/***************************************************************************
* Author: Isai Damier
* Title: Singly Linked List
* 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.
**************************************************************************/
public class SinglyLinkedList {
Node head = null;
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
* P-shaped LinkedList with the same head and linear section;
* only the direction of the circular portion is reversed.
*****************************************************************/
public Node cycleStart() {
if (null == head || null == head.next) {
return null;
}
//slow and fast both started at head; after one step,
//slow is at head.right and fast is at head.right.right
Node slow = head.next;
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
slow = head;
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};
SinglyLinkedList linkedList = new SinglyLinkedList();
for (int i = 0; i < input.length; i++) {
linkedList.addToTail(input[i]);
}
Node cy = linkedList.find(18);
linkedList.tail.right = cy;
assertEquals(cy, linkedList.cycleStart());
}
}
