Linked Lists
2015, Fall
Pusan National University
Ki-Joune Li
PNU
STEM
Problems of Array

Lack of Dynamic Properties


Insertion
Deletion



Moving elements: expensive operation
Max. Size of Array
Linked List


More dynamic data structure than Array
No subscript (or index)

Only Linear Search is possible
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PNU
STEM
Linked List : Example
전도연 9
전지현 7
김희선 6
강혜정 5
Insert
(선호도 순으로)
이영애 8
3
PNU
STEM
Linked List : Data Structures
Node
전도연 9
Data
Link to the next node
Class LinkedList {
private:
Node *first;
public:
insert(DataType data,Node *q);
insert(Node *p);
delete(Node *p);
Node *search(condition);
};
Class Node {
friend class LinkedList;
private:
DataType
data;
Node
*next;
};
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Linked List : Operations
Insert after p
Delete node
LinkedList::insert(DataType data,Node *p) {
Node *newNode=new Node(data);
if(first==NULL) {
first=newNode; newNode->next=NULL
}
else {
newNode->next=p->next; p->next=newNode;
}
};
LinkedList::delete(Node *p,*q) {
// delete node p after q
if(q==NULL) first=first->next;
else q->next=p->next;
delete p;
};
q
p: node to delete
Search with conditions
Node *LinkedList::search(Condition condition) {
for(Node *ptr=first;ptr!=NULL; ptr=ptr->next) {
if(checkCondition(condition)==TRUE) return ptr;
}
return NULL;
};
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Stacks by Linked List
Class Stack {
private:
LinkedList
*list;
public:
push(DataType data);
DataType pop();
};
Pop: Remove from the first
DataType LinkedList::deleteFirst() {
if(first==NULL) ListEmpty();
DataType tmpData=first->data;
Node *tmpNode=first;
first=first->next;
delete tmpNode;
return tmpData;
};
Push(Linked List): Insert at first
LinkedList::insertFirst(DataType data) {
Node *newNode=new Node(data);
newNode->next=temp;
first=newNode;
};
Top
Top
Time Complexity: O(1)
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PNU
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Stacks by Linked List
Class Stack {
private:
LinkedList
*list;
public:
push(DataType data);
DataType pop();
};
Push
Stack::push(DataType data) {
list->insertFirst(data);
};
Pop
DataType Stack::pop() {
return list->deleteFirst(data);
};
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PNU
STEM
Queues by Linked List
Class Queue {
private:
Node *list;
public:
insert(DataType data);
DataType delete();
};
first
Insert: Insert at last
LinkedList::insert(DataType data) {
Node *newNode=new Node(data);
if(first==NULL) {
first=newNode;
return;
}
Node *p=first; Node *q;
while(p!=NULL) {
q=p;
p=p->next; Time Complexity: O(n)
}
q->next=newNode;
};
Why not pointer to the last ?
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Circular List
O(n) operations to
reach to the last node
first
Insert: Insert at last
last
Delete : delete the first
DataType CircularList::delete() {
if(last==NULL) QueueEmpty();
DataType tmpData=last->data;
Node *first=last->next;
last->next=first->next;
delete first;
O(1)
retun tmpData;
};
CircularList::insert(DataType data) {
Node *newNode=new Node(data);
if(last==NULL) {
last=newNode; last->next=last;
return;
}
newNode->next=last->next;
O(1)
last->next=newNode;
};
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Circular List with Head Node
Empty List
Head
Empty node with ptr to next
Head
newNode
Insert: Insert at first (with head node)
CircularList::insert(DataType data) {
Node *newNode=new Node(data);
newNode->next=head->next;
head->next=newNode;
};
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PNU
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Application of List: Polynomials
a = 3 x 14 + 2 x 8 + 3
3
14
2
8
b = 12 x 14 + 7
12
14
7
0
Coef
3
0
N
N
Exp
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PNU
STEM
Adding Polynomials
a = 3 x 14 + 2 x 8 + 3
3
14
2
8
b = 12 x 14 + 7 x 5
12
14
7
5
c=a+b
15
14
2
8
3
0
7
5
3
0
N
N
N
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PNU
STEM
Erasing Linked List
Class LinkedList {
private:
Node *first;
public:
LinkedList();
~LinkedList();
};
first
Become garbage
void LinkedList::~LinkedList() {
Node
*ptr=first;
while(first!=NULL) {
ptr=first->next;
delete first;
}
};
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STEM
Maintaining Available Node List
Destructor
Class LinkedList {
private:
Node *first;
public:
LinkedList();
~LinkedList();
};
void LinkedList::~LinkedList() {
Node
*ptr=first;
while(first!=NULL) {
ptr=first->next;
delete first;
}
};
Insert after p
LinkedList::insert(DataType data,Node *p) {
Node *newNode=new Node(data);
if(first==NULL) {
first=newNode; newNode->next=NULL
}
else {
newNode->next=p->next; p->next=newNode;
}
};
Delete node
LinkedList::delete(Node *p,*q) {
// delete node p after q
if(q==NULL) first=first->next;
else q->next=p->next;
delete p;
};
time consuming operations
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PNU
STEM
Maintaining Available Node List
Class CircularList {
private:
Node
*first;
static Node *av=NULL;
public:
CircularList();
~CircularList();
};
first
av
Available Empty
Node List
For add operation
Node *CircularList::getNode() {
Node *newNode;
if(av==NULL) newNode=new Node();
else {
newNode=av;
av=av->next;
}
return newNode;
}
void CircularList::~CircularList() {
if(first!=NULL) {
Node *second=first->next;
first->next=av;
first=NULL;
av=second;
}
}
replace Node *newNode=new Node(data);  Node *newNode=getNode();
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PNU
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Application of List : Sparse Matrix
0
0
11
0
0
13
0
12
0
0
0
0
0
14
0
-4
0
0
0
-8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-9
0
0
0
0
0
row
col
down
right
0
6 7
7
02
11
05
13
10
12
16
14
21
-4
25
-8
2
11
if ishead=NO
if ishead=YES
down
value
right
next
51
-9
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PNU
STEM
Application of List : Sparse Matrix
Circular Linked List with header node
6
7
7
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PNU
STEM
Application of List : Sparse Matrix
Circular Lined List for the header nodes (using right field)
6
7
7
18
PNU
STEM
Application of List : Sparse Matrix
Circular Linked List for the header nodes using down field
0
2
11
19
PNU
STEM
List for Sparse Matrix : Insert
0
0
11
0
0
13
0
12
0
0
0
0
0
14
0
-4
10
0
0
-8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-9
0
0
0
0
0
6 7
7
02
11
05
13
10
12
16
14
21
-4
22
10
25
-8
22
10
O (max{r,c})
51
9
20
PNU
STEM
Doubly Linked List
Linked List : inefficient to go back
Head
Why not double links ?
0
0
14
8
0
21
PNU
STEM
Doubly Linked List : Insertion and
Deletion
0
Insertion
x
0
14
8
0
p
20
void DoublyLinkedList::Insert(DblNode *p,*x) {
p->leftLink=x; p->rightLink=x->rightLink;
x->rightLink->leftLink=p; x->rightLink=p;
}
O (1)
Deletion
0
0
14
8
0
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PNU
STEM
Representation of Polynomial
P = x10 y3 z2 + 2 x8 y3 z2 + 3 x8 y2 z2 + x4 y4 z + 6 x3 y4 z + 2 y z
Coef
Exp_x
Exp_y
Exp_z
next
Coef
Exp_x
Exp_y
next
P = x10 y3 + 2 x8 y3 + 3 x8 y2 + x4 y4 + 6 x3 y4 + 2 y
Depends on the number of variables
NOT a General Representation
How to represent it in more general way ?
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PNU
STEM
A General Way to Represent Polynomial
P = x10 y3 z2 + 2 x8 y3 z2 + 3 x8 y2 z2 + x4 y4 z + 6 x3 y4 z + 2 y z
P = ( (x10 + 2 x8 ) y3 + 3 x8 y2 ) z2 + ( ( x4 + 6 x3 ) y4 + 2 y ) z
P211(x)
P212(x)
P22 (x)
P1(z)
P22(y)
P21(y)
Nested Polynomial
Nested Linked List
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PNU
STEM
Generalized Lists

Definition


A = (a0, a1, a2, an-1) where ai is ATOMIC NODE or a LIST
When ai is a list, it is called SUBLIST.

Linear List

Example




Reusability of Generalized List : Shared List
D=() : NULL
A=(a, (b, c)) : Finite
B=(A, A, ()) = ((a, (b, c)), (a, (b, c)), ())
C=(a, C) = (a, (a, (a, …)))) : Infinite
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Implementation of Generalized List
Node / List
Data of Node
Node
Flag
Data
DLink
Next
Pointer to List
Class GenList {
private:
GenListNode *first;
public:
...
};
Class GenListNode {
friend class GenList;
private:
Boolean
flag;
Node
*next;
union {
GenListNode *dlink;
DataType
data;
};
};
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PNU
STEM
Generalized List : Example
P = ( (x10 + 2 x8 ) y3 + 3 x8 y2 ) z2 + ( ( x4 + 6 x3 ) y4 + 2 y ) z
N z
L
N y
2
L
L
3
L
2
N y
2
L
N x
N x
N x
N 3 8
N 1 10
N 2 8
4
L
1
N x
N 0 0
N 1 4
N 6 3
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PNU
STEM
Generalized List : Example
D=()
A=(a, (b, c))
B=(A, A, ())
C=(a, C)
A
N a
L
N b
B
L
L
C
N a
L
N c
L
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PNU
STEM
Operation of Generalized List: Copy
A=((a, b), ((c, d), e))
A
L
N a
void GenList:copy(const GenList& l) {
first=copy(l.first);
}
One visit per node :
Linear Scan :
O(m )
Not Circular like
C=(a, C)
L
N b
L
N e
L c
N d
GenListNode *GenList:copy(const GenListNode *p) {
GenListNode *q=NULL;
if(p!=NULL) {
q=new GenListNode;
q->flag=p->flag;
if(p->flat==NODE) q->data=p->data;
else q->dlink=copy(p->dlink);
q->next=copy(p->next);
}
return q;
}
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PNU
STEM
Operation of Generalized List: Equal
s
l=((a, b), ((c, d), e))
m=((a, b), ((c, f), e))
l
L
int operator==(const GenList& l,m) {
return equal(l.first,m.first);
}
int equal(GenListNode *s, *t) {
x=FALSE;
if(s and t are null), return TRUE;
if(s and t are not null), {
if(s and p are node) {
if(s->data==t->data) x=TRUE;
else x=FALSE;
}
else x=equal(s->dlink,t->dlink);
}
if(x==TRUE) return(s->next,t->next);
return FALSE;
}
N a
L
N b
L
N e
N c
N d
t
m
L
N a
L
N b
L
N e
N c
N f
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PNU
STEM
Shared Linked List: Reference Counter
D=()
A=(a, (b, c))
B=(A, A, ())
C=(a, C)
Deletion of A with care
Shared List
A
N a
Head node
with reference counter
L
N b
N c
A
B
L
L
C
N a
L
L
N 3
N a
L
N b
N c
Delete list when reference counter = 0
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PNU
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Example: Design Shape List
P
Total Area of P ?
Data: Closed Geometry
Circle
Rectangle
Polygon
Triangle
32