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Questions and Answers
What is the optimal load factor range for hash tables in general?
What is the optimal load factor range for hash tables in general?
In the given Python implementation of a hash table using collections.defaultdict, what is the default value for a new key?
In the given Python implementation of a hash table using collections.defaultdict, what is the default value for a new key?
Which operation in a hash map allows you to check if a key is present in the map?
Which operation in a hash map allows you to check if a key is present in the map?
What is the time complexity of adding a key-value pair to a hash map, assuming no collisions?
What is the time complexity of adding a key-value pair to a hash map, assuming no collisions?
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In the quadratic probing collision resolution technique, the bucket is incremented by what function?
In the quadratic probing collision resolution technique, the bucket is incremented by what function?
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What is a hashing function used for?
What is a hashing function used for?
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Which method is commonly used for resolving collisions in hash maps?
Which method is commonly used for resolving collisions in hash maps?
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What is the purpose of understanding load factors in hash maps?
What is the purpose of understanding load factors in hash maps?
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Which factor helps minimize collisions in a hash map?
Which factor helps minimize collisions in a hash map?
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What does 'Separate Chaining' refer to in the context of collision resolution?
What does 'Separate Chaining' refer to in the context of collision resolution?
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How does a more balanced hashing function benefit a hash map?
How does a more balanced hashing function benefit a hash map?
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Study Notes
Hash Maps
Hash maps, also known as hash tables or dictionaries, are data structures used to store key-value pairs efficiently by using a hash function to compute an index into an array of buckets. This allows for quick retrieval times due to the mapping of keys to indices. There are several important aspects to consider when working with hash maps, including the choice of hashing function, handling collisions, understanding load factors, implementing hash tables, and operating on hash tables.
Hashing Function
A hashing function is a mathematical algorithm that takes a variable size input (the key) and converts it into a fixed size output (a hash code), which is usually an integer between 0 and n-1. In Python, the built-in hash() function is commonly used as the hashing function. The more balanced the hash function is, the more evenly the keys will be distributed across the array of buckets, which helps to minimize collisions and improve the overall performance of the hash map.
Collision Resolution
When two keys hash to the same index, a situation known as a collision occurs. There are several methods to resolve collisions:
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Chaining: This is the most common method for collision resolution. Each bucket in the hash table is a linked list, allowing multiple values to be stored at the same index.
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Separate Chaining: Each bucket in the hash table contains a separate hash table, which can store multiple values.
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Linear Probing: When a collision occurs, the bucket is incremented by a fixed number (called the probe sequence) until an empty slot is found.
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Quadratic Probing: Similar to linear probing, but the bucket is incremented by a quadratic function instead of a linear function.
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Double Hashing: This is a combination of linear probing and quadratic probing, where two hash functions are used—one for the hash table index and one for the probe sequence.
Load Factor
The load factor of a hash map is a measure of how full the hash map is. It is calculated by dividing the number of stored key-value pairs by the total number of buckets in the hash map. A load factor of 1 means that the hash map is completely full.
A load factor between 0.7 and 0.9 is generally considered optimal for hash tables, as it provides a good balance between memory usage and retrieval time. However, this may vary depending on the specific use case and hash function used.
Hash Table Implementation
A hash table implementation in Python can be achieved using the collections.defaultdict class, which automatically initializes new values using a given default value. Here's an example:
from collections import defaultdict
h = defaultdict(lambda: 0)
h = 10
h = 20
This creates a hash table where the default value for each key is 0. The key-value pair (1, 10) is added to the hash table, and the key-value pair (2, 20) overwrites the previous key-value pair for key 2.
Hash Map Operations
Hash maps support several operations:
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Adding a key-value pair: You can add a key-value pair to a hash map using the
add()method. For example,h.add(1, 10)adds the key-value pair (1, 10) to the hash map. -
Removing a key-value pair: You can remove a key-value pair from a hash map using the
pop()method. For example,h.pop(1)removes the key-value pair (1, 10) from the hash map. -
Getting a value by key: You can retrieve a value from a hash map using the
get()method. For example,h.get(1)returns the value 10 for key 1. -
Checking if a key is present: You can check if a key is present in a hash map using the
key()method. For example,h.key(1)returns True if key 1 is present in the hash map. -
Iterating over key-value pairs: You can iterate over the key-value pairs in a hash map using the
items()method. For example,for k, v in h.items():prints the key-value pairs (1, 10) and (2, 20).
Hash maps are a powerful and efficient data structure for storing key-value pairs, and understanding their inner workings is essential for making the most of them.
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Description
Learn about key concepts such as hashing functions, collision resolution methods like chaining and probing, load factors, hash table implementations in Python using defaultdict, and operations like adding, removing, getting values, checking key presence, and iterating over key-value pairs in hash maps.
