<p>Given the <code>head</code> of a linked list and a value <code>x</code>, partition it such that all nodes <strong>less than</strong> <code>x</code> come before nodes <strong>greater than or equal</strong> to <code>x</code>.</p>

<p>You should <strong>preserve</strong> the original relative order of the nodes in each of the two partitions.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/04/partition.jpg" style="width: 662px; height: 222px;" />
<pre>
<strong>Input:</strong> head = [1,4,3,2,5,2], x = 3
<strong>Output:</strong> [1,2,2,4,3,5]
</pre>

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

<pre>
<strong>Input:</strong> head = [2,1], x = 2
<strong>Output:</strong> [1,2]
</pre>

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

<ul>
	<li>The number of nodes in the list is in the range <code>[0, 200]</code>.</li>
	<li><code>-100 &lt;= Node.val &lt;= 100</code></li>
	<li><code>-200 &lt;= x &lt;= 200</code></li>
</ul>

/**
 * Definition for singly-linked list.
 * struct ListNode {
 *     int val;
 *     ListNode *next;
 *     ListNode() : val(0), next(nullptr) {}
 *     ListNode(int x) : val(x), next(nullptr) {}
 *     ListNode(int x, ListNode *next) : val(x), next(next) {}
 * };
 */
class Solution {
public:
    ListNode* partition(ListNode* head, int x) {
        // Two dummy nodes to start the two separate lists
        ListNode* before_head = new ListNode(0); // Head of the list for nodes less than x
        ListNode* after_head = new ListNode(0);  // Head of the list for nodes greater or equal to x

        // Pointers to track the current end of the before and after lists
        ListNode* before = before_head;
        ListNode* after = after_head;

        // Traverse the original list and partition the nodes
        while (head) {
            if (head->val < x) {
                before->next = head; // Add node to the end of the before list
                before = before->next;
            } else {
                after->next = head; // Add node to the end of the after list
                after = after->next;
            }
            head = head->next; // Move to the next node in the original list
        }

        // Connect the end of the before list to the head of the after list
        after->next = nullptr; // Ensure the end of the after list points to null
        before->next = after_head->next; // Join the two lists

        // The head of the new list is the next node of the before_head dummy node
        return before_head->next;
    }
};

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