algorithm analy-sis
Suppose there are n containers with a volume of V, in which the number of articles in the first container is x _ i (i = 1, 2, …, n). The goal of the average loss algorithm is to find a way to make the number of items in each container equal, that is, x_ 1=x_2=…=x_n, while ensuring that the total number of items in all containers is equal, that is, x_ 1+x_2+…+x_n=nV. There are many ways to realize the equal loss algorithm.
One of the basic methods is to divide the goods equally with an extra container. Specifically, if there are n containers with a volume of V and n+/kloc-0 containers with a volume of V' (where V' >: V), the items in the first n containers can be poured into the n+ 1 th container, so that the number of items in each container is equal.
Then, the items in the (n+ 1) th container can be redistributed to the first n containers, so that the number of items in each container is still equal. Repeat this process until the number of items in each container is equal and the total number of items in all containers is equal. ?
Matters needing attention
It should be noted that the average loss algorithm is only applicable to a limited number of containers and articles. If the number of articles is infinite, or the number of containers is infinite, then the average loss algorithm is not applicable. ?
Chapter IX Influence of Arithmetic on Later Generations
Influence on Ancient Mathematics in China
As an important work of China's ancient mathematics, Nine Chapters Arithmetic has played an important role in promoting the development of China's ancient mathematics. The mathematical problems involved in this book are extensive and in-depth, including elementary arithmetic, algebra and geometry. Nine Chapters Arithmetic has laid a solid foundation for the development of ancient mathematics in China by discussing these problems.
Influence on world mathematics
Nine-chapter arithmetic not only had a far-reaching impact on ancient mathematics in China, but also had an important impact on world mathematics. With the spread of China culture, Nine Chapters Arithmetic has also spread to other countries, such as Japan and North Korea.
On the basis of absorbing Nine Chapters of Arithmetic, these countries have developed their own unique mathematical systems in combination with their own actual conditions. Therefore, Nine Chapters Arithmetic has become an important milestone in the history of world mathematics development.
Influence on modern mathematics
Nine Chapters of Arithmetic also has a certain influence on modern mathematics. Although modern mathematics has developed to a higher level, the mathematical problems involved in Nine Arithmetic Chapters are still of great significance.
For example, the discussion of fractions, decimals, multiplication and division in Nine Chapters of Arithmetic provides important enlightenment for the development of modern mathematics. In addition, some problems in Nine Chapters Arithmetic have also been applied to other fields of modern mathematics, such as algebra and geometry.