Hash tables are powerful data structures that store information as key-value pairs. They provide extremely fast access to data, with an average time complexity of O(1) for lookups, insertions, and deletions. The magic behind hash tables is the hash function, which converts each key into a numeric index. This index determines where in the underlying array the value will be stored. For example, when we add the key 'John' with value 25, the hash function might map 'John' to index 2. Similarly, 'Lisa' maps to index 5, and 'Sam' to index 7. This direct mapping is what makes hash tables so efficient for data retrieval.
The heart of a hash table is its hash function. This function takes a key as input and produces an integer that serves as the index in the array. A good hash function should distribute values evenly across the array to minimize collisions. Let's see how this works with a simple example. When we hash the key 'Lisa', we might first convert each character to its ASCII value: L is 76, i is 105, s is 115, and a is 97. Then we add these values together to get 393. Finally, we take the modulo of this sum with the table size, which is 8 in our example. So 393 modulo 8 equals 1, meaning 'Lisa' should be stored at index 1 in our hash table. Common hashing methods include the division method, multiplication method, and universal hashing.
A collision occurs when two different keys hash to the same index. For example, if both 'Lisa' and 'Mary' hash to index 5, we have a collision. There are several strategies to handle this. The first approach is separate chaining, where each array slot contains a linked list of all key-value pairs that hash to that index. When a collision occurs, we simply add the new entry to the linked list. The second approach is open addressing. With linear probing, if a collision occurs at index 5, we try the next slot at index 6. If that's also occupied, we continue to index 7, and so on until we find an empty slot. Other variations include quadratic probing, which checks slots at quadratic distances, and double hashing, which uses a second hash function to determine the step size.
Hash tables support three fundamental operations: insert, search, and delete. In Python, dictionaries are implemented as hash tables. To insert a key-value pair, we simply assign a value to a key, like student_ages['John'] equals 25. To search for a value, we access it using the key: student_ages['Lisa']. And to delete an entry, we use the del keyword: del student_ages['John']. The performance of hash tables is what makes them so valuable. In the average case, all these operations take constant time, O(1), regardless of how many items are in the table. This is because the hash function directly computes the storage location. However, in the worst case, when many keys collide and end up in the same bucket, performance can degrade to O(n), where n is the number of entries. The space complexity is O(n), as we need space proportional to the number of items stored.
To summarize what we've learned about hash tables: They are data structures that store key-value pairs, providing extremely efficient data retrieval. The hash function is the core component that converts keys into array indices. When different keys hash to the same index, we use collision resolution techniques like separate chaining or open addressing. The power of hash tables comes from their performance - insert, search, and delete operations all have an average time complexity of O(1), making them constant-time regardless of the size of the data set. Hash tables are ubiquitous in computer science, used in databases, caches, symbol tables, and as built-in data structures in many programming languages like Python dictionaries, JavaScript objects, and Java HashMaps. Understanding hash tables is essential for efficient algorithm design and implementation.