1. Extensible Array C and Data Structures Baojian Hua bjhua@ustc.edu.cn

2. Linear Data Structures A linear list (list) consists of: a collection of data elements e1, e2, …, en elements are ordered: e1 ≤ e2 ≤ … ≤ en ei is called an predecessor of e_{i+1} e_{i+1} is called a successor of ei every element has at most one successor and one predecessor

3. Linear Data Structures Typical operations on linear list : // create an empty list newList (); // the length of a list l length (list l); // insert element x at position i in l, 0<=i<n insert (list l, x, i); // return the i-th element nth (list l, i); // delete the element at position i in l, 0<=i<n delete (list l, i); // apply function f to each element in l foreach (list l, f);

4. Polymorphic Abstract Data Types in C // in “list.h” #ifndef LIST_H #define LIST_H typedef struct listStruct *list; list newList (); int length (list l); poly nth (list l, int n); // “poly”? void insert (list l, poly x, int i); poly delete (list l, int i); void foreach (list l, void (*f)(poly)); #endif

5. Implementations Two typical implementation techniques: array-based linked structure-based We next consider the first, and leave the second to the next slide

6. Implementation Using Array The straightforward method to implement this interface (ADT) is to use an array and the array may not be full, so we must keep a “ tail ” tag to record its tail (the position of its last elements) 0 n-1

7. Implementation Using Array The straightforward method to implement this interface is to use an array and the array may not be full, so we must keep a “ tail ” tag to record its tail (the position of its last elements) 0 n-1 tail

8. Array-based Implementation // Combine these above observations, we have: // in file “arrayList.c” #include #include “list.h” #define INIT_LENGTH 32 #define EXT_FACTOR 2 struct listStruct { poly *array; int max; int tail; }; 0 n-1 array max tail l

9. Operation: “ newList ” list newList () { list l = (list)malloc (sizeof (*l)); l->array = malloc (INIT_LENTH * sizeof(poly)); l->max = INIT_LENTH; l->tail = 0; return l; }

10. Operation: “ newList ” list newList () { list l = (list)malloc (sizeof (*l)); l->array = malloc (INIT_LENTH * sizeof(poly)); l->max = INIT_LENTH; l->tail = 0; return l; } $#%& %$&^ @#%$ l

11. Operation: “ newList ” list newList () { list l = (list)malloc (sizeof (*l)); l->array = malloc (INIT_LENTH * sizeof(poly)); l->max = INIT_LENTH; l->tail = 0; return l; } 0 n-1 array %$&^ @#%$ l

12. Operation: “ newList ” list newList () { list l = (list)malloc (sizeof (*l)); l->array = malloc (INIT_LENTH * sizeof(poly)); l->max = INIT_LENTH ; l->tail = 0; return l; } 0 n-1 array max @#%$ l

13. Operation: “ newList ” list newList () { list l = (list)malloc (sizeof (*l)); l->array = malloc (INIT_LENTH * sizeof(poly)); l->max = INIT_LENTH ; l->tail = 0; return l; } 0 n-1 array max tail l

14. Operation: “ length ” int length (list l) { // note that we omit such checks in the next // for clarity. However, You should always do // such kind of checks in your code. assert(l); return l->tail; } 0 n-1 array max tail l

15. Operation: “ nth ” poly nth (list l, int i) { if (i =l->tail) error (“invalid index”); poly temp; temp = *((l->array)+i); return temp; } 0 n-1 array max tail l

16. Operation: “ nth ” poly nth (list l, int i) { if (i =l->tail) error (“invalid index”); poly temp; temp = *((l->array)+i); return temp; } 0 n-1 array max tail l i temp

17. Operation: “ insert ” void insert (list l, poly x, int i) { if (i l->tail) error (“invalid index”); //move the data …; } 0 n-1 array max tail l i

18. Operation: “ insert ” void insert (list l, poly x, int i) { if (i l->tail) error (“invalid index”); for (int j=l->tail; j>i; j--) (l->array)[j] = (l->array)[j-1]; …; } 0 n-1 array max tail l i j

19. Operation: “ insert ” void insert (list l, poly x, int i) { if (i l->tail) error (“invalid index”); for (int j=l->tail; j>i; j--) (l->array)[j] = (l->array)[j-1]; …; } 0 n-1 array max tail l i j

20. Operation: “ insert ” void insert (list l, poly x, int i) { if (i l->tail) error (“invalid index”); for (int j=l->tail; j>i; j--) (l->array)[j] = (l->array)[j-1]; …; } 0 n-1 array max tail l i j

21. Operation: “ insert ” void insert (list l, void *x, int i) { if (i l->tail) error (“invalid index”); for (int j=l->tail; j>i; j--) (l->array)[j] = (l->array)[j-1]; (l->array)[i] = x; } x 0 n-1 array max tail l i j

22. Operation: “ insert ” void insert (list l, void *x, int i) { if (i l->tail) error (“invalid index”); for (int j=l->tail; j>i; j--) (l->array)[j] = (l->array)[j-1]; (l->array)[i] = x; (l->tail)++; } x 0 n-1 array max tail l i j

23. Perfect? What if the initial input arguments look like this one? direct data movement will incur an out-of-bound error! 0 n-1 array max tail l i

24. Extensible Array void insert (list l, poly x, int i) { if (i l->tail) error (“invalid index”); // if l is full, extend l->array by a factor… if (l->tail==l->max) { l->array = realloc (l->array, EXT_FACTOR*(l->max)*sizeof(poly)); l->max *= EXT_FACTOR; } // data movement as discussed above…; }

25. Extensible Array 0 n-1 array max tail l i 02n-1 i l->array = realloc (l->array, EXT_FACTOR*(l->max)*sizeof(poly)); n-1

26. Extensible Array 0 n-1 array max tail l i 02n-1 i n-1 l->array = realloc (l->array, EXT_FACTOR*(l->max)*sizeof(poly));

27. Extensible Array 0 n-1 array max tail l i 02n-1 i l->max *= EXT_FACTOR; l->array = realloc (l->array, EXT_FACTOR*(l->max)*sizeof(poly));

28. Extensible Array array max tail l 02n-1 i n-1

29. Operation: “ delete ” The “ delete ” operation is reverse operation of the “ insert ” operation also involves data movement should we shrink the extensible array, when there are few elements in it (say ½ data item left)? See the programming assignment

30. Operation: “ foreach ” void foreach (list l, void (*f)(poly)) { for (int i=0; i tail; i++) f (*(l->array + i)); return; } 0 n-1 array max tail l

31. Summary Linear list ADT: a collection of ordered data element each item has no more than one successor or predecessor Extensible array-based implementation maintain internally a dynamically extensible array bad performance with insert or delete space waste