</strong> &quot;cabac&quot;
<strong>Explanation:</strong> 
str1 = &quot;abac&quot; is a subsequence of &quot;cabac&quot; because we can delete the first &quot;c&quot;.
str2 = &quot;cab&quot; is a subsequence of &quot;cabac&quot; because we can delete the last &quot;ac&quot;.
The answer provided is the shortest such string that satisfies these properties.
</pre>

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

<pre>
<strong>Input:</strong> str1 = &quot;aaaaaaaa&quot;, str2 = &quot;aaaaaaaa&quot;
<strong>Output:</strong> &quot;aaaaaaaa&quot;
</pre>

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

<ul>
	<li><code>1 &lt;= str1.length, str2.length &lt;= 1000</code></li>
	<li><code>str1</code> and <code>str2</code> consist of lowercase English letters.</li>
</ul>

class Solution:
    def shortestCommonSupersequence(self, str1: str, str2: str) -> str:
        n, m = len(str1), len(str2)
        longest = [[[0, 's'] for j in range(m + 1)] for i in range(n + 1)]

        for i in range(1, n + 1):
            for j in range(1, m + 1):
                if str1[i - 1] == str2[j - 1]:
                    longest[i][j] = [longest[i - 1][j - 1][0] + 1, 's']
                elif longest[i - 1][j][0] > longest[i][j - 1][0]:
                    longest[i][j] = [longest[i-1][j][0], 'u']
                else:
                    longest[i][j] = [longest[i][j - 1][0], 'l']
        
        i, j, lasti, lastj = n, m, n, m

        ans = ""
        while i > 0 and j > 0:
            if longest[i][j][1] == 's':
                ans = str1[i - 1] + str1[i: lasti] + str2[j: lastj] + ans 
                i, j = i - 1, j - 1
                lasti, lastj = i, j
            elif longest[i][j][1] == 'u':
                i = i - 1
            else:
                j = j - 1

        ans = str1[: lasti] + str2[: lastj] + ans 

        return ans
107958