摘要： 针对目前求解0-1 背包问题算法的优缺点，开发了一种新的非递归算法。从计算0-1 背包问题最优值的递归方程出发，使用形式推导技术及序列抽象数据类型。在开发出循环不变式的同时，归纳得到用抽象程序设计语言Apla描述的非递归算法，并形式化证明了其正确性，在相关工具及部件库的支持下进一步得到C++程序。理论分析和实验结果表明，该算法的时间耗费受背包容量变化的影响很小，是一种有效的方案。

关键词: 0-1背包问题, 非递归算法, 循环不变式

Abstract: According to the features of the existed algorithms of 0-1 knapsack problem, a new non-recursive algorithm is formally derived in the paper. From the recursive equations for computing optimal value of 0-1 knapsack problem, by employing the formal derivation technique and abstract data type, sequence, achieves loop invariant and non-recursive Apla abstract algorithm. The Apla algorithm is verified formally, and further transformed to C++ program by related tool and component library. The theoretical analysis and experimental results show that the time complexity of new algorithm is little affected by bag capacity.

Key words: 0-1 knapsack problem, non-recursive algorithm, loop invariant

中图分类号: 

• TP311