trees
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Symbol Red-black Table Review
Symbol table: key-value pair abstraction.
Insert a value with specified key.
Search for value given key.
Delete value with given key.
Different implementations
Array
Linked list
BST (binary search tree)
Complexity
Randomized BST.
Guarantee of ~c lg N time per operation (probabilistic).
Need subtree count in each node.
Need random numbers for each insert/delete op.
2-3-4 tree
2-3-4 tree. Generalize
node to allow multiple
keys; help to keep tree
balanced.
Perfect balance. Every
path from root to leaf has
same length.
Allow 1, 2, or 3 keys per
node.
2-node: one key, two
children.
3-node: two keys, three
children.
4-node: three keys, four
children.
Search
Compare search key against keys in node.
Find interval containing search key.
Ex. Search for L
Insert (1)
Search to bottom for key.
Ex. Insert B
Insert (2)
2-node at bottom: convert to 3-node.
3-node at bottom: convert to 4-node.
Ex. Insert B
Transformation
Local transformations should be applied to keep the
tree balanced.
Ensures that most recently seen node is not a 4-node.
Transformations to split 4-nodes:
Growth of a tree
Growth of a tree (cont.)
Complexity
Worst case: lg N [all 2-nodes]
Best case: log4 N = 1/2 lg N [all 4-nodes]
Between 10 and 20 for a million nodes.
Between 15 and 30 for a billion nodes.
Red-black tree
Represent 2-3-4 tree as a BST.
Use "internal" left-leaning edges for 3- and 4- nodes.
1-1 correspondence between 2-3-4 and left-leaning red-black
trees.
Insert implementation
Complexity
Libfdr
Libfdr is a library which contains an
implementation for generic red-black trees in C
Download and compile instructions at
http://www.cs.utk.edu/~plank/plank/classes/cs36
0/360/notes/Libfdr/
Jval datatype
A big union to represent a generic data type
typedef union {
int i;
long l;
float f;
double d;
void *v;
char *s;
char c;
unsigned char uc;
short sh;
unsigned short ush;
unsigned int ui;
int iarray[2];
float farray[2];
char carray[8];
unsigned char ucarray[8];
} Jval;
Jval usage
Use Jval to store an integer
Jval j;
j.i = 4;
Jval.h defines a whole bunch of prototypes for
``constructor functions.''
extern Jval new_jval_i(int);
extern new_jval_f(float);
extern Jval Jval new_jval_d(double);
extern Jval new_jval_v(void *);
extern Jval new_jval_s(char *);
Example:
Jval j = new_jval_i(4);
JRB datatype
JRB is defined as a pointer to a node of the tree
typedef struct jrb_node {
unsigned char red;
unsigned char internal;
unsigned char left;
unsigned char roothead;
struct jrb_node *flink;
struct jrb_node *blink;
struct jrb_node *parent;
Jval key;
Jval val;
} *JRB;
JRB API (1)
Make a new tree
Insert a new node to a tree
JRB make_jrb();
JRB jrb_insert_str(JRB tree, char *key, Jval val);
JRB jrb_insert_int(JRB tree, int ikey, Jval val);
JRB jrb_insert_dbl(JRB tree, double dkey, Jval val);
JRB jrb_insert_gen(JRB tree, Jval key, Jval val, int
(*func)(Jval,Jval));
Find a node via key
JRB jrb_find_str(JRB root, char *key);
JRB jrb_find_int(JRB root, int ikey);
JRB jrb_find_dbl(JRB root, double dkey);
JRB jrb_find_gen(JRB root, Jval, int (*func)(Jval, Jval));
JRB API (2)
Free a node (but not the key or val)
Free all the tree
void jrb_delete_node(JRB node);
void jrb_free_tree(JRB root);
Navigation in the tree
#define jrb_first(n) (n->flink)
#define jrb_last(n) (n->blink)
#define jrb_next(n) (n->flink)
#define jrb_prev(n) (n->blink)
#define jrb_empty(t) (t->flink == t)
#define jrb_nil(t) (t)
#define jrb_traverse(ptr, lst) \
for(ptr = jrb_first(lst); ptr != jrb_nil(lst); ptr = jrb_next(ptr))
Quiz 1
Try to compile and run some example
programs (using libfdr) given at
http://www.cs.utk.edu/~plank/plank/classes/cs36
0/360/notes/JRB/
Quiz 2
Use libfdr to write the phone book program
(add, delete, modify phone numbers). The
phone book should be stored in a file.
NB: In the JRB, the insert function always
creates a new node event the key exists
already in the tree.
You should check the existence of a record before
insert it in the tree
Instruction
Create a phone book
JRB book = make_jrb();
Insert a new entry
jrb_insert_str(book, strdup(name),
new_jval_l(number));
You must allocate memory to store the name for the new
nodes key. This memory should to be free when we
delete all the key.
Navigation
jrb_traverse(node, book)
/* code to do something on node */
Solution
phonebook_jrb.c