Overview of binomial pyramids based on different number systems

Vasiliy K. Gulakov, Konstantin V. Gulakov


The article provides an overview of binomial data structures based on various number systems. This approach improves the performance of operations on binomial pyramids, such as increasing and decreasing the number of elements, inserting elements, merging pyramids. Various number systems are considered: binary, redundant, nonzero, regular, oblique, and their combinations. The structure of binomial pyramids is well described by a binary number equal to the number of elements in the pyramid. By working with these numbers, you can efficiently perform various operations on pyramidal structures. The problem with representing a binary number is that increasing or decreasing the number by one can cause many of the digits of the number to cascade, which affects the result in the worst case. In order to get away from this situation, other number systems are used. The article briefly discusses various number systems, their combinations and their capabilities.

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