In this tutorial, you will learn ** what a hash table** is. Additionally, you will discover working examples of

**hash table**operations in C, C++, Java, and Python.

Contents

## What is a hash table?

A ** hash table** is a type of data structure that stores key-values Paris. The key is shipped off a hash work that performs the arithmetic procedure on it. The outcome (generally called the hash value or hash) is the index of the key-value pair in the hash table.

A **Hash table** is a data structure that represents data as **key-value** pairs. Each key is mapped to a value in the hash table. The keys are used for indexing the values/data. A comparable approach is applied by an associative array.

Data is represented in a key value pair with the assistance of keys as demonstrated in the figure below. Each data is associated with a key. The key is an integer that highlight the data.

## 1. Direct Address Table

A direct address table is used when the measure of space used by the table isn’t an issue for the program. Here, we assume that

- the keys are little integers
- the number of keys isn’t excessively huge, and
- no two data have a similar key

A pool of integers is taken called universe U = {0, 1, … ., n-1}.

Each slot of a direct address table T[0…n-1] contains a pointer to the element that corresponds to the data.

The index of the array T is the key itself and the content of T is a pointer to the set [key, element]. If there is no element for a key then, it is left as NULL.

Sometimes, the key itself is the data.

**Pseudocode for operations**

directAddressSearch(T, k) return T[k] directAddressInsert(T, x) T[x.key] = x directAddressDelete(T, x) T[x.key] = NIL

**Limitations of a Direct Address Table**

- The value of the key ought to be little.
- The number of keys should be little enough so it doesn’t cross the size limit of an array.

## 2. Hash Table

In a **hash table**, the keys are processed to create another index that maps to the necessary elements. This process is called hashing.

Let h(x) be a hash function and k be a key.

h(k) is calculated and it is used as an index for the element.

**Limitations of a Hash Table**

- On the off chance that a similar index is created by the hash work for various keys at that point, conflict arises. The present circumstance is called a collision.

To keep away from this, a reasonable hash work is picked. In any case, it is difficult to create all extraordinary keys on the grounds that |U|>m. Subsequently, a decent hash function may not prevent the collisions totally anyway it can decrease the number of collisions.

Notwithstanding, we have different strategies to resolve collision.

## Advantages of the hash table over direct address table:

The fundamental issues with the direct address table are the size of the array and the potentially enormous value of a key. The hash work decreases the scope of the index and hence the size of the array is likewise diminished.

For instance, If k = 9845648451321, at that point h(k) = 11 (by using some hash function). This helps in saving the memory wasted while providing the index of 9845648451321 to the array

## Collision resolution by chaining

In this strategy, if a hash work produces a similar index for various elements, these elements are stored in a similar index by using a doubly linked list.

On the off chance that j is the slot for different elements, it contains a pointer to the head of the list of elements. In the event that no elements is available, j contains NIL.

### Pseudocode for operations

chainedHashSearch(T, k) return T[h(k)] chainedHashInsert(T, x) T[h(x.key)] = x //insert at the head chainedHashDelete(T, x) T[h(x.key)] = NIL

## Python, Java, C and C++ Implementation

**Python **

# Python program to demonstrate working of HashTable hashTable = [[],] * 10 def checkPrime(n): if n == 1 or n == 0: return 0 for i in range(2, n//2): if n % i == 0: return 0 return 1 def getPrime(n): if n % 2 == 0: n = n + 1 while not checkPrime(n): n += 2 return n def hashFunction(key): capacity = getPrime(10) return key % capacity def insertData(key, data): index = hashFunction(key) hashTable[index] = [key, data] def removeData(key): index = hashFunction(key) hashTable[index] = 0 insertData(123, "apple") insertData(432, "mango") insertData(213, "banana") insertData(654, "guava") print(hashTable) removeData(123) print(hashTable)

**Java**

// Java program to demonstrate working of HashTable import java.util.*; class HashTable { public static void main(String args[]) { Hashtable<Integer, Integer> ht = new Hashtable<Integer, Integer>(); ht.put(123, 432); ht.put(12, 2345); ht.put(15, 5643); ht.put(3, 321); ht.remove(12); System.out.println(ht); } }

**C**

// Implementing hash table in C #include <stdio.h> #include <stdlib.h> struct set { int key; int data; }; struct set *array; int capacity = 10; int size = 0; int hashFunction(int key) { return (key % capacity); } int checkPrime(int n) { int i; if (n == 1 || n == 0) { return 0; } for (i = 2; i < n / 2; i++) { if (n % i == 0) { return 0; } } return 1; } int getPrime(int n) { if (n % 2 == 0) { n++; } while (!checkPrime(n)) { n += 2; } return n; } void init_array() { capacity = getPrime(capacity); array = (struct set *)malloc(capacity * sizeof(struct set)); for (int i = 0; i < capacity; i++) { array[i].key = 0; array[i].data = 0; } } void insert(int key, int data) { int index = hashFunction(key); if (array[index].data == 0) { array[index].key = key; array[index].data = data; size++; printf("\n Key (%d) has been inserted \n", key); } else if (array[index].key == key) { array[index].data = data; } else { printf("\n Collision occured \n"); } } void remove_element(int key) { int index = hashFunction(key); if (array[index].data == 0) { printf("\n This key does not exist \n"); } else { array[index].key = 0; array[index].data = 0; size--; printf("\n Key (%d) has been removed \n", key); } } void display() { int i; for (i = 0; i < capacity; i++) { if (array[i].data == 0) { printf("\n array[%d]: / ", i); } else { printf("\n key: %d array[%d]: %d \t", array[i].key, i, array[i].data); } } } int size_of_hashtable() { return size; } int main() { int choice, key, data, n; int c = 0; init_array(); do { printf("1.Insert item in the Hash Table" "\n2.Remove item from the Hash Table" "\n3.Check the size of Hash Table" "\n4.Display a Hash Table" "\n\n Please enter your choice: "); scanf("%d", &choice); switch (choice) { case 1: printf("Enter key -:\t"); scanf("%d", &key); printf("Enter data -:\t"); scanf("%d", &data); insert(key, data); break; case 2: printf("Enter the key to delete-:"); scanf("%d", &key); remove_element(key); break; case 3: n = size_of_hashtable(); printf("Size of Hash Table is-:%d\n", n); break; case 4: display(); break; default: printf("Invalid Input\n"); } printf("\nDo you want to continue (press 1 for yes): "); scanf("%d", &c); } while (c == 1); }

**C++**

// Implementing hash table in C++ #include <iostream> #include <list> using namespace std; class HashTable { int capacity; list<int> *table; public: HashTable(int V); void insertItem(int key, int data); void deleteItem(int key); int checkPrime(int n) { int i; if (n == 1 || n == 0) { return 0; } for (i = 2; i < n / 2; i++) { if (n % i == 0) { return 0; } } return 1; } int getPrime(int n) { if (n % 2 == 0) { n++; } while (!checkPrime(n)) { n += 2; } return n; } int hashFunction(int key) { return (key % capacity); } void displayHash(); }; HashTable::HashTable(int c) { int size = getPrime(c); this->capacity = size; table = new list<int>[capacity]; } void HashTable::insertItem(int key, int data) { int index = hashFunction(key); table[index].push_back(data); } void HashTable::deleteItem(int key) { int index = hashFunction(key); list<int>::iterator i; for (i = table[index].begin(); i != table[index].end(); i++) { if (*i == key) break; } if (i != table[index].end()) table[index].erase(i); } void HashTable::displayHash() { for (int i = 0; i < capacity; i++) { cout << "table[" << i << "]"; for (auto x : table[i]) cout << " --> " << x; cout << endl; } } int main() { int key[] = {231, 321, 212, 321, 433, 262}; int data[] = {123, 432, 523, 43, 423, 111}; int size = sizeof(key) / sizeof(key[0]); HashTable h(size); for (int i = 0; i < n; i++) h.insertItem(key[i], data[i]); h.deleteItem(12); h.displayHash(); }

## Good Hash Functions

A good hash work has the accompanying attributes.

- It ought not to create keys that are too enormous and the bucket space is little. Space is wasted.
- The keys produced ought to be neither very close nor too far in range.
- The collision should be minimized however much as possible.

Some of the methods used for hashing are:

### Division Method

If k is a key and m is the size of the hash table, the hash function h() is calculated as:

h(k) = k mod m

For instance, If the size of a hash table is 10 and k = 112 then h(k) = 112 mod 10 = 2. The value of m should not be the powers of 2. This is on the grounds that the powers of 2 in the binary format are 10, 100, 1000, … . At the point when we discover k mod m, we will consistently get the lower request p-bits.

if m = 22, k = 17, then h(k) = 17 mod 22 = 10001 mod 100 = 01 if m = 23, k = 17, then h(k) = 17 mod 22 = 10001 mod 100 = 001 if m = 24, k = 17, then h(k) = 17 mod 22 = 10001 mod 100 = 0001 if m = 2p, then h(k) = p lower bits of m

#### Multiplication Method

h(k) = ⌊m(kA mod 1)⌋

where,

kA mod 1 gives the fractional part kA,

⌊ ⌋ gives the floor value

A is any constant. The value of A lies between 0 and 1. But, an optimal choice will be ≈ (√5-1)/2 suggested by Knuth.

#### Universal Hashing

In Universal hashing, the hash function is chosen at random independent of keys.

## Open Addressing

Different values can be stored in a single slot in a typical hash table.

By using open addressing, each slot is either loaded up with a single key or left NIL. All the elements are stored in the hash table itself.

Not at all like chaining, numerous elements can’t be found a way into a similar opening.

Open addressing is fundamentally a collision settling method. A portion of the techniques used by open addressing are:

### Linear Probing

In linear probing, collision is resolved by checking the next slot.

h(k, i) = (h′(k) + i) mod m

where,

i = {0, 1, ….}

h'(k) is a new hash function

In the event that an impact happens at h(k, 0), at that point h(k, 1) is checked. Thusly, the value of I is increased straightly.

The issue with linear testing is that a group of nearby spaces is filled. While inserting another element, the whole cluster should be navigated. This adds to the time needed to perform the procedure on the hash table.

## Quadratic Probing

In quadratic probing, the spacing between the slots is increased (greater than one) by using the following relation.

h(k, i) = (h′(k) + c1i + c2i2) mod m

where,

c1 and c2 are positive auxiliary constants,

i = {0, 1, ….}

## Double hashing

On the off chance that a collision happens subsequent to applying a hash function h(k), at that point another hash function is calculated for finding the next slot.

h(k, I) = (h1(k) + ih2(k)) mod m

## Hash Table Applications

Hash tables are implemented where

constant time lookup and insertion is required

cryptographic applications

indexing data is required

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