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Polynomials via Linked Lists




This experiment guides you using Linked lists in a practical example. This is useful if you want to understand linked lists or if you want to see a realistic, applied example of pointer-intensive code.


Linked lists are useful to study for two reasons. Most obviously, linked lists are a data structure which you may want to use in real programs. Seeing the strengths and weaknesses of linked lists will give you an appreciation of the some of the time, space, and code issues which are useful to thinking about any data structures in general.Somewhat less obviously, linked lists are great way to learn about pointers. In fact, you may never use a linked list in a real program, but you are certain to use lots of pointers. Linked list problems are a nice combination of algorithms and pointer manipulation. Traditionally, linked lists have been the domain where beginning programmers get the practice to really understand pointers.


Why Linked Lists?


 Linked lists and arrays are similar since they both store collections of data. The terminology is that arrays and linked lists store "elements" on behalf of "client" code. The specific type of element is not important since essentially the same structure works to store elements of any type. One way to think about linked lists is to look at how arrays work and think about alternate approaches.


The disadvantages of arrays are...



  1. The size of the array is fixed to some elements. Most often this size is specified at compile time with a simple declaration such as in the example above . With a little extra effort, the size of the array can be deferred until the array is created at runtime, but after that it remains fixed. (extra for experts) You can go to the trouble of dynamically allocating an array in the heap and then dynamically resizing it with realloc(), but that requires some real programmer effort.
  2. Because of (1), the most convenient thing for programmers to do is to allocate arrays which seem "large enough". Although convenient, this strategy has two disadvantages:
  3. a)most of the time there are just 20 or 30 elements in the array and 70% of the space in the array really is wasted. b) If the program ever needs to process more than fixed size, the code breaks. A surprising amount of commercial code has this sort of naive array allocation which wastes space most of the time and crashes for special occasions. (Extra for experts) For relatively large arrays (larger than 8k bytes), the virtual memory system may partially compensate for this problem, since the "wasted" elements are never touched.
  4. Inserting new elements at the front is potentially expensive because existing elements need to be shifted over to make room.



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