<p>You are given a binary string <code>s</code>. You are allowed to perform two types of operations on the string in any sequence:</p>

<ul>
	<li><strong>Type-1: Remove</strong> the character at the start of the string <code>s</code> and <strong>append</strong> it to the end of the string.</li>
	<li><strong>Type-2: Pick</strong> any character in <code>s</code> and <strong>flip</strong> its value, i.e., if its value is <code>&#39;0&#39;</code> it becomes <code>&#39;1&#39;</code> and vice-versa.</li>
</ul>

<p>Return <em>the <strong>minimum</strong> number of <strong>type-2</strong> operations you need to perform</em> <em>such that </em><code>s</code> <em>becomes <strong>alternating</strong>.</em></p>

<p>The string is called <strong>alternating</strong> if no two adjacent characters are equal.</p>

<ul>
	<li>For example, the strings <code>&quot;010&quot;</code> and <code>&quot;1010&quot;</code> are alternating, while the string <code>&quot;0100&quot;</code> is not.</li>
</ul>

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

<pre>
<strong>Input:</strong> s = &quot;111000&quot;
<strong>Output:</strong> 2
<strong>Explanation</strong>: Use the first operation two times to make s = &quot;100011&quot;.
Then, use the second operation on the third and sixth elements to make s = &quot;10<u>1</u>01<u>0</u>&quot;.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;010&quot;
<strong>Output:</strong> 0
<strong>Explanation</strong>: The string is already alternating.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;1110&quot;
<strong>Output:</strong> 1
<strong>Explanation</strong>: Use the second operation on the second element to make s = &quot;1<u>0</u>10&quot;.
</pre>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 10<sup>5</sup></code></li>
	<li><code>s[i]</code> is either <code>&#39;0&#39;</code> or <code>&#39;1&#39;</code>.</li>
</ul>

class Solution:
    def minFlips(self, s: str) -> int:
        output = float('inf')
        n = len(s)

        target1 = ''.join(['1' if i % 2 == 0 else '0' for i in range(2 * n)])
        target2 = ''.join(['1' if i % 2 == 1 else '0' for i in range(2 * n)])
        count1 = 0
        count2 = 0

        for i in range(n):
            if s[i] != target1[i]:
                count1 += 1
            if s[i] != target2[i]:
                count2 += 1
        output = min(count1, count2)
        
        s = s + s # extend the string! and then compare (unless we use (i - 1 + n) % n for cyclic)

        for i in range(n, 2 * n):
            if s[i - n] != target1[i- n]:
                count1 -= 1
            if s[i - n] != target2[i - n]:
                count2 -= 1

            if s[i] != target1[i]:
                count1 += 1
            if s[i] != target2[i]:
                count2 += 1

            output = min(output, count1, count2)

        return output

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