<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:
        n = len(s)
        s2 = s + s  # Double the string to simulate rotations
        alt1, alt2 = "", ""  # Create two alternating patterns
        
        # Build the alternating patterns
        for i in range(2 * n):
            if i % 2 == 0:
                alt1 += '0'
                alt2 += '1'
            else:
                alt1 += '1'
                alt2 += '0'
        
        # Initialize the flip counts for the first window
        flips1, flips2 = 0, 0
        min_flips = float('inf')
        
        # Check the minimum flips required for the first window of size `n`
        for i in range(n):
            if s2[i] != alt1[i]:
                flips1 += 1
            if s2[i] != alt2[i]:
                flips2 += 1

        # Start sliding the window over the doubled string
        min_flips = min(flips1, flips2)
        
        # Slide the window across the doubled string
        for i in range(n, 2 * n):
            # Remove the left character of the window
            if s2[i - n] != alt1[i - n]:
                flips1 -= 1
            if s2[i - n] != alt2[i - n]:
                flips2 -= 1
            
            # Add the right character of the window
            if s2[i] != alt1[i]:
                flips1 += 1
            if s2[i] != alt2[i]:
                flips2 += 1

            # Update the minimum flips found
            min_flips = min(min_flips, flips1, flips2)

        return min_flips

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