Grokking Algorithm Complexity and Big-O
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Hash Table and Set
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Hash Tables and Sets are powerful data structures used for fast data storage and retrieval. Both utilize hashing to map data to unique indexes, allowing for quick access. Sets, often implemented using hash tables, are collections that store unique elements with no particular order.

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Key Characteristics

  • Hash Table:
    • Stores key-value pairs, allowing fast lookups, insertions, and deletions by key.
    • Collisions are resolved through methods like chaining (linked lists) or open addressing (probing).
  • Set:
    • Stores unique values with no specific order.
    • Designed for quick checks of existence (contains) without duplicates.

Basic Operations on Hash Table

Python3
Python3
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Basic Operations on Hash Set

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Python3
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Complexity Analysis

Time Complexity Analysis for Hash Table and Set Operations

OperationHash TableSetExplanation
InsertionAverage O(1), Worst O(n)Average O(1), Worst O(n)Hashes the key and stores the value at the calculated index.
DeletionAverage O(1), Worst O(n)Average O(1), Worst O(n)Finds and removes the key by hashing and locating the index.
Search (contains)Average O(1), Worst O(n)Average O(1), Worst O(n)Checks for the existence of a key by hashing it.
Access by KeyAverage O(1), Worst O(n)N/ADirect lookup of a value using its unique key.
  • Average O(1): For both hash tables and sets, operations are generally constant time due to hashing.
  • Worst Case O(n): When hash collisions occur, operations degrade to O(n) as elements are stored in lists, requiring linear time to access.

Space Complexity for Hash Table and Set

The space complexity for both hash tables and sets is O(n), where n is the number of elements. Each element has an associated hash and bucket, so the space required grows linearly with the number of entries.

  • Space Complexity: O(n), as each entry in a hash table or set requires a unique bucket and additional space for the hash function’s metadata.

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