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Iterative Algorithm to Insert at Tail of a Linked List...

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• Suppose you have a linked list at "head":

     head
      +--------+     +--------+    -->+--------+    -->+--------+
      |        |---->| info1  |   /   | info2  |   /   | info3  |
      +--------+     |        |  /    |        |  /    |        |
                     +--------+ /     +--------+ /     +--------+
                     | ref1   |-      | ref2   |-      | null   |
                     +--------+       +--------+       +--------+
   

  And you have a linked list element at "elem":

     elem
      +--------+     +--------+
      |        |---->| infoX  | (information has been filled in)
      +--------+     |        |
                     +--------+
                     | ????   | (don't care, because we know there
                     +--------+  is no "next" element)
   

• Here is an example of how the linked list is stored in memory:

   Memory:
          +---------------+
    head: |  8000         |-------------------------------+
          +---------------+                               |
          |               |                               |
  	  .......                                       |
  	  .......                                       |
          +---------------+                               |
    8000  |  info1        |  Linked list element 1  <-----+
          +---------------+
          | ref1=10000    |-------------------------------------+
          +---------------+                                     |
          |               |                                     |
          +---------------+                                     |
  	  .......                                             |
  	  .......                                             |
          +---------------+                                     |
    9000  |  info3        |  Linked list element 3 <----+       |
          +---------------+                             |       |
          | ref3=0 (null) |                             |       |
          +---------------+                             |       |
  	  .......                                     |       |
  	  .......                                     |       |
          +---------------+                             |       |
   10000  |  info2        |  Linked list element 2      | <-----+
          +---------------+                             |
          | ref2=9000     |-----------------------------+
          +---------------+
  	  .......
  	  .......
          +---------------+
    elem: |  20000        |-----------------------------+
          +---------------+                             |
  	  .......                                     |
  	  .......                                     |
          +---------------+                             |
   20000  |  infoX        | New linked list element <---+
          +---------------+
          | refX=????     |
          +---------------+
   

  • Notice that the "links" are memory addresses and the linked list can be found by tracing/following the addresses in the "linkage" field

• Inserting the element pointed by "elem" at the tail of the linked is realised by making the last element in the linked list point to the element pointed by "elem".

  This process is illustrated by the following diagram:

  Before insertion:

     head
      +--------+     +--------+    -->+--------+    -->+--------+
      |        |---->| info1  |   /   | info2  |   /   | info3  |
      +--------+     |        |  /    |        |  /    |        |
                     +--------+ /     +--------+ /     +--------+
                     | ref1   |-      | ref2   |-      | null   |
                     +--------+       +--------+       +--------+
     elem
      +--------+     +--------+
      |        |---->| infoX  | 
      +--------+     |        |
                     +--------+
                     | ????   | 
                     +--------+ 
   

  After insertion:

     head
      +--------+     +--------+    -->+--------+    -->+--------+
      |        |---->| info1  |   /   | info2  |   /   | info3  |
      +--------+     |        |  /    |        |  /    |        |
                     +--------+ /     +--------+ /     +--------+
                     | ref1   |-      | ref2   |-      | ref3   |--+
                     +--------+       +--------+       +--------+  |
     elem                                                          |
      +--------+     +--------+                                    |
      |        |---->| infoX  |<-----------------------------------+
      +--------+     |        |
                     +--------+
                     | null   | 
                     +--------+ 
   

• Here is an example of actually happens within the computer memory when you "link" a new element to the list:

   Memory:
          +---------------+
    head: |  8000         |-------------------------------+
          +---------------+                               |
          |               |                               |
  	  .......                                       |
  	  .......                                       |
          +---------------+                               |
    8000  |  info1        |  Linked list element 1  <-----+
          +---------------+
          | ref1=10000    |-------------------------------------+
          +---------------+                                     |
          |               |                                     |
          +---------------+                                     |
  	  .......                                             |
  	  .......                                             |
          +---------------+                                     |
    9000  |  info3        |  Linked list element 3 <----+       |
          +---------------+                             |       |
          | ref3=20000    |-----------------------------|---+   |
          +---------------+                             |   |   |
  	  .......                                     |   |   |
  	  .......                                     |   |   |
          +---------------+                             |   |   |
   10000  |  info2        |  Linked list element 2      | <-----+
          +---------------+                             |   |
          | ref2=9000     |-----------------------------+   |
          +---------------+                                 |
  	  .......                                         |
  	  .......                                         |
          +---------------+                                 |
    elem: |  20000        |-----------------------------+   |
          +---------------+                             |   |
  	  .......                                     |   |
  	  .......                                     |   |
          +---------------+                             |   |
   20000  |  infoX        | New linked list element <---+---+
          +---------------+
          | refX=null     |
          +---------------+
   

  • Notice the change of the address value in the last element of the linked list.

    This address (20000) is also the address of the list element pointed to by "elem"

  • The other change is the linkage value of the new last element. It must contain ZERO (null) to indicate the end of the list.

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• Iterative algorithm to insert list element at tail
  • Linking a new list element to the end of a list can be achieve by an iterative algorithm as follows:

    We must make a distinction between inserting into an empty list and a non-empty list....

    • If the list at head is empty:

         elem.next = null;
         head = elem; (new head)
       

    • If the list at head is not empty:

         ptr = "Find the last element in the list at head";
         ptr.next = elem;
         elem.next = null; (head remains unchanged)
       

  • The following is a Java program containing an Insert function that inserts the "newelem" list element at the tail of a linked list that begins at "head":

    static ListElement Insert(ListElement head, ListElement newelem) { ListElement ptr; // local variable to run down the list if (head == null) { // Empty list, make "newelem" the first element newelem.next = null; // Mark last element return(newelem); } else { // find the last element ptr = head; while (ptr.next != null) ptr = ptr.next; ptr.next = newelem; // Link new to the last element newelem.next = null; // Mark last element return(head); } }

    This function will return the head of the new list (with the "newelem" inserted.

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  • Since we are discussing recursion, I will not spend time discussing the iterative algorithm

    But I will show you the code -- you can study it on your own.

    The following program fragment shows how to use this function:

    ptr = new ListElement(); // Create a new list element .... (initialize the list element) head = Insert(head, ptr); // Insert new element into list

  • Program in Java with iterative algorithm to link at tail of list: click here

  • Program in M68000 assembler with iterative algorithm to link at tail of list: click here

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• A note on allocating memory space for a new list element
  • In Java:

    ListELement ptr; ptr = new ListElement(); // Create a new list element

    Recall that the new operator will:

    Reserve (= allocate) some (enough) memory space to store a ListElement typed object And return the location (= address) of the reserved memory space

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  • To similate the effect of the new operator, I have written the malloc() function that does the following:

    The function malloc takes one input parameter in D0 D0 = the number of bytes of memory you want to reserve The malloc (memory allocate) function will reserve the amount of bytes of memory given in D0. The function malloc then returns the location (address) of the start of reserved memory in register A0.

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  • Example:

    Java: ListELement ptr; ptr = new ListElement(); ptr.value = 1234; M68000 equivalent: // ptr = new ListElement(); move.l #8, d0 reserve 8 byte for a List object jsr malloc move.l a0, ptr put address in ptr // ptr.value = 1234; movea.l ptr, a0 move.l #1234, (a0)