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

DetectLLCycle.java

//Floyd's cycle-finding algorithm 
public ListNode detectCycle(ListNode head) {
    if(head == null)
        return null;

    ListNode fast = head;
    ListNode slow = head;

    while(fast.next != null && fast.next.next != null) {
        fast = fast.next.next;
        slow = slow.next;

        if(fast == slow) {
            // Linked List has a loop
            // Let distance from head to start of loop be A
            // Let distance of the loop be B + C
            // Let slow pointer travel A + B
            // Since fast pointer is twice as fast, it travels A + B + C + B, or 2(A + B)
            // 2(A + B) = A + 2B + C => A = C
            // So, let the slow node complete the loop (C steps)
            // In the mean time, bring fast node to head and move it at the same speed as slow's
            // Both nodes will intersect at the starting point 
            fast = head;
            while(slow != fast) {
                slow = slow.next;
                fast = fast.next;
            }
            return slow;
        }
    }
    return null;
}