三变量Frobenius问题的快速算法
A fast algorithm for the Frobenius problem in three variables
AI总结：
本文针对三变量Frobenius问题提出一种新算法，其基础与Tripathi算法相同但实现显著不同，并证明其最坏情况时间复杂度同样为A的对数函数。
摘要：
给定三个正整数构成的集合 {a1, a2, a3}，记作 A，三变量 Frobenius 问题是指找出不能表示为以下形式的最大整数，其中 x1、x2 和 x3 为非负整数：x1*a1 + x2*a2 + x3*a3。已知最快的三变量 Frobenius 问题求解算法由 H. Greenberg 于 1988 年提出，其最坏情况时间复杂度是 A 的对数函数。2017 年，A. Tripathi 提出了另一个求解同一问题的算法。本文提出一个算法，其基础与 Tripathi 的算法相同。然而，本文提出的算法与 Tripathi 的算法有显著不同，我们证明其最坏情况时间复杂度也是 A 的对数函数。
英文摘要：
Given a set of three positive integers {a1, a2, a3}, denoted A, the Frobenius problem in three variables is to find the greatest integer which cannot be expressed in the following form, where x1, x2 and x3 are non-negative integers: x1*a1 + x2*a2 + x3*a3 The fastest known algorithm for solving the three variable case of the Frobenius problem was invented by H. Greenberg in 1988 whose worst case time complexity is a logarithmic function of A. In 2017 A. Tripathi presented another algorithm for solving the same problem. This article presents an algorithm whose foundation is the same as Tripathi's. However, the algorithm presented here is significantly different from Tripathi's and we show that its worst case time complexity also is a logarithmic function of A
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