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Design O(1) random-sampling set
Problem Statement
Design a data structure that supports the following operations, each in expected O(1) time:
insert(x): Adds an elementxto the set.remove(x): Removes an elementxfrom the set.get_random(): Returns a uniformly random element from the current set of present items.
Requirements
- Core Implementation: Detail the algorithms and data structures you would use to achieve the O(1) expected time complexity for all operations.
- Edge Cases: Explain how your design handles specific edge cases, such as deleting the last element from the set or managing "gaps" that might arise from removals.
- Testing Uniformity: Describe a method or strategy to test the uniformity of the
get_random()operation.
Extensions (Discussion)
Discuss potential extensions to your design and their impact on complexity:
- Supporting Duplicates: How would you modify your data structure to allow multiple instances of the same element
x? - Thread-Safety: How would you make your data structure thread-safe for concurrent access?
AI interview prep
Core dilemma
Achieving O(1) expected time for both arbitrary element removal and uniform random sampling, which typically have conflicting data structure requirements.
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Design O(1) random-sampling set
Problem Statement
Design a data structure that supports the following operations, each in expected O(1) time:
insert(x): Adds an elementxto the set.remove(x): Removes an elementxfrom the set.get_random(): Returns a uniformly random element from the current set of present items.
Requirements
- Core Implementation: Detail the algorithms and data structures you would use to achieve the O(1) expected time complexity for all operations.
- Edge Cases: Explain how your design handles specific edge cases, such as deleting the last element from the set or managing "gaps" that might arise from removals.
- Testing Uniformity: Describe a method or strategy to test the uniformity of the
get_random()operation.
Extensions (Discussion)
Discuss potential extensions to your design and their impact on complexity:
- Supporting Duplicates: How would you modify your data structure to allow multiple instances of the same element
x? - Thread-Safety: How would you make your data structure thread-safe for concurrent access?