<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* sortList(ListNode* head, ListNode* follow=nullptr, double pivot=0.0) {
        if(!head){return follow;}
        ListNode* smaller=new ListNode(-1);
        ListNode* csmaller=smaller;
        ListNode* larger=new ListNode(-1);
        ListNode* clarger=larger;
        ListNode* cur = head;
        int smaller_count = 0;
        double smaller_total = 0;
        int larger_count = 0;
        double larger_total = 0;
        bool sorted=true;
        int prev=cur->val;
        while(cur){
            if(sorted && cur->val<prev){ sorted=false; prev=cur->val;}
            if(cur->val <= pivot){
                smaller_count++;
                smaller_total += cur->val;
                auto s = cur;
                cur=cur->next;
                s->next = nullptr;
                csmaller->next = s;
                csmaller = s;
            }
            else{
                larger_count++;
                larger_total += cur->val;
                auto s = cur;
                cur=cur->next;
                s->next = nullptr;
                clarger->next = s;
                clarger= s;
            }
        }
        {// delete dummy
            //auto t = smaller;
            smaller = smaller->next;
            //delete t;
            //t = larger;
            larger= larger->next;
            //delete t;
        }
        ListNode* rl = nullptr;
        if(larger_count==0){
            if(sorted){
                csmaller->next = follow;
                return smaller;
            }
            rl = follow;
        }
        else{
            rl = sortList(larger,follow,larger_total/larger_count);
        }
        auto ll = smaller_count!=0 ? sortList(smaller,rl,smaller_count!=0 ? smaller_total/smaller_count : 0) : rl;
        return ll;
    }
};
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