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:
- K is converted into a small integer (called its hash code) using a hash function.
- 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.
- 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:
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 elementsmap.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;} |
Java
// Java program to implement Rehashingimport 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 Rehashingclass 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#
using System;using System.Collections.Generic;public class Map { private class MapNode { public int key; public int value; public MapNode next; public MapNode(int key, int value) { this.key = key; this.value = value; this.next = null; } } private List<MapNode> buckets; private int size; private int numBuckets; private double DEFAULT_LOAD_FACTOR = 0.75; public Map() { numBuckets = 5; buckets = new List<MapNode>(numBuckets); for (int i = 0; i < numBuckets; i++) { buckets.Add(null); } } private int getBucketInd(int key) { int hashCode = key.GetHashCode(); return (hashCode % numBuckets); } public void insert(int key, int value) { int bucketInd = getBucketInd(key); MapNode head = buckets[bucketInd]; while (head != null) { if (head.key == key) { head.value = value; return; } head = head.next; } MapNode newElementNode = new MapNode(key, value); head = buckets[bucketInd]; newElementNode.next = head; buckets[bucketInd] = newElementNode; size++; double loadFactor = (1.0 * size) / numBuckets; if (loadFactor > DEFAULT_LOAD_FACTOR) { Console.WriteLine(loadFactor + " is greater than " + DEFAULT_LOAD_FACTOR); Console.WriteLine( "Therefore Rehashing will be done."); rehash(); Console.WriteLine("New Size of Map: " + numBuckets); } Console.WriteLine("Number of pairs in the Map: " + size); } private void rehash() { Console.WriteLine("\n***Rehashing Started***\n"); // The present bucket list is made temp List<MapNode> temp = buckets; // New bucketList of double the old size is created numBuckets *= 2; buckets = new List<MapNode>(numBuckets); for (int i = 0; i < numBuckets; i++) { 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; for (int i = 0; i < temp.Count; 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; } } Console.WriteLine("***Rehashing Done***\n"); }}class Program { static void Main(string[] args) { Map map = new 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); }}//This Code is Contributed by NarasingaNikhil |
Javascript
// javascript program to implement Rehashingclass Map { constructor() { // The bucket array where // the nodes containing K-V pairs are stored this.buckets = []; this.numBuckets = 5; // No. of pairs stored - n this.size = 0; // Default loadFactor this.DEFAULT_LOAD_FACTOR = 0.75; for (let i = 0; i < this.numBuckets; i++) { this.buckets.push(null); } } getBucketInd(key) { //Using the inbuilt function from the object class let hashCode = key.toString().hashCode(); // array index = hashCode%numBuckets return (hashCode % this.numBuckets); } insert(key, value) { //Getting the index at which it needs to be inserted let bucketInd = this.getBucketInd(key); // The first node at that index let head = this.buckets[bucketInd]; // First, loop through all the nodes present at that index // to check if the key already exists while (head) { //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 let newElementNode = new MapNode(key, value); //The head node at the index head = this.buckets[bucketInd]; // the new node is inserted // by making it the head // and it's next is the previous head newElementNode.next = head; this.buckets[bucketInd] = newElementNode; this.size++; let loadFactor = (1.0 * this.size) / this.numBuckets; if (loadFactor > this.DEFAULT_LOAD_FACTOR) { console.log(loadFactor + " is greater than " + this.DEFAULT_LOAD_FACTOR); //If the load factor is > 0.75, rehashing is done console.log( "Therefore Rehashing will be done.");//Rehash this.rehash(); console.log("New Size of Map: " + this.numBuckets); } console.log("Number of pairs in the Map: " + this.size); } rehash() { console.log("\n***Rehashing Started***\n");//he present bucket list is made temp let temp = this.buckets; // New bucketList of double the old size is created this.numBuckets *= 2; //Initialised to null this.buckets = []; for (let i = 0; i < this.numBuckets; i++) { this.buckets.push(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 this.size = 0; for (let i = 0; i < temp.length; i++) { let head = temp[i]; while (head) { let key = head.key; let val = head.value;//calling the insert function for each node in temp // as the new list is now the bucketArray this.insert(key, val); head = head.next; } } console.log("***Rehashing Done***\n"); }}class MapNode { constructor(key, value) { this.key = key; this.value = value; this.next = null; }}String.prototype.hashCode = function () { let hash = 0; if (this.length == 0) { return hash; } for (let i = 0; i < this.length; i++) { let char = this.charCodeAt(i); hash = ((hash << 5) - hash) + char; hash = hash & hash; // Convert to 32bit integer } return hash;}let map = new Map();// Inserting elementsmap.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);//Code is contributed by NarasingaNikhil |
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
Auxiliary space : O(n).
The time complexity of the rehash operation is O(n) and the
Auxiliary space: O(n).
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