<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 longestsubseq(self, s, t):
        rows, cols = len(s)+1 , len(t)+1
        dp = [[""]*cols for _ in range(rows)]
        for i in range(rows-2,-1,-1):
            for j in range(cols-2,-1,-1):
                if s[i] == t[j]:
                    dp[i][j] = s[i] + dp[i+1][j+1]
                else:
                    if len(dp[i+1][j])>len(dp[i][j+1]):
                        dp[i][j] = dp[i+1][j]
                    else:
                        dp[i][j] = dp[i][j+1]
        return dp[0][0]

    def shortestCommonSupersequence(self, str1: str, str2: str) -> str:
        sub = self.longestsubseq(str1,str2)
        p1 = p2 = sp = 0
        ans = ""
        while sp < len(sub):
            while str1[p1] != sub[sp]:
                ans = ans + str1[p1]
                p1 += 1
            while str2[p2] != sub[sp]:
                ans = ans + str2[p2]
                p2 += 1
            ans = ans + sub[sp]
            sp += 1
            p1 += 1
            p2 += 1
            
        if p1 < len(str1):
            ans = ans + str1[p1:]
        if p2 < len(str2):
            ans = ans + str2[p2:]
        return ans
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