OBJECT: Introduction and implementation of hashing (hash tables)
In computing, a hash table (hash map) is a data structure which implements an associative array abstract data type, a structure that can map keys to values. A hash table uses a hash function to compute an index into an array of buckets or slots, from which the desired value can be found.
Ideally, the hash function will assign each key to a unique bucket, but most hash table designs employ an imperfect hash function, which might cause hash collisions where the hash function generates the same index for more than one key. Such collisions must be accommodated in some way.
In a well-dimensioned hash table, the average cost (number of instructions) for each lookup is independent of the number of elements stored in the table. Many hash table designs also allow arbitrary insertions and deletions of key-value pairs, at (amortized]) constant average cost per operation.
In many situations, hash tables turn out to be more efficient than search trees or any other table lookup structure. For this reason, they are widely used in many kinds of computer software, particularly for associative arrays, database indexing, caches, and sets. The idea of hashing is to distribute the entries (key/value pairs) across an array of buckets. Given a key, the algorithm computes an index that suggests where the entry can be found:
index = f(key, array_size) Often this is done in two steps: hash = hashfunc(key)
index = hash % array_size
In this method, the hash is independent of the array size, and it is then reduced to an index (a number between 0 and array_size − 1) using the modulo operator (%).
In the case that the array size is a power of two, the remainder operation is reduced to masking, which improves speed, but can increase problems with a poor hash function.
Choosing a hash function:
A good hash function and implementation algorithm are essential for good hash table performance, but may be difficult to achieve.
Uniformity is sometimes difficult to ensure by design, but may be evaluated empirically using statistical tests, e.g., a Pearson's chi-squared test for discrete uniform distributions
Perfect hash function:
If all keys are known ahead of time, a perfect hash function can be used to create a perfect hash table that has no collisions. If minimal perfect hashing is used, every location in the hash table can be used as well.
Perfect hashing allows for constant time lookups in all cases. This is in contrast to most chaining and open addressing methods, where the time for lookup is low on average, but may be very large, O(n), for instance when all the keys hash to a few values.
Hash Functions:
A hash function is a function which transforms a key into a natural number called a hash value, i.e.
f : K → H,
where K is the set of keys and H is a set of natural numbers. Function f is a many-to-one function. If two different
keys, say k1 and k2, k1 6= k2 have the same hash value, i.e. f(k1)f(k2) then the two keys are said to collide and the
corresponding records are called synonyms. Two restrictions are imposed on f: 1. For any k ∈K the value should be obtained as fast as possible.
2. It must minimize the number of collisions. An example of hash function is:
f(k) = γ(k) modulus B,
where γ is a function which maps a key to a natural number, and B is a natural number, possibly prime. The expression
of function γ depends on the keys. If the keys are numeric, the γ(k) = k. The simplest function γ on alphanumeric keys
is the sum of the (ASCII) codes for each character of the key. IMPLEMENTATION:
#include<cstdlib> #include<string> #include<cstdio> using namespace std;
const int TABLE_SIZE = 128;
/*
* HashEntry Class Declaration
*/
class HashEntry
{
public:
int key;
int value;
HashEntry(int key, int value)
{
this->key = key;
this->value = value;
}
};
/*
* HashMap Class Declaration
*/
{
private:
HashEntry **table;
public:
HashMap()
{
table = new HashEntry * [TABLE_SIZE];
for (int i = 0; i< TABLE_SIZE; i++)
{
table[i] = NULL;
}
}
/*
* Hash Function
*/
int HashFunc(int key)
{
return key % TABLE_SIZE;
}
/*
* Insert Element at a key
*/
void Insert(int key, int value)
{
while (table[hash] != NULL && table[hash]->key != key)
{
hash = HashFunc(hash + 1);
}
if (table[hash] != NULL)
delete table[hash];
table[hash] = new HashEntry(key, value);
}
/*
* Search Element at a key
*/
int Search(int key)
{
int hash = HashFunc(key);
while (table[hash] != NULL && table[hash]->key != key)
{
hash = HashFunc(hash + 1);
}
if (table[hash] == NULL)
return -1;
else
return table[hash]->value;
}
* Remove Element at a key
*/
void Remove(int key)
{
int hash = HashFunc(key);
while (table[hash] != NULL)
{
if (table[hash]->key == key)
break;
hash = HashFunc(hash + 1);
}
if (table[hash] == NULL)
{
cout<<"No Element found at key "<<key<<endl;
return;
}
else
{
delete table[hash];
}
cout<<"Element Deleted"<<endl;
}
~HashMap()
{
{
if (table[i] != NULL)
delete table[i];
delete[] table;
}
}
};
/*
* Main Contains Menu
*/
int main()
{
HashMap hash;
int key, value;
int choice;
while (1)
{
cout<<"\n---"<<endl;
cout<<"Operations on Hash Table"<<endl;
cout<<"\n---"<<endl;
cout<<"1.Insert element into the table"<<endl;
cout<<"2.Search element from the key"<<endl;
cout<<"3.Delete element at a key"<<endl;
cout<<"4.Exit"<<endl;
cin>>choice;
switch(choice)
{
case 1:
cout<<"Enter element to be inserted: ";
cin>>value;
cout<<"Enter key at which element to be inserted: ";
cin>>key;
hash.Insert(key, value);
break;
case 2:
cout<<"Enter key of the element to be searched: ";
cin>>key;
if (hash.Search(key) == -1)
{
cout<<"No element found at key "<<key<<endl;
continue;
}
else
{
cout<<"Element at key "<<key<<" : ";
cout<<hash.Search(key)<<endl;
}
break;
cout<<"Enter key of the element to be deleted: ";
cin>>key;
hash.Remove(key);
break;
case 4:
exit(1);
default:
cout<<"\nEnter correct option\n";
}
}
return 0;
}
OUTPUT:
Operations on Hash Table
---1.Insert element into the table
2.Search element from the key
3.Delete element at a key
4.Exit
Enter your choice: 1
Enter element to be inserted: 12
Enter key at which element to be inserted: 1
---Operations on Hash Table
---1.Insert element into the table
2.Search element from the key
3.Delete element at a key
4.Exit
Enter your choice: 1
Enter element to be inserted: 24
Enter key at which element to be inserted: 2
---Operations on Hash Table
---1.Insert element into the table
2.Search element from the key
3.Delete element at a key
4.Exit
Enter your choice: 1
Enter element to be inserted: 36
Enter key at which element to be inserted: 3
---1.Insert element into the table
2.Search element from the key
3.Delete element at a key
4.Exit
Enter your choice: 1
Enter element to be inserted: 48
Enter key at which element to be inserted: 4
---Operations on Hash Table
---1.Insert element into the table
2.Search element from the key
3.Delete element at a key
4.Exit
Enter your choice: 1
Enter element to be inserted: 60
Enter key at which element to be inserted: 5
---Operations on Hash Table
---1.Insert element into the table
2.Search element from the key
3.Delete element at a key
4.Exit
Enter your choice: 2
Enter key of the element to be searched: 3
Element at key 3 : 36
---Operations on Hash Table
---1.Insert element into the table
2.Search element from the key
3.Delete element at a key
4.Exit
Enter your choice: 2
Enter key of the element to be searched: 5
Element at key 5 : 60
---Operations on Hash Table
---1.Insert element into the table
2.Search element from the key
3.Delete element at a key
4.Exit
Enter your choice: 3
Enter key of the element to be deleted: 4
Element Deleted
---Operations on Hash Table
---1.Insert element into the table
2.Search element from the key
3.Delete element at a key
4.Exit
Enter your choice: 2
Enter key of the element to be searched: 4
No element found at key 4
---Operations on Hash Table
2.Search element from the key
3.Delete element at a key
4.Exit
Enter your choice: 2
Enter key of the element to be searched: 2
Element at key 2 : 24
---Operations on Hash Table
---1.Insert element into the table
2.Search element from the key
3.Delete element at a key
4.Exit
Enter your choice: 4
