<p>Given the <code>head</code> of a linked list, return <em>the list after sorting it in <strong>ascending order</strong></em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/14/sort_list_1.jpg" style="width: 450px; height: 194px;" />
<pre>
<strong>Input:</strong> head = [4,2,1,3]
<strong>Output:</strong> [1,2,3,4]
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/14/sort_list_2.jpg" style="width: 550px; height: 184px;" />
<pre>
<strong>Input:</strong> head = [-1,5,3,4,0]
<strong>Output:</strong> [-1,0,3,4,5]
</pre>

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

<pre>
<strong>Input:</strong> head = []
<strong>Output:</strong> []
</pre>

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

<ul>
	<li>The number of nodes in the list is in the range <code>[0, 5 * 10<sup>4</sup>]</code>.</li>
	<li><code>-10<sup>5</sup> &lt;= Node.val &lt;= 10<sup>5</sup></code></li>
</ul>

<p>&nbsp;</p>
<p><strong>Follow up:</strong> Can you sort the linked list in <code>O(n logn)</code> time and <code>O(1)</code> memory (i.e. constant space)?</p>

/**
 * 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 *tail, *nextSubList;

    ListNode* sortList(ListNode* head) {
        if (head == nullptr || head->next == nullptr) return head;
        int n = getSize(head);
        ListNode *sentinel = new ListNode(0, head);
        for (int size = 1; size < n; size *= 2) {
            ListNode *start  = sentinel->next;
            tail = sentinel;
            while (start != nullptr) {
                if (start->next == nullptr) {
                    tail->next = start;
                    break;
                }
                ListNode *mid = getMid(start, size);
                merge(start, mid);
                start = nextSubList;
            }
        }
        return sentinel->next;
    }

    int getSize(ListNode* head) {
        int n = 0;
        while (head != nullptr) {
            n++;
            head = head->next;
        }
        return n;
    }

    ListNode* getMid(ListNode* start, int size) {
        ListNode *midPrev = start;
        ListNode *end = start->next;
        for (int i = 1; i < size && midPrev->next != nullptr; i++) {
            midPrev = midPrev->next;
            if (end->next != nullptr) {
                end = (end->next->next != nullptr) ? end->next->next : end->next;
            }
        }
        ListNode *mid = midPrev->next;
        nextSubList = end->next;
        midPrev->next = nullptr;
        end->next = nullptr;
        return mid;
    }

    void merge(ListNode* l1, ListNode* l2) {
        ListNode *sentinel = new ListNode(), *curr = sentinel;
        while (l1 != nullptr && l2 != nullptr) {
            if (l1->val < l2->val) {
                curr->next = l1;
                l1 = l1->next;
            } else {
                curr->next = l2;
                l2 = l2->next;
            }
            curr = curr->next;
        }
        curr->next = (l1 != nullptr) ? l1 : l2;

        while (curr->next != nullptr) curr = curr->next;

        tail->next = sentinel->next;
        tail = curr;
    }
};
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