Hash Dictionary

A Hash Dictionary is a data structure that uses hashing to store key-value pairs. Hashing enables constant-time complexity for search, insertion, and deletion operations on average, making hash dictionaries ideal for scenarios with large datasets and frequent updates.

Efficiency of Hash Dictionaries

Hash dictionaries offer O(1) average time complexity for search, insert, and delete operations. However, in rare cases, collisions can lead to O(n) time complexity.

Key Concepts

• Hashing: A process that converts a key into an integer index in an array, allowing constant-time access.
• Dictionary Interface: The Dictionary interface can be implemented to use a hash map as the underlying structure for managing key-value pairs.

Operations on a Hash Dictionary

1. Inserting a Value

To insert a value, the key is hashed to produce an index. If the index is empty, the key-value pair is stored. If a collision occurs, open addressing or chaining resolves the conflict.

Pseudocode

function insert(hashTable, key, value):
    index = hash(key)
    if hashTable[index] is empty:
        hashTable[index] = new Entry(key, value)
    else:
        handleCollision(hashTable, index, key, value)

Time Complexity

• Average-case: O(1), as each key is mapped to a unique index.
• Worst-case: O(n), if many collisions occur.

2. Searching for a Value

To search for a value, the key is hashed to find the index. If there’s no entry at that index, the key isn’t in the dictionary. If a collision resolution method is used, it must be accounted for.

Pseudocode

function search(hashTable, key):
    index = hash(key)
    if hashTable[index] contains key:
        return hashTable[index].value
    else:
        return resolveCollision(hashTable, index, key)

Time Complexity

• Average-case: O(1).
• Worst-case: O(n), with many collisions.

3. Removing a Value

To remove an entry, hash to locate the index, then mark the entry as deleted. Collision resolution methods ensure any linked entries are retrievable.

Pseudocode

function remove(hashTable, key):
    index = hash(key)
    if hashTable[index] contains key:
        hashTable[index] = null  // Or mark as deleted
    else:
        resolveRemoveCollision(hashTable, index, key)

Time Complexity

• Average-case: O(1).
• Worst-case: O(n).

Algorithm Complexity

• Insertion: O(1) on average, due to hashing.
• Search: O(1) on average, due to direct index access.
• Deletion: O(1) on average.

Limitation of Hash Dictionaries

Hash dictionaries have O(1) average performance, but poor hash functions and collision handling can degrade performance to O(n).

Example Code in Java

Here’s how a hash dictionary can be implemented to support the Dictionary interface:

public class HashDictionary<K, V> implements Dictionary<K, V> {
    private static final int INITIAL_CAPACITY = 16;
    private Entry<K, V>[] table;
    private int size;
 
    public HashDictionary() {
        table = new Entry[INITIAL_CAPACITY];
        size = 0;
    }
 
    private int hash(K key) {
        return (key.hashCode() & 0x7fffffff) % table.length;
    }
 
    public V insert(K key, V value) {
        int index = hash(key);
        if (table[index] == null) {
            table[index] = new Entry<>(key, value);
        } else {
            Entry<K, V> current = table[index];
            while (current != null) {
                if (current.getKey().equals(key)) {
                    V oldValue = current.getValue();
                    current.setValue(value);
                    return oldValue;
                }
                if (current.next == null) break;
                current = current.next;
            }
            current.next = new Entry<>(key, value);
        }
        size++;
        return value;
    }
 
    public V search(K key) {
        int index = hash(key);
        Entry<K, V> entry = table[index];
        while (entry != null) {
            if (entry.getKey().equals(key)) {
                return entry.getValue();
            }
            entry = entry.next;
        }
        return null;
    }
 
    public V remove(K key) {
        int index = hash(key);
        Entry<K, V> current = table[index];
        Entry<K, V> previous = null;
        while (current != null) {
            if (current.getKey().equals(key)) {
                if (previous == null) {
                    table[index] = current.next;
                } else {
                    previous.next = current.next;
                }
                size--;
                return current.getValue();
            }
            previous = current;
            current = current.next;
        }
        return null;
    }
 
    private static class Entry<K, V> {
        private final K key;
        private V value;
        private Entry<K, V> next;
 
        Entry(K key, V value) {
            this.key = key;
            this.value = value;
            this.next = null;
        }
 
        public K getKey() { return key; }
        public V getValue() { return value; }
        public void setValue(V value) { this.value = value; }
    }
}

Summary

A hash dictionary provides fast search, insertion, and deletion with an average O(1) complexity due to direct hashing. However, performance depends on a good hash function and effective collision handling. Hash tables are ideal for large datasets where efficient updates are crucial.