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Language/Type: C++ linked lists pointers
Author: Marty Stepp (on 2016/06/16)

Write a member function named partitionSort that could be added to the LinkedIntList class. Your function should assume that the linked list's elements are already sorted by absolute value, and rearrange the list into sorted order. Suppose a LinkedList variable named list stores the values below. Notice that the values are in order of absolute value; that is, they would be in sorted order if you ignored the sign of each value. The call of list.partitionSort(); should reorder the values into sorted, non-decreasing order (including sign).

{0, 0, -3, 3, -5, 7, -9, -10, 10, -11, -11, 11, -11, 12, -15}    list before call

                                                                 list after call of
{-15, -11, -11, -11, -10, -9, -5, -3, 0, 0, 3, 7, 10, 11, 12}    list.partitionSort();

Because the list is sorted by absolute value, you can solve this problem very efficiently. Your solution is required to run in O(N) time where N is the length of the list. If the list is empty or contains only one element, it should be unchanged by a call to your function. The behavior of your function is undefined if the initial list is not already sorted by absolute value; you do not need to handle that case.

Constraints: Do not modify the data field of existing nodes. Do not create any new nodes by calling new ListNode(...). You may create as many ListNode* pointers as you like, though. Do not call any member functions of the LinkedIntList. For example, do not call add, remove, or size. You may, of course, refer to the private member variables inside the LinkedIntList. Note that the list does not have a size or m_size field. Do not use any auxiliary data structures such as arrays, vectors, queues, maps, sets, strings, etc. Do not leak memory. Your code must run in no worse than O(N) time, where N is the length of the list. Your code must solve the problem by making only a single traversal over the list, not multiple passes.

Write the member function as it would appear in LinkedIntList.cpp. You do not need to declare the function header that would appear in LinkedIntList.h. Assume that you are adding this method to the LinkedIntList class as defined below:

class LinkedIntList {
    ListNode* front;   // nullptr for an empty list
    your code goes here;
Type your C++ solution code here:

This is a member function problem. Submit a member function that will become part of an existing C++ class. You do not need to write the complete class, just the member function described in the problem.

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