1) Separate chaining is an open hashing technique that uses linked lists to handle collisions. Each index in the hash table points to the head of a linked list of records with the same hash value. 2) Operations like search, insert and delete have average time complexity of O(1+α) where α is the load factor, as records are stored in linked lists after hashing. 3) Advantages are it never fills up and is less sensitive to hash function quality, while disadvantages include poorer cache performance than open addressing and wasted space due to unused indexes.

1. Sanjivani Rural Education Society’s
Sanjivani College of Engineering, Kopargaon-423 603
(An Autonomous Institute, Affiliated to Savitribai Phule Pune University, Pune)
NACC ‘A’ Grade Accredited, ISO 9001:2015 Certified
Department of Computer Engineering
(NBA Accredited)
Subject- Data Structures-I(CO203)
Unit III- Collision Resolution Strtergies

2. Collision Resolution Strategies
• If the element to be inserted is mapped with the same location where an
element is already inserted then collision occurs and it must be resolved.
• Open Hashing:
• Allows record to be stored in unlimited space(which can be a hard disk).
• It places no limitation in the size of tables.
• Records are partitioned into b buckets.
• Each bucket in the hash table is header of the linked list of records mapped to
that buckets. e.g. separate chaining.
DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon 2

3. • Closed Hashing:
• uses fixed space for storage and thus limits the size of hash table.
• In this technique, hash table keeps the elements in the bucket itself.no. of records
depends on the no. of slots in bucket.
• It involves open addressing techniques like Linear probing, Quadratic probing,
Rehashing etc.
DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon 3

4.  Separate Chaining(Open Hashing):
• Separate list of all elements mapped to the same value is maintained.
• The idea is to make each bucket of hash table point to a linked list of records that
have same hash function value.
• It is used when there is no limit on memory space.
• Let us consider a simple hash function as “key mod 7” and sequence of keys as
50, 700, 76, 85, 92, 73, 101.
DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon 4

5. DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon 5

6. • in practice the table size can be significantly large and the hash function can be
even more complex, also the data being hashed would be more complex and
non-primitive, but the idea remains the same.
• Advantages:
1) Simple to implement. We require a good hash function to guarantee even
distribution of the values.
2) Hash table never fills up, we can always add more elements to the chain.
3) Less sensitive to the hash function or load factors.
4) It is mostly used when it is unknown how many and how frequently keys may
be inserted or deleted.DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon 6

7. • Disadvantages:
1) Cache performance of chaining is not good as keys are stored using a linked
list. Open addressing provides better cache performance as everything is stored
in the same table.
2) Wastage of Space (Some Parts of hash table are never used)
3) The lookups/inserts/updates can become linear [O(N)] instead of constant time
[O(1)] if the hash function has too many collisions.
4) Uses extra space for links.
DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon 7

8. • Operations on Hash Table:
1.Initialize(): headers of all lists are set to NULL.
DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon 8
#define MAX 10
struct node
{
int prn;
char name[10];
char name[10];
struct node *next;
} node *ht[MAX];
void initialize()
{
int i;
for(i=0;i<MAX;i++)
{
ht[i]=NULL;
}

9. • Insert()- insert element at the end link list
DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon 9
void insert()
{
int addr,key,name;
node *ptr,*temp;
cout<<“enter student prn”;
cin>>prn;
cout<<“enter name”;
cin>> name;
temp=new node;
temp->prn=prn;
temp->name=name;
addr=key % MAX;
if(ht[addr]==NULL)
{
ht[addr]=temp;
else
{
ptr=ht[addr];
while(ptr->next!=NULL)
{
ptr=ptr->next;
}
ptr->next=temp;
}
}

10. e.g. 0,1,4,7,11,24,67,33,34,77,53 No. of
bucket=10
DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon 10
0
1
2
3
4
5
6
7
8
9
700 NULL
e.g. 50,700,76,85,92,73,101 size of table is 7
50 85 92 NULL
73 101 NULL
76 NULL

11. • Search() -> search an
element in the hash
table
DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon 11
node * search()
{
int addr,key;
cout<<“Enter the element to be search”;
cin<<key;
addr=key%MAX;
ptr=ht[addr]
while(ptr!=NULL && key!=ptr->data)
{
ptr=ptr->next;
}
if(key==ptr->data)
{
cout<<“Key Found”;
return(ptr);
}
return NULL; }

12. DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon 12
void display()
{
hash *ptr;
for(i=0;i<MAX;i++)
{
ptr=ht[i];
while(ptr!=NULL)
{
cout<<ptr->prn<<“t”<<ptr->name<<“->”;
ptr=ptr->next;
}
}
}

13. DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon 13
Delete()
{
int addr;
node *ptr,*prev,*temp;
cout<<“enter data to be
deleted”;
cin>>key;
addr=key%MAX;
prev=ptr=ht[addr];
if(ptr->data==key)
{
prev=prev->next;
ht[addr]=prev;
delete(ptr);
}
else
{
while(ptr->data!=key && ptr->next!=NULL)
{
prev=ptr;
ptr=ptr->next;
}
if(ptr->data==key)
{
prev->next=ptr->next;
delete(ptr);
}
}//end of else
} //end of function

14. • Time Complexity:
Search= O(1+α ) where α is loading factor
Insert/Delete: O(1+α )
DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon 14