<p>There are <code>n</code> dominoes in a line, and we place each domino vertically upright. In the beginning, we simultaneously push some of the dominoes either to the left or to the right.</p>

<p>After each second, each domino that is falling to the left pushes the adjacent domino on the left. Similarly, the dominoes falling to the right push their adjacent dominoes standing on the right.</p>

<p>When a vertical domino has dominoes falling on it from both sides, it stays still due to the balance of the forces.</p>

<p>For the purposes of this question, we will consider that a falling domino expends no additional force to a falling or already fallen domino.</p>

<p>You are given a string <code>dominoes</code> representing the initial state where:</p>

<ul>
	<li><code>dominoes[i] = &#39;L&#39;</code>, if the <code>i<sup>th</sup></code> domino has been pushed to the left,</li>
	<li><code>dominoes[i] = &#39;R&#39;</code>, if the <code>i<sup>th</sup></code> domino has been pushed to the right, and</li>
	<li><code>dominoes[i] = &#39;.&#39;</code>, if the <code>i<sup>th</sup></code> domino has not been pushed.</li>
</ul>

<p>Return <em>a string representing the final state</em>.</p>

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

<pre>
<strong>Input:</strong> dominoes = &quot;RR.L&quot;
<strong>Output:</strong> &quot;RR.L&quot;
<strong>Explanation:</strong> The first domino expends no additional force on the second domino.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://s3-lc-upload.s3.amazonaws.com/uploads/2018/05/18/domino.png" style="height: 196px; width: 512px;" />
<pre>
<strong>Input:</strong> dominoes = &quot;.L.R...LR..L..&quot;
<strong>Output:</strong> &quot;LL.RR.LLRRLL..&quot;
</pre>

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

<ul>
	<li><code>n == dominoes.length</code></li>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>dominoes[i]</code> is either <code>&#39;L&#39;</code>, <code>&#39;R&#39;</code>, or <code>&#39;.&#39;</code>.</li>
</ul>

class Solution:
    def pushDominoes(self, dominoes: str) -> str:
        # Convert the string to a list for easier manipulation
        dominoes = list(dominoes)
        n = len(dominoes)
        
        # Initialize pointers
        left = 0
        right = 0
        
        # Function to process a segment of dominoes
        def process_segment(left, right, dominoes):
            if dominoes[left] == 'R' and dominoes[right] == 'L':
                # Split the segment into two halves
                mid = (left + right) // 2
                if (right - left + 1) % 2 == 0:
                    dominoes[left:mid+1] = ['R'] * (mid - left + 1)
                    dominoes[mid+1:right+1] = ['L'] * (right - mid)
                else:
                    dominoes[left:mid] = ['R'] * (mid - left)
                    dominoes[mid+1:right+1] = ['L'] * (right - mid)
            elif dominoes[left] == 'R':
                dominoes[left:right+1] = ['R'] * (right - left + 1)
            elif dominoes[right] == 'L':
                dominoes[left:right+1] = ['L'] * (right - left + 1)
            
        # Traverse the dominoes
        while right < n:
            if dominoes[right] == '.':
                right += 1
            else:
                process_segment(left, right, dominoes)
                left = right
                right += 1
        
        # Process the last segment if it ends with 'R'
        if dominoes[left] == 'R':
            dominoes[left:] = ['R'] * (n - left)
        
        # Convert the list back to a string
        return ''.join(dominoes)

# Example usage:
solution = Solution()
print(solution.pushDominoes("RR.L"))  # Output: "RR.L"
print(solution.pushDominoes(".L.R...LR..L.."))  # Output: "LL.RR.LLRRLL.."
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