Implementing own Hash Table with Open Addressing Linear Probing

Prerequisite – Hashing Introduction, Implementing our Own Hash Table with Separate Chaining in Java
In Open Addressing, all elements are stored in the hash table itself. So at any point, size of table must be greater than or equal to total number of keys (Note that we can increase table size by copying old data if needed).

• Insert(k) – Keep probing until an empty slot is found. Once an empty slot is found, insert k.
• Search(k) – Keep probing until slot’s key doesn’t become equal to k or an empty slot is reached.
• Delete(k) – Delete operation is interesting. If we simply delete a key, then search may fail. So slots of deleted keys are marked specially as “deleted”.

Here, to mark a node deleted we have used dummy node with key and value -1. 
Insert can insert an item in a deleted slot, but search doesn’t stop at a deleted slot.
The entire process ensures that for any key, we get an integer position within the size of the Hash Table to insert the corresponding value. 
So the process is simple, user gives a (key, value) pair set as input and based on the value generated by hash function an index is generated to where the value corresponding to the particular key is stored. So whenever we need to fetch a value corresponding to a key that is just O(1).

Implementation:

CPP

#include <bits/stdc++.h>
using namespace std;

// template for generic type
template <typename K, typename V>

// Hashnode class
class HashNode {
public:
    V value;
    K key;

    // Constructor of hashnode
    HashNode(K key, V value)
    {
        this->value = value;
        this->key = key;
    }
};

// template for generic type
template <typename K, typename V>

// Our own Hashmap class
class HashMap {
    // hash element array
    HashNode<K, V>** arr;
    int capacity;
    // current size
    int size;
    // dummy node
    HashNode<K, V>* dummy;

public:
    HashMap()
    {
        // Initial capacity of hash array
        capacity = 20;
        size = 0;
        arr = new HashNode<K, V>*[capacity];

        // Initialise all elements of array as NULL
        for (int i = 0; i < capacity; i++)
            arr[i] = NULL;

        // dummy node with value and key -1
        dummy = new HashNode<K, V>(-1, -1);
    }
    // This implements hash function to find index
    // for a key
    int hashCode(K key)
    {
        return key % capacity;
    }

    // Function to add key value pair
    void insertNode(K key, V value)
    {
        HashNode<K, V>* temp = new HashNode<K, V>(key, value);

        // Apply hash function to find index for given key
        int hashIndex = hashCode(key);

        // find next free space
        while (arr[hashIndex] != NULL
               && arr[hashIndex]->key != key
               && arr[hashIndex]->key != -1) {
            hashIndex++;
            hashIndex %= capacity;
        }

        // if new node to be inserted
        // increase the current size
        if (arr[hashIndex] == NULL
            || arr[hashIndex]->key == -1)
            size++;
        arr[hashIndex] = temp;
    }

    // Function to delete a key value pair
    V deleteNode(int key)
    {
        // Apply hash function
        // to find index for given key
        int hashIndex = hashCode(key);

        // finding the node with given key
        while (arr[hashIndex] != NULL) {
            // if node found
            if (arr[hashIndex]->key == key) {
                HashNode<K, V>* temp = arr[hashIndex];

                // Insert dummy node here for further use
                arr[hashIndex] = dummy;

                // Reduce size
                size--;
                return temp->value;
            }
            hashIndex++;
            hashIndex %= capacity;
        }

        // If not found return null
        return NULL;
    }

    // Function to search the value for a given key
    V get(int key)
    {
        // Apply hash function to find index for given key
        int hashIndex = hashCode(key);
        int counter = 0;

        // finding the node with given key
        while (arr[hashIndex] != NULL) { // int counter =0; // BUG!

            if (counter++ > capacity) // to avoid infinite loop
                return NULL;

            // if node found return its value
            if (arr[hashIndex]->key == key)
                return arr[hashIndex]->value;
            hashIndex++;
            hashIndex %= capacity;
        }

        // If not found return null
        return NULL;
    }

    // Return current size
    int sizeofMap()
    {
        return size;
    }

    // Return true if size is 0
    bool isEmpty()
    {
        return size == 0;
    }

    // Function to display the stored key value pairs
    void display()
    {
        for (int i = 0; i < capacity; i++) {
            if (arr[i] != NULL && arr[i]->key != -1)
                cout << "key = " << arr[i]->key
                     << "  value = "
                     << arr[i]->value << endl;
        }
    }
};

// Driver method to test map class
int main()
{
    HashMap<int, int>* h = new HashMap<int, int>;
    h->insertNode(1, 1);
    h->insertNode(2, 2);
    h->insertNode(2, 3);
    h->display();
    cout << h->sizeofMap() << endl;
    cout << h->deleteNode(2) << endl;
    cout << h->sizeofMap() << endl;
    cout << h->isEmpty() << endl;
    cout << h->get(2);

    return 0;
}

Output

key = 1  value = 1
key = 2  value = 3
2
3
1
0
0

Complexity analysis for Insertion:

• Time Complexity:
  • Best Case: O(1)
  • Worst Case: O(N). This happens when all elements have collided and we need to insert the last element by checking free space one by one.
  • Average Case: O(1) for good hash function, O(N) for bad hash function
• Auxiliary Space: O(1)

Complexity analysis for Deletion:

• Time Complexity:
  • Best Case: O(1)
  • Worst Case: O(N)
  • Average Case: O(1) for good hash function; O(N) for bad hash function
• Auxiliary Space: O(1) 

Complexity analysis for Searching:

• Time Complexity:
  • Best Case: O(1)
  • Worst Case: O(N)
  • Average Case: O(1) for good hash function; O(N) for bad hash function
• Auxiliary Space: O(1) for search operation

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