Linked List Cycle II

Given a linked list, return the node where the cycle begins. If there is no cycle, return null.

Follow up:
Can you solve it without using extra space?

/**
 * Definition for singly-linked list.
 * struct ListNode {
 *     int val;
 *     ListNode *next;
 *     ListNode(int x) : val(x), next(NULL) {}
 * };
 */
class Solution {
public:
    ListNode *detectCycle(ListNode *head) 
    {
        if(head==NULL || head->next==NULL) return NULL;
        //check if cycle exist
        ListNode* p1=head;
        ListNode* p2=head;
        while(true)
        {
            p1=p1->next;
            p2=p2->next;
            if(p2==NULL || p2->next==NULL) return NULL;
            p2=p2->next;
            if(p1==p2) break;
        }
        p2=head;
        while(p1!=p2)
        {
            p1=p1->next;
            p2=p2->next;
        }
        return p1;
    }
};