![]() ![]() Splay Trees were used as cumulative frequency tables in order to maintain Dynamic arithmetic data compression. Splay Trees were used in order to make Distribution Systems Evaluation simpler. W Jones in his work proposes the use of splay trees in arithmetic data compression. Splay Trees have also been used in Data Compression Algorithms. Wei Zhou, Zilong Tan, Shaowen Yao, and Shipu Wang proposed their work on Efficient Resource Location in P2P Networks. Dynamic Scheme for Packet Classification was done by Nizar Ben Neji and Adel Bouhoula. Splay Trees have been found in the field of networking as well. Subrata Mondal used Splay Trees in Cache replacement Algorithms. Martel have described in their paper some applications splay trees are most suited for, such as faster query execution using better cache management. Because of its insert and search rules Splay Trees have been used for this purpose. ![]() Splay Tree is a data structure which is ideal for caching. The remainder of the paper is structured in the following manner: Section II describes the past work done in the field, Section III discusses the mathematical and computational foundations underlying our method, Section IV describes our framework as well as our algorithm, Section V contains an analysis of the results in comparison to other techniques, section VI describes how this technique specifically excels in the expansion of binomial expressions, and finally Section VII offers conclusions and direction for future work. ![]() Finally, we perform a comparative analysis of the performance of our technique alongside conventional arrays and the Binary Search Tree. Furthermore, we discuss memory and space optimizations that have been implemented to further enhance the performance of the Splay Tree. In this paper, we explore a novel method of using a Splay Tree to compute binomial coefficients, as opposed to using an array. The array implementation of binomial coefficients is a classic dynamic programming technique. Therefore, owing to the cascading benefits, it is important to find an efficient method of computing binomial coefficients. Additionally, binomial coefficients are used in multiplication of large numbers using binomial expansion, and are used in generating all possible permutations/combinations of sets. Binomial coefficients have many specific and generic applications in mathematics as well as in computation, including computation of Catalan numbers and in statistics. ![]()
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