"""
https://leetcode.com/problems/insertion-sort-list/
Sort a linked list using insertion sort.


A graphical example of insertion sort. The partial sorted list (black) initially contains only the first element in the list.
With each iteration one element (red) is removed from the input data and inserted in-place into the sorted list
 

Algorithm of Insertion Sort:

Insertion sort iterates, consuming one input element each repetition, and growing a sorted output list.
At each iteration, insertion sort removes one element from the input data, finds the location it belongs within the sorted list, and inserts it there.
It repeats until no input elements remain.

Example 1:

Input: 4->2->1->3
Output: 1->2->3->4
Example 2:

Input: -1->5->3->4->0
Output: -1->0->3->4->5
"""

# time complexity: O(n^2), space complexity: O(1)


# Definition for singly-linked list.
# class ListNode:
#     def __init__(self, val=0, next=None):
#         self.val = val
#         self.next = next
class Solution:
    def insertionSortList(self, head: ListNode) -> ListNode:
        newhead = ListNode(0, head)
        prev = newhead
        node = head
        while node and node.next:
            if node.val <= node.next.val:
                node = node.next
            else:
                prev = newhead
                nodeToInsert = node.next
                node.next = node.next.next
                while prev.next and prev.next.val <= nodeToInsert.val:
                    prev = prev.next
                nodeToInsert.next = prev.next
                prev.next = nodeToInsert
        return newhead.next
