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Load Factor and Rehashing

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  • Difficulty Level : Medium
  • Last Updated : 21 Jan, 2023
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Prerequisites: Hashing Introduction and Collision handling by separate chaining

How hashing works:

For insertion of a key(K) – value(V) pair into a hash map, 2 steps are required: 
 

  1. K is converted into a small integer (called its hash code) using a hash function.
  2. The hash code is used to find an index (hashCode % arrSize) and the entire linked list at that index(Separate chaining) is first searched for the presence of the K already.
  3. If found, it’s value is updated and if not, the K-V pair is stored as a new node in the list.

Complexity and Load Factor

  • For the first step, the time taken depends on the K and the hash function. 
    For example, if the key is a string “abcd”, then it’s hash function may depend on the length of the string. But for very large values of n, the number of entries into the map, and length of the keys is almost negligible in comparison to n so hash computation can be considered to take place in constant time, i.e, O(1).
  • For the second step, traversal of the list of K-V pairs present at that index needs to be done. For this, the worst case may be that all the n entries are at the same index. So, time complexity would be O(n). But, enough research has been done to make hash functions uniformly distribute the keys in the array so this almost never happens.
  • So, on an average, if there are n entries and b is the size of the array there would be n/b entries on each index. This value n/b is called the load factor that represents the load that is there on our map.
  • This Load Factor needs to be kept low, so that number of entries at one index is less and so is the complexity almost constant, i.e., O(1).

Rehashing:

Rehashing is the process of increasing the size of a hashmap and redistributing the elements to new buckets based on their new hash values. It is done to improve the performance of the hashmap and to prevent collisions caused by a high load factor.

When a hashmap becomes full, the load factor (i.e., the ratio of the number of elements to the number of buckets) increases. As the load factor increases, the number of collisions also increases, which can lead to poor performance. To avoid this, the hashmap can be resized and the elements can be rehashed to new buckets, which decreases the load factor and reduces the number of collisions.

During rehashing, all elements of the hashmap are iterated and their new bucket positions are calculated using the new hash function that corresponds to the new size of the hashmap. This process can be time-consuming but it is necessary to maintain the efficiency of the hashmap.

Why rehashing?
Rehashing is needed in a hashmap to prevent collision and to maintain the efficiency of the data structure.

As elements are inserted into a hashmap, the load factor (i.e., the ratio of the number of elements to the number of buckets) increases. If the load factor exceeds a certain threshold (often set to 0.75), the hashmap becomes inefficient as the number of collisions increases. To avoid this, the hashmap can be resized and the elements can be rehashed to new buckets, which decreases the load factor and reduces the number of collisions. This process is known as rehashing.

Rehashing can be costly in terms of time and space, but it is necessary to maintain the efficiency of the hashmap.

How Rehashing is done?
Rehashing can be done as follows:

  • For each addition of a new entry to the map, check the load factor.
  • If it’s greater than its pre-defined value (or default value of 0.75 if not given), then Rehash.
  • For Rehash, make a new array of double the previous size and make it the new bucketarray.
  • Then traverse to each element in the old bucketArray and call the insert() for each so as to insert it into the new larger bucket array.

Program to implement Rehashing:

Java




// Java program to implement Rehashing
 
import java.util.ArrayList;
 
class Map<K, V> {
 
    class MapNode<K, V> {
 
        K key;
        V value;
        MapNode<K, V> next;
 
        public MapNode(K key, V value)
        {
            this.key = key;
            this.value = value;
            next = null;
        }
    }
 
    // The bucket array where
    // the nodes containing K-V pairs are stored
    ArrayList<MapNode<K, V> > buckets;
 
    // No. of pairs stored - n
    int size;
 
    // Size of the bucketArray - b
    int numBuckets;
 
    // Default loadFactor
    final double DEFAULT_LOAD_FACTOR = 0.75;
 
    public Map()
    {
        numBuckets = 5;
 
        buckets = new ArrayList<>(numBuckets);
 
        for (int i = 0; i < numBuckets; i++) {
            // Initialising to null
            buckets.add(null);
        }
        System.out.println("HashMap created");
        System.out.println("Number of pairs in the Map: " + size);
        System.out.println("Size of Map: " + numBuckets);
        System.out.println("Default Load Factor : " + DEFAULT_LOAD_FACTOR + "\n");
    }
 
    private int getBucketInd(K key)
    {
 
        // Using the inbuilt function from the object class
        int hashCode = key.hashCode();
 
        // array index = hashCode%numBuckets
        return (hashCode % numBuckets);
    }
 
    public void insert(K key, V value)
    {
        // Getting the index at which it needs to be inserted
        int bucketInd = getBucketInd(key);
 
        // The first node at that index
        MapNode<K, V> head = buckets.get(bucketInd);
 
        // First, loop through all the nodes present at that index
        // to check if the key already exists
        while (head != null) {
 
            // If already present the value is updated
            if (head.key.equals(key)) {
                head.value = value;
                return;
            }
            head = head.next;
        }
 
        // new node with the K and V
        MapNode<K, V> newElementNode = new MapNode<K, V>(key, value);
 
        // The head node at the index
        head = buckets.get(bucketInd);
 
        // the new node is inserted
        // by making it the head
        // and it's next is the previous head
        newElementNode.next = head;
 
        buckets.set(bucketInd, newElementNode);
 
        System.out.println("Pair(" + key + ", " + value + ") inserted successfully.\n");
 
        // Incrementing size
        // as new K-V pair is added to the map
        size++;
 
        // Load factor calculated
        double loadFactor = (1.0 * size) / numBuckets;
 
        System.out.println("Current Load factor = " + loadFactor);
 
        // If the load factor is > 0.75, rehashing is done
        if (loadFactor > DEFAULT_LOAD_FACTOR) {
            System.out.println(loadFactor + " is greater than " + DEFAULT_LOAD_FACTOR);
            System.out.println("Therefore Rehashing will be done.\n");
 
            // Rehash
            rehash();
 
            System.out.println("New Size of Map: " + numBuckets + "\n");
        }
 
        System.out.println("Number of pairs in the Map: " + size);
        System.out.println("Size of Map: " + numBuckets + "\n");
    }
 
    private void rehash()
    {
 
        System.out.println("\n***Rehashing Started***\n");
 
        // The present bucket list is made temp
        ArrayList<MapNode<K, V> > temp = buckets;
 
        // New bucketList of double the old size is created
        buckets = new ArrayList<MapNode<K, V> >(2 * numBuckets);
 
        for (int i = 0; i < 2 * numBuckets; i++) {
            // Initialised to null
            buckets.add(null);
        }
        // Now size is made zero
        // and we loop through all the nodes in the original bucket list(temp)
        // and insert it into the new list
        size = 0;
        numBuckets *= 2;
 
        for (int i = 0; i < temp.size(); i++) {
 
            // head of the chain at that index
            MapNode<K, V> head = temp.get(i);
 
            while (head != null) {
                K key = head.key;
                V val = head.value;
 
                // calling the insert function for each node in temp
                // as the new list is now the bucketArray
                insert(key, val);
                head = head.next;
            }
        }
 
        System.out.println("\n***Rehashing Ended***\n");
    }
 
    public void printMap()
    {
 
        // The present bucket list is made temp
        ArrayList<MapNode<K, V> > temp = buckets;
 
        System.out.println("Current HashMap:");
        // loop through all the nodes and print them
        for (int i = 0; i < temp.size(); i++) {
 
            // head of the chain at that index
            MapNode<K, V> head = temp.get(i);
 
            while (head != null) {
                System.out.println("key = " + head.key + ", val = " + head.value);
 
                head = head.next;
            }
        }
        System.out.println();
    }
   
      //Function to get an element from Map
      public V getValue(K key){
          //Get actual index of the key
        int actualIndex = getBucketInd(key);
        MapNode<K,V> temp = buckets.get(actualIndex);
          //Search for key in list
        while(temp != null){
            if(temp.key == key){
                return temp.value;
            }
            temp = temp.next;
        }
        return null;
    }
}
 
public class GFG {
 
    public static void main(String[] args)
    {
 
        // Creating the Map
        Map<Integer, String> map = new Map<Integer, String>();
 
        // Inserting elements
        map.insert(1, "Geeks");
        map.printMap();
 
        map.insert(2, "forGeeks");
        map.printMap();
 
        map.insert(3, "A");
        map.printMap();
 
        map.insert(4, "Computer");
        map.printMap();
 
        map.insert(5, "Portal");
        map.printMap();
       
      //Get element from Map
      int key = 4;
      String value = map.getValue(key);
      System.out.println("Value at key "+ key +" is: "+ value);
    }
}

Python3




# Python3 program to implement Rehashing
 
class Map:
 
    class MapNode:
        def __init__(self,key,value):
            self.key=key
            self.value=value
            self.next=None
 
    # The bucket array where
    # the nodes containing K-V pairs are stored
    buckets=list()
 
    # No. of pairs stored - n
    size=0
 
    # Size of the bucketArray - b
    numBuckets=0
 
    # Default loadFactor
    DEFAULT_LOAD_FACTOR = 0.75
 
    def __init__(self):
        Map.numBuckets = 5
 
        Map.buckets = [None]*Map.numBuckets
 
        print("HashMap created")
        print("Number of pairs in the Map: " + str(Map.size))
        print("Size of Map: " + str(Map.numBuckets))
        print("Default Load Factor : " + str(Map.DEFAULT_LOAD_FACTOR) + "\n")
 
    def getBucketInd(self,key):
 
        # Using the inbuilt function from the object class
        hashCode = hash(key)
 
        # array index = hashCode%numBuckets
        return (hashCode % Map.numBuckets)
 
    def insert(self,key,value):
 
        # Getting the index at which it needs to be inserted
        bucketInd = self.getBucketInd(key)
 
        # The first node at that index
        head = Map.buckets[bucketInd]
 
        # First, loop through all the nodes present at that index
        # to check if the key already exists
        while (head != None):
 
            # If already present the value is updated
            if (head.key==key):
                head.value = value
                return
            head = head.next
 
        # new node with the K and V
        newElementNode = Map.MapNode(key, value)
 
        # The head node at the index
        head = Map.buckets[bucketInd]
 
        # the new node is inserted
        # by making it the head
        # and it's next is the previous head
        newElementNode.next = head
 
        Map.buckets[bucketInd]= newElementNode
 
        print("Pair(\" {} \", \" {} \") inserted successfully.".format(key,value))
 
        # Incrementing size
        # as new K-V pair is added to the map
        Map.size+=1
 
        # Load factor calculated
        loadFactor = (1* Map.size) / Map.numBuckets
 
        print("Current Load factor = " + str(loadFactor))
 
        # If the load factor is > 0.75, rehashing is done
        if (loadFactor > Map.DEFAULT_LOAD_FACTOR):
            print(str(loadFactor) + " is greater than " + str(Map.DEFAULT_LOAD_FACTOR))
            print("Therefore Rehashing will be done.")
 
            # Rehash
            self.rehash()
 
            print("New Size of Map: " + str(Map.numBuckets))
 
        print("Number of pairs in the Map: " + str(Map.size))
        print("Size of Map: " + str(Map.numBuckets))
 
    def rehash(self):
 
        print("\n***Rehashing Started***\n")
 
        # The present bucket list is made temp
        temp = Map.buckets
 
        # New bucketList of double the old size is created
        buckets =(2 * Map.numBuckets)
 
        for i in range(2 * Map.numBuckets):
            # Initialised to null
            Map.buckets.append(None)
 
        # Now size is made zero
        # and we loop through all the nodes in the original bucket list(temp)
        # and insert it into the new list
        Map.size = 0
        Map.numBuckets *= 2
 
        for i in range(len(temp)):
 
            # head of the chain at that index
            head = temp[i]
 
            while (head != None):
                key = head.key
                val = head.value
 
                # calling the insert function for each node in temp
                # as the new list is now the bucketArray
                self.insert(key, val)
                head = head.next
 
        print("\n***Rehashing Ended***")
 
    def printMap(self):
 
        # The present bucket list is made temp
        temp = Map.buckets
 
        print("Current HashMap:")
        # loop through all the nodes and print them
        for i in range(len(temp)):
 
            # head of the chain at that index
            head = temp[i]
 
            while (head != None):
                print("key = \" {} \", val = {}" .format(head.key,head.value))
 
                head = head.next
        print()
 
 
if __name__ == '__main__':
    # Creating the Map
    map = Map()
 
    # Inserting elements
    map.insert(1, "Geeks")
    map.printMap()
 
    map.insert(2, "forGeeks")
    map.printMap()
 
    map.insert(3, "A")
    map.printMap()
 
    map.insert(4, "Computer")
    map.printMap()
 
    map.insert(5, "Portal")
    map.printMap()
 
# This code is contributed by Amartya Ghosh

C++




#include <iostream>
#include <vector>
#include <functional>
 
class Map {
 
private:
    class MapNode {
    public:
        int key;
        int value;
        MapNode* next;
 
        MapNode(int key, int value) {
            this->key = key;
            this->value = value;
            this->next = NULL;
        }
    };
 
    // The bucket array where
    // the nodes containing K-V pairs are stored
    std::vector<MapNode*> buckets;
 
    // No. of pairs stored - n
    int size;
 
    // Size of the bucketArray - b
    int numBuckets;
 
    // Default loadFactor
    double DEFAULT_LOAD_FACTOR = 0.75;
 
    int getBucketInd(int key) {
        // Using the inbuilt function from the object class
        int hashCode = std::hash<int>()(key);
 
        // array index = hashCode%numBuckets
        return (hashCode % numBuckets);
    }
 
public:
    Map() {
        numBuckets = 5;
 
        buckets.resize(numBuckets);
 
        std::cout << "HashMap created" << std::endl;
        std::cout << "Number of pairs in the Map: " << size << std::endl;
        std::cout << "Size of Map: " << numBuckets << std::endl;
        std::cout << "Default Load Factor : " << DEFAULT_LOAD_FACTOR << std::endl;
    }
 
    void insert(int key, int value) {
        // Getting the index at which it needs to be inserted
        int bucketInd = getBucketInd(key);
 
        // The first node at that index
        MapNode* head = buckets[bucketInd];
 
        // First, loop through all the nodes present at that index
        // to check if the key already exists
        while (head != NULL) {
            // If already present the value is updated
            if (head->key == key) {
                head->value = value;
                return;
            }
            head = head->next;
        }
 
        // new node with the K and V
        MapNode* newElementNode = new MapNode(key, value);
 
        // The head node at the index
        head = buckets[bucketInd];
 
        // the new node is inserted
        // by making it the head
        // and it's next is the previous head
        newElementNode->next = head;
 
        buckets[bucketInd] = newElementNode;
 
        std::cout << "Pair(" << key << ", " << value << ") inserted successfully." << std::endl;
 
        // Incrementing size
        // as new K-V pair is added to the map
        size++;
 
        // Load factor calculated
        double loadFactor = (1 * size) / numBuckets;
 
        std::cout << "Current Load factor = " << loadFactor << std::endl;
 
        // If the load factor is > 0.75, rehashing is done
        if (loadFactor > DEFAULT_LOAD_FACTOR) {
            std::cout << loadFactor << " is greater than " << DEFAULT_LOAD_FACTOR << std::endl;
std::cout << "Therefore Rehashing will be done." << std::endl;
 
        // Rehash
        rehash();
 
        std::cout << "New Size of Map: " << numBuckets << std::endl;
    }
 
    std::cout << "Number of pairs in the Map: " << size << std::endl;
}
 
void rehash() {
    std::cout << "\n***Rehashing Started***\n" << std::endl;
 
    // The present bucket list is made temp
    std::vector<MapNode*> temp = buckets;
 
    // New bucketList of double the old size is created
    buckets.resize(2 * numBuckets);
 
    for (int i = 0; i < 2 * numBuckets; i++) {
        // Initialised to null
        buckets[i] = NULL;
    }
 
    // Now size is made zero
    // and we loop through all the nodes in the original bucket list(temp)
    // and insert it into the new list
    size = 0;
    numBuckets *= 2;
 
    for (int i = 0; i < temp.size(); i++) {
        // head of the chain at that index
        MapNode* head = temp[i];
 
        while (head != NULL) {
            int key = head->key;
            int val = head->value;
 
            // calling the insert function for each node in temp
            // as the new list is now the bucketArray
            insert(key, val);
            head = head->next;
        }
    }
 
    std::cout << "***Rehashing Done***\n" << std::endl;
}
};
 
int main() {
Map map;
// Inserting elements
map.insert(1, 1);
map.insert(2, 2);
map.insert(3, 3);
map.insert(4, 4);
map.insert(5, 5);
map.insert(6, 6);
map.insert(7, 7);
map.insert(8, 8);
map.insert(9, 9);
map.insert(10, 10);
 
return 0;
}

Output: 

HashMap created
Number of pairs in the Map: 0
Size of Map: 5
Default Load Factor : 0.75

Pair(1, Geeks) inserted successfully.

Current Load factor = 0.2
Number of pairs in the Map: 1
Size of Map: 5

Current HashMap:
key = 1, val = Geeks

Pair(2, forGeeks) inserted successfully.

Current Load factor = 0.4
Number of pairs in the Map: 2
Size of Map: 5

Current HashMap:
key = 1, val = Geeks
key = 2, val = forGeeks

Pair(3, A) inserted successfully.

Current Load factor = 0.6
Number of pairs in the Map: 3
Size of Map: 5

Current HashMap:
key = 1, val = Geeks
key = 2, val = forGeeks
key = 3, val = A

Pair(4, Computer) inserted successfully.

Current Load factor = 0.8
0.8 is greater than 0.75
Therefore Rehashing will be done.


***Rehashing Started***

Pair(1, Geeks) inserted successfully.

Current Load factor = 0.1
Number of pairs in the Map: 1
Size of Map: 10

Pair(2, forGeeks) inserted successfully.

Current Load factor = 0.2
Number of pairs in the Map: 2
Size of Map: 10

Pair(3, A) inserted successfully.

Current Load factor = 0.3
Number of pairs in the Map: 3
Size of Map: 10

Pair(4, Computer) inserted successfully.

Current Load factor = 0.4
Number of pairs in the Map: 4
Size of Map: 10


***Rehashing Ended***

New Size of Map: 10

Number of pairs in the Map: 4
Size of Map: 10

Current HashMap:
key = 1, val = Geeks
key = 2, val = forGeeks
key = 3, val = A
key = 4, val = Computer

Pair(5, Portal) inserted successfully.

Current Load factor = 0.5
Number of pairs in the Map: 5
Size of Map: 10

Current HashMap:
key = 1, val = Geeks
key = 2, val = forGeeks
key = 3, val = A
key = 4, val = Computer
key = 5, val = Portal

 

The time complexity of the insert operation is O(1) and the 
Auxilairy space :  O(n)

The time complexity of the rehash operation is O(n) and the 
Auxiliary space: O(n).


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