Insert into a Cyclic Sorted List.py

'''
Given a node from a cyclic linked list which is sorted in ascending order, write a function to insert a value into the list such that it remains a cyclic sorted list. The given node can be a reference to any single node in the list, and may not be necessarily the smallest value in the cyclic list.

If there are multiple suitable places for insertion, you may choose any place to insert the new value. After the insertion, the cyclic list should remain sorted.

If the list is empty (i.e., given node is null), you should create a new single cyclic list and return the reference to that single node. Otherwise, you should return the original given node.

The following example may help you understand the problem better:

 



In the figure above, there is a cyclic sorted list of three elements. You are given a reference to the node with value 3, and we need to insert 2 into the list.

 

 

 



The new node should insert between node 1 and node 3. After the insertion, the list should look like this, and we should still return node 3.
'''

"""
# Definition for a Node.
class Node(object):
    def __init__(self, val, next):
        self.val = val
        self.next = next
"""
class Solution(object):
    def insert(self, head, insertVal):
        """
        :type head: Node
        :type insertVal: int
        :rtype: Node
        """
        if not head:
            node = Node(insertVal, None)
            node.next = node
            return node
        
        small = head
        large = head
        tmp = head.next
        
        while tmp != head:
            if tmp.val < small.val:
                small = tmp
            if tmp.val > large.val:
                large = tmp
            tmp = tmp.next
        
        if small.val == large.val or insertVal <= small.val or insertVal >= large.val:
            node = Node(insertVal, large.next)
            large.next = node
            return head
        
        tmp = small
        while not (tmp.val <= insertVal <= tmp.next.val):
            tmp = tmp.next
        
        node = Node(insertVal, tmp.next)
        tmp.next = node
        return head