Core Concepts
Sierpinski 삼각형 데이터 구조는 배열 작업을 효율적으로 수행합니다.
Abstract
Abstract:
Fenwick tree: Efficient for updating values and calculating prefix sums in O(log2 N) time.
Novel data structure: Sierpinski triangle-like structure, O(log3 N) time.
Connection to quantum computing for optimality.
Introduction: Fenwick Trees:
Binary tree for storing frequencies and cumulative frequency tables.
Applications in quantum simulation of fermionic systems.
Useful for updating data in an array and calculating prefix sums efficiently.
Construction of the Sierpinski Tree:
Directed tree with N nodes, algorithm for construction.
Full tree with 3k nodes, algorithm for other values of N.
Recursive definition of the tree's elements.
Array Update and Prefix Sum Complexity:
Time complexity of O(log3 N) for operations.
Definitions and lemma for increasing function of N.
Theorem proving complexity bounds.
Discussion:
Comparison with Fenwick tree in quantum computing.
Optimality of Sierpinski tree structure.
Potential improvements for reducing average weight.
Acknowledgements and References.
Stats
Fenwick tree는 값을 업데이트하고 접두사 합을 계산하는 데 사용됩니다.
Sierpinski 삼각형 데이터 구조는 O(log3 N) 시간에 작업을 수행합니다.
연구는 양자 컴퓨팅과의 연결을 강조합니다.
Quotes
"The Fenwick tree has the advantage of performing both operations in O(log2 N) time."
"We will now describe a novel data structure similar to the Fenwick tree, but with a structure resembling the Sierpinski triangle."