minimum-add-to-make-parentheses-valid

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Algorithms

A parentheses string is valid if and only if:

<ul>
	<li>It is the empty string,</li>
	<li>It can be written as <code>AB</code> (<code>A</code> concatenated with <code>B</code>), where <code>A</code> and <code>B</code> are valid strings, or</li>
	<li>It can be written as <code>(A)</code>, where <code>A</code> is a valid string.</li>
</ul>

You are given a parentheses string <code>s</code>. In one move, you can insert a parenthesis at any position of the string.

<ul>
	<li>For example, if <code>s = &quot;()))&quot;</code>, you can insert an opening parenthesis to be <code>&quot;(()))&quot;</code> or a closing parenthesis to be <code>&quot;())))&quot;</code>.</li>
</ul>

Return the minimum number of moves required to make <code>s</code> valid.

&nbsp;
Example 1:

<pre>
Input: s = &quot;())&quot;
Output: 1
</pre>

Example 2:

<pre>
Input: s = &quot;(((&quot;
Output: 3
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= s.length &lt;= 1000</code></li>
	<li><code>s[i]</code> is either <code>&#39;(&#39;</code> or <code>&#39;)&#39;</code>.</li>
</ul>