check-if-an-original-string-exists-given-two-encoded-strings

Check if an Original String Exists Given Two Encoded Strings

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An original string, consisting of lowercase English letters, can be encoded by the following steps:

<ul>
	<li>Arbitrarily split it into a sequence of some number of non-empty substrings.</li>
	<li>Arbitrarily choose some elements (possibly none) of the sequence, and replace each with its length (as a numeric string).</li>
	<li>Concatenate the sequence as the encoded string.</li>
</ul>

For example, one way to encode an original string <code>&quot;abcdefghijklmnop&quot;</code> might be:

<ul>
	<li>Split it as a sequence: <code>[&quot;ab&quot;, &quot;cdefghijklmn&quot;, &quot;o&quot;, &quot;p&quot;]</code>.</li>
	<li>Choose the second and third elements to be replaced by their lengths, respectively. The sequence becomes <code>[&quot;ab&quot;, &quot;12&quot;, &quot;1&quot;, &quot;p&quot;]</code>.</li>
	<li>Concatenate the elements of the sequence to get the encoded string: <code>&quot;ab121p&quot;</code>.</li>
</ul>

Given two encoded strings <code>s1</code> and <code>s2</code>, consisting of lowercase English letters and digits <code>1-9</code> (inclusive), return <code>true</code> if there exists an original string that could be encoded as both <code>s1</code> and <code>s2</code>. Otherwise, return <code>false</code>.

Note: The test cases are generated such that the number of consecutive digits in <code>s1</code> and <code>s2</code> does not exceed <code>3</code>.

&nbsp;
Example 1:

<pre>
Input: s1 = &quot;internationalization&quot;, s2 = &quot;i18n&quot;
Output: true
Explanation: It is possible that &quot;internationalization&quot; was the original string.
- &quot;internationalization&quot; 
 -&gt; Split: [&quot;internationalization&quot;]
 -&gt; Do not replace any element
 -&gt; Concatenate: &quot;internationalization&quot;, which is s1.
- &quot;internationalization&quot;
 -&gt; Split: [&quot;i&quot;, &quot;nternationalizatio&quot;, &quot;n&quot;]
 -&gt; Replace: [&quot;i&quot;, &quot;18&quot;, &quot;n&quot;]
 -&gt; Concatenate: &quot;i18n&quot;, which is s2
</pre>

Example 2:

<pre>
Input: s1 = &quot;l123e&quot;, s2 = &quot;44&quot;
Output: true
Explanation: It is possible that &quot;leetcode&quot; was the original string.
- &quot;leetcode&quot; 
 -&gt; Split: [&quot;l&quot;, &quot;e&quot;, &quot;et&quot;, &quot;cod&quot;, &quot;e&quot;]
 -&gt; Replace: [&quot;l&quot;, &quot;1&quot;, &quot;2&quot;, &quot;3&quot;, &quot;e&quot;]
 -&gt; Concatenate: &quot;l123e&quot;, which is s1.
- &quot;leetcode&quot; 
 -&gt; Split: [&quot;leet&quot;, &quot;code&quot;]
 -&gt; Replace: [&quot;4&quot;, &quot;4&quot;]
 -&gt; Concatenate: &quot;44&quot;, which is s2.
</pre>

Example 3:

<pre>
Input: s1 = &quot;a5b&quot;, s2 = &quot;c5b&quot;
Output: false
Explanation: It is impossible.
- The original string encoded as s1 must start with the letter &#39;a&#39;.
- The original string encoded as s2 must start with the letter &#39;c&#39;.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= s1.length, s2.length &lt;= 40</code></li>
	<li><code>s1</code> and <code>s2</code> consist of digits <code>1-9</code> (inclusive), and lowercase English letters only.</li>
	<li>The number of consecutive digits in <code>s1</code> and <code>s2</code> does not exceed <code>3</code>.</li>
</ul>

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