一种贪心的丢弃数字的算法

IF 1.1 3区计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Journal of Functional Programming Pub Date : 2021-01-24 DOI:10.1017/S0956796821000198

R. Bird, Shin-Cheng Mu

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引用次数: 1

摘要

考虑下面的难题:给定一个数字，去掉k位，使得到的数字尽可能大。我们采用了各种技术来推导出这个难题的线性时间解:我们通过谓词逻辑证明贪婪算法的结构，使用依赖类型的证明助手给出贪婪条件的建设性证明，并通过方程推理计算贪婪步骤以及最终的线性时间优化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A greedy algorithm for dropping digits

Abstract Consider the following puzzle: given a number, remove k digits such that the resulting number is as large as possible. Various techniques are employed to derive a linear-time solution to the puzzle: we justify the structure of a greedy algorithm by predicate logic, give a constructive proof of the greedy condition using a dependently typed proof assistant and calculate the greedy step as well as the final, linear-time optimisation by equational reasoning.

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来源期刊

Journal of Functional Programming 工程技术-计算机：软件工程

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Functional Programming is the only journal devoted solely to the design, implementation, and application of functional programming languages, spanning the range from mathematical theory to industrial practice. Topics covered include functional languages and extensions, implementation techniques, reasoning and proof, program transformation and synthesis, type systems, type theory, language-based security, memory management, parallelism and applications. The journal is of interest to computer scientists, software engineers, programming language researchers and mathematicians interested in the logical foundations of programming.