最省刻度尺设计的组合差集递推算法OA北大核心CSTPCD
A recursive algorithm of combinatorial difference set design for least scale number on ruler
在长度为n(n≥2为正整数)的直尺上最少刻多少个刻度就能度量1到n的所有长度,这便是至今未解决的最省刻度尺问题.阐明了最省刻度尺与极小优美图之间的关系,给出了计算最省刻度尺的所有最省刻度值的组合差集递推算法,得到长度为3～40的最省刻度尺的所有最省刻度值,同时,结合图论模型,给出了长度为41～82的最省刻度尺的最省刻度值.
For a positive integer n≥2,what is the minimum number of ticks to be engraved on an unscaled ruler of length n to measure all lengths from 1 to n.This is an unsolved problem of ruler with least number of scales.This paper clarifies the relationship between ruler with the least number of scales and the minimal graceful graph,and a combined difference recursive algorithm for calculating all the least scale values of ruler with the least number of scales is given.This algorithm calculates that the length is 3 to all the minimum scale values of the most scale-saving ruler of 40,and combined with the graph theory model,the minimum scale values of ruler with least number of scales with lengths from 41 to 82 are given.
唐保祥;任韩
天水师范学院 数学与统计学院,甘肃 天水 741001华东师范大学 数学科学学院,上海 200062
数学
最省刻度尺优美标号极小优美图优美标号算法组合差集递推算法
ruler with least number of scalesgraceful labelingminimal graceful graphgraceful labeling algorithmcombinatorial difference recursive algorithm
《浙江大学学报（理学版）》 2024 (002)
178-185 / 8
国家自然科学基金资助项目(11171114).
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