Cycle Startby Isai Damier, Android Engineer @ Google

```/***************************************************************************
* Author: Isai Damier
* Project: geekviewpoint
* Package: datastructure
*
* Description: A LinkedList is a data structure that allows access
*   to a collection of data using pointers/references. While an
*   array can also be defined as above, LinkedLists and arrays differ
*   in how they are stored in memory and in the operations they
*   allow. Unlike an array that must be stored in a block of memory,
*   the nodes of a LinkedList can be stored anywhere because each
*   node has a reference to the node that succeeds it. Because the
*   nodes are stored so loosely, inserting nodes into a LinkedList
*   is easy; whereas in an array, all the succeeding elements must
*   be shifted. Of course, insertion also means changing the size of
*   the array, which means creating the entire array anew.
*
*   Perhaps the greatest beauty of LinkedList is that it allows
*   accessing an entire sequence of nodes using only one variable:
*   a reference to the first node in the sequence.
*
*   Countless operations can be performed on LinkedLists. Following
*   are a few, ranging from the common to the very interesting.
**************************************************************************/

Node tail = null;

/*****************************************************************
* Time Complexity of Solution:
*   O(n).
*
* Description: If this LinkedList contains a loop/cycle, indicate
*   the node where the cycle/loop begins. Understand that this
*   LinkedList is not necessary circular: maybe it is; may be it
*   is not. The LinkedList may be P-shaped. This algorithm will
*   work either way.
*
* Technical Details: This algorithm was invented by R. W. Floyd.
*   The basis for the algorithm is that if a path eventually
*   loops, then two travelers walking at different speed will
*   keep meeting each other.
*
*   Particularly. Let x and y be travelers such that y is walking
*   twice as fast as x (i.e. y = 2x). Further, let s be the place
*   where x and y first started walking at the same time. Then
*   when x and y meet again, the distance from s to the start of
*   the loop is the exact same distance from the present meeting
*   place of x and y to the start of the loop.
*
*   BTY: reversing a P-shaped LinkedList still results in a
*     only the direction of the circular portion is reversed.
*****************************************************************/
public Node cycleStart() {
return null;
}
//slow and fast both started at head; after one step,
Node fast = slow.next;
//each keep walking until they meet again.
while (slow != fast) {
slow = slow.next;
try {
fast = fast.next.next;
} catch (NullPointerException n) {
return null;//no cycle if null exception
}
}//while
//from head to beginning of loop is same as from fast to
//beginning of loop
while (slow != fast) {
slow = slow.next;
fast = fast.next;
}
return slow;//beginning of loop
}
}```
```public class SinglyLinkedListTest {

/**
* Test of cycleStart method, of class SinglyLinkedList.
*/
@Test
public void testCycleStart() {
System.out.println("cycleStart");
int[] input = {9, 4, 5, 2, 1, 12, 6, 7, 4, 8, 3, 0, 16, 19, 11};