0-1背包问题是经典的组合优化问题与NP完全问题,具有重要的应用价值与理论意义.本文使用PAR(Partition and Recurrence)方法形式化推导了0-1背包问题的高效动态规划算法程序.通过类比分析,该问题的若干变形问题的算法也可推导得到,算法...0-1背包问题是经典的组合优化问题与NP完全问题,具有重要的应用价值与理论意义.本文使用PAR(Partition and Recurrence)方法形式化推导了0-1背包问题的高效动态规划算法程序.通过类比分析,该问题的若干变形问题的算法也可推导得到,算法通过PAR平台的自动生成系统转换成可执行语言程序并运行通过,保证了该类0-1背包问题算法的正确性和可靠性.本文主要的贡献是将PAR方法推广到能处理带约束条件的组合优化类问题,大大扩展了PAR方法的应用范围,为形式化开发高效高可信组合优化类算法开辟了一条新途径.展开更多
Partition-and-Recur (PAR) method is a simple and useful formal method. It can be used to design and testify algo-rithmic programs. In this paper, we propose that PAR method is an effective formal method on solving com...Partition-and-Recur (PAR) method is a simple and useful formal method. It can be used to design and testify algo-rithmic programs. In this paper, we propose that PAR method is an effective formal method on solving combinatorics problems. Furthermore, we formally derive combinatorics problems by PAR method, which cannot only simplify the process of algorithmic program's designing, but also improve its automatization, standardization and correctness. We develop algorithms for two typical combinatorics problems, the number of string scheme and the number of error per-mutation scheme. Lastly, we obtain accurate C++ programs which are transformed by automatic transforming system of PAR platform.展开更多
文摘0-1背包问题是经典的组合优化问题与NP完全问题,具有重要的应用价值与理论意义.本文使用PAR(Partition and Recurrence)方法形式化推导了0-1背包问题的高效动态规划算法程序.通过类比分析,该问题的若干变形问题的算法也可推导得到,算法通过PAR平台的自动生成系统转换成可执行语言程序并运行通过,保证了该类0-1背包问题算法的正确性和可靠性.本文主要的贡献是将PAR方法推广到能处理带约束条件的组合优化类问题,大大扩展了PAR方法的应用范围,为形式化开发高效高可信组合优化类算法开辟了一条新途径.
文摘Partition-and-Recur (PAR) method is a simple and useful formal method. It can be used to design and testify algo-rithmic programs. In this paper, we propose that PAR method is an effective formal method on solving combinatorics problems. Furthermore, we formally derive combinatorics problems by PAR method, which cannot only simplify the process of algorithmic program's designing, but also improve its automatization, standardization and correctness. We develop algorithms for two typical combinatorics problems, the number of string scheme and the number of error per-mutation scheme. Lastly, we obtain accurate C++ programs which are transformed by automatic transforming system of PAR platform.
