Find Intersection
by Isai Damier, Android Engineer @ Google

/***************************************************************************
 * 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: Find the node (intersection) where the two given
   *   LinkedList coalesce.
   *
   * Technical Details: The idea is that two linked lists form a Y-shaped
   *   structure. The structure may be degenerated. As shown below, the use
   *   of a hashmap greatly reduces the complexity of the problem.
   *
   *
   *   To keep things simple, we consider t2 and t2 equal iff they both
   *   point to the same memory location. A broader definition of
   *   equality: Two nodes t2 and t1 are equal if they and their respective
   *   sublists are equal.
   *****************************************************************/
  static public Node findIntersection(Node head1, Node head2) {
    Map<Node, Boolean> intersect = new HashMap<Node, Boolean>();
    for (Node t = head1; null != t; t = t.next) {
      intersect.put(t, true);
    }
    //first duplicate is intersection
    for (Node t = head2; null != t; t = t.next) {
      if (null != intersect.get(t)) {
        return t;
      }
    }
    return null;
  }
}

public class SinglyLinkedListTest {

  /**
   * Test of findIntersection method, of class SinglyLinkedList.
   */
  @Test
  public void testFindIntersection() {
    System.out.println("findIntersection");
    int[] in_1 = {29, 14, 35, 2, 1, 12, 6, 7, 4, 8, 3, 0, 16, 19, 11};
    int[] in_2 = {99, 78, 8, 3, 23};

    SinglyLinkedList list_1 = new SinglyLinkedList();
    SinglyLinkedList list_2 = new SinglyLinkedList();

    for (int i = 0; i < in_1.length; i++) {
      list_1.addToTail(in_1[i]);
    }
    assertEquals(in_1.length, list_1.size());

    for (int i = 0; i < in_2.length; i++) {
      list_2.addToTail(in_2[i]);
    }
    assertEquals(in_2.length, list_2.size());

    //set intersection: list_1 and list_2 form a Y at element 6
    int exp = 6;
    Node found = list_1.find(exp);
    assertNotNull(found);
    list_2.addAllToTail(found);
    assertEquals(14, list_2.size());
    Node n = SinglyLinkedList.findIntersection(list_1.head, list_2.head);

    assertEquals(exp, n.data);
  }
}