remove-outermost-parentheses

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Algorithms

A valid parentheses string is either empty <code>&quot;&quot;</code>, <code>&quot;(&quot; + A + &quot;)&quot;</code>, or <code>A + B</code>, where <code>A</code> and <code>B</code> are valid parentheses strings, and <code>+</code> represents string concatenation.

<ul>
	<li>For example, <code>&quot;&quot;</code>, <code>&quot;()&quot;</code>, <code>&quot;(())()&quot;</code>, and <code>&quot;(()(()))&quot;</code> are all valid parentheses strings.</li>
</ul>

A valid parentheses string <code>s</code> is primitive if it is nonempty, and there does not exist a way to split it into <code>s = A + B</code>, with <code>A</code> and <code>B</code> nonempty valid parentheses strings.

Given a valid parentheses string <code>s</code>, consider its primitive decomposition: <code>s = P1 + P2 + ... + Pk</code>, where <code>Pi</code> are primitive valid parentheses strings.

Return <code>s</code> after removing the outermost parentheses of every primitive string in the primitive decomposition of <code>s</code>.

&nbsp;
Example 1:

<pre>
Input: s = &quot;(()())(())&quot;
Output: &quot;()()()&quot;
Explanation: 
The input string is &quot;(()())(())&quot;, with primitive decomposition &quot;(()())&quot; + &quot;(())&quot;.
After removing outer parentheses of each part, this is &quot;()()&quot; + &quot;()&quot; = &quot;()()()&quot;.
</pre>

Example 2:

<pre>
Input: s = &quot;(()())(())(()(()))&quot;
Output: &quot;()()()()(())&quot;
Explanation: 
The input string is &quot;(()())(())(()(()))&quot;, with primitive decomposition &quot;(()())&quot; + &quot;(())&quot; + &quot;(()(()))&quot;.
After removing outer parentheses of each part, this is &quot;()()&quot; + &quot;()&quot; + &quot;()(())&quot; = &quot;()()()()(())&quot;.
</pre>

Example 3:

<pre>
Input: s = &quot;()()&quot;
Output: &quot;&quot;
Explanation: 
The input string is &quot;()()&quot;, with primitive decomposition &quot;()&quot; + &quot;()&quot;.
After removing outer parentheses of each part, this is &quot;&quot; + &quot;&quot; = &quot;&quot;.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= s.length &lt;= 105</code></li>
	<li><code>s[i]</code> is either <code>&#39;(&#39;</code> or <code>&#39;)&#39;</code>.</li>
	<li><code>s</code> is a valid parentheses string.</li>
</ul>