1 CSE1301 Computer Programming: Lecture 30 Linked Lists (Part 2)

2 Topics Sorted linked list The “free” list Adding to a linked list Deleting from a linked list

3 struct ListElementRec { int item; int next; }; typedef struct ListElementRec ListElement; ListElement list[maxListLength]; int first; Recall: Linked List END first 1

4 Delete an Item: Typical Case first END Example: Delete item 8

first END Delete an Item: Typical Case (cont) Example: Delete item 8

first END Delete an Item: Typical Case (cont) Example: Delete item 8

first END Delete an Item: Typical Case (cont) Example: Delete item 8

8 Delete the Last Item first END Example: Delete item 9

first END 9 Delete the Last Item (cont) Delete last item: Delete item 9 Example: Delete item 9

first END Delete the Last Item (cont) Example: Delete item 9

first END Delete the First Item Example: Delete item 2

first END Delete the First Item (cont) Example: Delete item 2

first 5 34 END Delete the First Item (cont) Example: Delete item 2

14 Filling In the Gaps Problem: How do we find a free slot if we want to insert a new item into the list?

15 Filling In the Gaps: Solution 1 Mark free slots with special value, and perform linear search first 1 53 END FREE const int END = -1; const int FREE = -2;

16 Filling In the Gaps: Solution 1 (cont) Mark free slots with special value, and perform linear search first 1 53 END FREE Example: Insert 5 into the linked list

17 Filling In the Gaps: Solution 1 (cont) Mark free slots with special value, and perform linear search Example: Insert 5 into the linked list first 1 53 END FREE 5

18 Filling In the Gaps: Solution 1 (cont) Mark free slots with special value, and perform linear search Example: Insert 5 into the linked list first FREE 5

19 Filling In the Gaps: Solution 1 (cont) Mark free slots with special value, and perform linear search Example: Insert 5 into the linked list first FREE END 5

20 Filling In the Gaps: Solution 1 (cont) Mark free slots with special value, and perform linear search Example: Insert 5 into the linked list first FREE END 5 Problem: Linear search for free slots

21 Filling In the Gaps: Solution 2 Close the gaps after a deletion, and always append at the end Example: Delete 4 from the linked list END 5 first 0 count 5

22 Filling In the Gaps: Solution 2 (cont) Close the gaps after a deletion, and always append at the end END 5 first 0 Example: Delete 4 from the linked list 5 count

23 Filling In the Gaps: Solution 2 (cont) Close the gaps after a deletion, and always append at the end END 5 first 0 Example: Delete 4 from the linked list 5 count

24 Filling In the Gaps: Solution 2 (cont) Close the gaps after a deletion, and always append at the end END 5 first 0 Example: Delete 4 from the linked list 5 count

25 Filling In the Gaps: Solution 2 (cont) Close the gaps after a deletion, and always append at the end first END 5 5 Example: Delete 4 from the linked list count

26 Filling In the Gaps: Solution 2 (cont) Close the gaps after a deletion, and always append at the end first END 5 5 Example: Delete 4 from the linked list count

27 Filling In the Gaps: Solution 2 (cont) Close the gaps after a deletion, and always append at the end first END 5 Example: Delete 4 from the linked list 4 count

28 Filling In the Gaps: Solution 2 (cont) Close the gaps after a deletion, and always append at the end first END 5 4 Example: Delete 4 from the linked list count Problem: Moving items and adjusting links

29 Filling In the Gaps: Solution 3 Link the free slots together to form a “free linked list” first 1 53 END 04 free 2

30 Filling In the Gaps: Solution 3 Link the free slots together to form a “free linked list” first 1 53 END 04 free 2 To linked list of items

31 Filling In the Gaps: Solution 3 (cont) Link the free slots together to form a “free linked list” first 1 53 END 04 free 2 To linked list of free elements

32 Initialization Begin with empty item list and a full free list first END free 0

33 Adding an Item -- Example 1 Add item with value = 5 (first item) Step 1: Ensure free != END first END free 0

34 Adding an Item -- Example 1 (cont) first END free 0 5 Step 2: Put value = 5 in the first free slot list[free].item = value;

35 Adding an Item -- Example 1 (cont) first 0 254END31 free 0 5 Step 3: Remember position of new item first=free;

36 Adding an Item -- Example 1 (cont) first 0 254END31 free 1 5 Step 4: Update the free linked list to next free slot free = list[free].next;

37 Adding an Item -- Example 1 (cont) first 0 254END3 free 1 5 Step 5: Put END marker in new element list[first].next = END;

38 Adding an Item -- Example first 0 254END3 free 1 5 Add item with value = 9 Step 1: Ensure free != END

39 Adding an Item -- Example 2 (cont) first 0 254END3 free 1 5 Step 2: Put value = 9 in the first free slot list[free].item = value; 9

40 Adding an Item -- Example 2 (cont) first 0 254END3 free 1 5 Step 3: Remember the position of the new item curr = free; 9 1 curr

41 Adding an Item -- Example 2 (cont) first 0 254END3 free 2 5 Step 4: Update the free linked list to next free slot free = list[free].next; 9 1 curr

42 Adding an Item -- Example 2 (cont) first 0 254END3 free 2 5 Step 5: Find the position of the preceding item prev = findPrevious(first,value,list); 9 1 curr prev 0

43 Adding an Item -- Example 2 (cont) first 0 END 54 3 free 2 5 Step 6: Link current item to the next item in the list list[curr].next = list[prev].next; 9 1 curr prev 0

44 Adding an Item -- Example 2 (cont) first 0 END54 31 free 2 5 Step 7: Insert current item after the previous item list[prev].next = curr; 9 1 curr prev 0

45 Adding an Item -- Code const int END = -1; int addItem (int first, int free, int value, ListElement *list) { int curr, prev; if (free != END) { list[free].item = value; curr = free; free = list[free].next; prev = findPrevious(first, value, list); /* assumption: the list is never empty */ list[curr].next = list[prev].next; list[prev].next = curr; return free; } else { printf(“Not enough space\n”); exit(1); }

46 Exercise 1 Given the list below, follow the algorithm for adding the following items in order: –Add 6: In the “middle” of list –Add 3: Becomes new first item in list Add an item to an empty list first 0 54END free 2 END

47 Deleting an Item -- Example Delete item with value = first 1 53 END 04 free 2

48 Deleting an Item -- Example (cont) Step 1: Find position of the item to be deleted curr = findIndex(first,value,list); first 1 53 END 04 free 2 curr 5

49 Deleting an Item -- Example (cont) Step 2: Ensure the item is in the list curr != END first 1 53 END 04 free 2 curr 5

50 Deleting an Item -- Example (cont) Step 3: Find the position of the previous item prev = findPrevious(first,value,list); first 1 53 END 04 free 2 curr 5 prev 1

51 Deleting an Item -- Example (cont) Step 4: Bypass the current item in the list list[prev].next = list[curr].next; first END 04 free 2 curr 5 prev 1

52 Deleting an Item -- Example (cont) Step 5: Link current position to first free slot list[curr].next = free; first END 04 free 2 curr 5 prev 1

53 Deleting an Item -- Example (cont) Step 6: Make current position the first free slot free = curr; first END 04 free 5 curr 5 prev 1

54 Deleting an Item -- Code const int END = -1; int deleteItem (int first, int free, int value, ListElement *list) { int curr, prev; curr = findIndex(first, value, list); /* assumption: the list is never empty */ if (curr == END) { printf("%d is NOT in the list\n", value); return free; } prev = findPrevious(first, value, list); /* assumption: the last item is never deleted */ list[prev].next = list[curr].next; list[curr].next = free; free = curr; return free; }

55 Exercise 2 Consider the following cases when deleting: –the first item in the linked list –the last item in the linked list –an item that is not in the linked list Modify the deleteItem function to allow – for the deletion of the first item – for the list to become empty Write the algorithm and the C code for –findIndex() : finding the index of the item with a given value –findPrev() : finding the index of the item previous to a given value

56 Main points Linked list –has an item list and a free list –makes it easier to add and delete elements –searching for an element is slow (linear)

57 Reading Knuth, Fundamental Algorithms, Section –pages (1st edition) –pages (3rd edition) Horowitz and Sahni, Fundamentals of Data Structures, Chapter 4, pages