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Bloom Filter for Efficient Set Membership Testing

Certification: Advanced Level Accuracy: 100% Submissions: 2 Points: 20

Write a Python program to implement a Bloom filter, a space-efficient probabilistic data structure used to test whether an element is a member of a set. A Bloom filter may have false positive matches, but false negatives are impossible. Your task is to implement the BloomFilter class with methods for adding elements and testing membership.

Example 1
    
  
  • Input: 
bloom = BloomFilter(size=10, hash_count=3)
bloom.add("apple")
bloom.add("banana")
print(bloom.contains("apple"))
print(bloom.contains("orange"))
    • 
  
  • Output: 
True
False
    • 
  
  • Explanation: 
    
      
      
    • Step 1: Initialize a Bloom filter with size 10 and 3 hash functions.
      • 
      
    • Step 2: Add "apple" and "banana" to the filter.
      • 
      
    • Step 3: Check if "apple" exists (returns True as expected).
      • 
      
    • Step 4: Check if "orange" exists (returns False as it wasn't added).
      • 
    
    
  
    •
Example 2
    
  
  • Input: 
bloom = BloomFilter(size=100, hash_count=5)
words = ["hello", "world", "python", "programming", "algorithm"]
for word in words:
    bloom.add(word)

tests = ["hello", "python", "java", "bloom", "filter"]
results = [bloom.contains(word) for word in tests]
    • 
  
  • Output: [True, True, False, False, False]
    • 
  
  • Explanation: 
    
      
      
    • Step 1: Initialize a Bloom filter with size 100 and 5 hash functions.
      • 
      
    • Step 2: Add multiple words to the filter.
      • 
      
    • Step 3: Test various words - correctly identifies existing and non-existing members.
      • 
    
    
  
    •
Constraints
    
  
  • 10 ≤ size ≤ 10^6 (size of the bit array)
    • 
  
  • 1 ≤ hash_count ≤ 10 (number of hash functions)
    • 
  
  • Input elements can be any hashable Python object
    • 
  
  • The false positive rate depends on the size of the filter and the number of hash functions
    • 
  
  • Time Complexity: O(k) for add and contains operations, where k is the number of hash functions
    • 
  
  • Space Complexity: O(m) where m is the size of the bit array
    •
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Hint
Solution

Solution Hints

    
  
  • Use a bit array (or a list of booleans) to represent the Bloom filter
    • 
  
  • Implement multiple hash functions using combinations of existing hash functions
    • 
  
  • Handle different types of input objects by converting them to strings first
    • 
  
  • Choose the size and number of hash functions based on the expected number of elements and desired false positive rate
    • 
  
  • Consider using the mmh3 library for efficient hash functions
    •

Steps to solve by this approach:

 Step 1: Initialize the BloomFilter with a bit array and specified number of hash functions
 Step 2: Implement hash functions that generate different hash values for each item
 Step 3: Create the add method that sets bits in the array based on hash values
 Step 4: Implement the contains method that checks if all relevant bits are set
 Step 5: Handle different input types by converting them to strings before hashing

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