渡河问题的矩阵表示与迭代算法

Matrix Representation of the River Crossing Problem and the Iterative Algorithm

为解决较复杂的渡河问题,提出用构建岸态矩阵来表示求解过程中左右河岸上同一时刻的人员组合状态;并引入表征小船上人员状况的摆渡算子,则问题的求解过程就可用从始点状态向着目标状态的逐次迭代来表示;而约束条件则由岸态矩阵的生成及算子的选取来实现。同时对运载能力n的取值范围作了较深入的讨论,并用图解算例加以验证。

In order to solve the complicated river crossing problem,this paper suggests building a shore state matrix to show the combination state of synchronous personnel around the river bank.The paper also introduces a ferry operator to indicate the staff position on the boat.Therefore,the problem-solving process can be shown by the successive iteration from the starting point state towards the target state,and the constraints can be achieved by shore state matrix generation and operator selection.Moreover,this paper gives a further discussion of the range of the carrying capacity of n and illustrates it with graphic examples.