LintCode - Copy List with Random Pointer

http://www.lintcode.com/en/problem/copy-list-with-random-pointer/

Description

A linked list is given such that each node contains an additional random pointer which could point to any node in the list or null.
Return a deep copy of the list.
- Challenge
Could you solve it with O(1) space?

Code - C++

/**
 * Definition for singly-linked list with a random pointer.
 * struct RandomListNode {
 *     int label;
 *     RandomListNode *next, *random;
 *     RandomListNode(int x) : label(x), next(NULL), random(NULL) {}
 * };
 */
class Solution {
public:
    /**
     * @param head: The head of linked list with a random pointer.
     * @return: A new head of a deep copy of the list.
     */
    void copyNext(RandomListNode* head) {
        while (head != NULL) {
            RandomListNode* newNode = new RandomListNode(head->label);
            newNode->random = head->random;
            newNode->next = head->next;
            head->next = newNode;
            head = head->next->next;
        }
    }
    void copyRandom(RandomListNode* head) {
        while (head != NULL) {
            if (head->next->random != NULL) {
                head->next->random = head->random->next;
            }
            head = head->next->next;
        }
    }
    RandomListNode* splitList(RandomListNode* head) {
        RandomListNode* newHead = head->next;
        while (head != NULL) {
            RandomListNode* temp = head->next;
            head->next = temp->next;
            head = head->next;
            if (temp->next != NULL) {
                temp->next = head->next;
            }
        }
        return newHead;
    }
    RandomListNode *copyRandomList(RandomListNode *head) {
        // write your code here
        if (head == NULL) {
            return NULL;
        }
        copyNext(head);
        copyRandom(head);
        return splitList(head);
    }
};

Tips:

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