Load Factor and Rehashing
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, 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, 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:
As the name suggests, rehashing means hashing again. Basically, when the load factor increases to more than its pre-defined value (default value of load factor is 0.75), the complexity increases. So to overcome this, the size of the array is increased (doubled) and all the values are hashed again and stored in the new double sized array to maintain a low load factor and low complexity.
Why rehashing?
Rehashing is done because whenever key value pairs are inserted into the map, the load factor increases, which implies that the time complexity also increases as explained above. This might not give the required time complexity of O(1).
Hence, rehash must be done, increasing the size of the bucketArray so as to reduce the load factor and the time complexity.
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 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(); } } 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(); } } |
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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
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