三向棋盘计数问题分析

Calculating formulas about the three-directional chessboard

定义m×n三向棋盘,利用T路计数原理,对三向棋盘计数问题进行分析,并分别对无障碍、存在障碍点和存在矩形障碍区域的三向棋盘计数问题进行探讨,寻求满足条件的棋盘走法数.文章建立三维坐标系,得到无障碍情形下、分别存在一个障碍点和存在两个障碍点情形下以及存在一个矩形障碍区域情形下两点间最短路线的走法数。

The m x n three-directional chessboard is defined, and its calculating formulas are analyzed by the use of the counting principle of T route. To obtain the appropriate calculating formulas, the calculating of the chessboard is studied under three conditions, namely, having no barriers, having barriers, and having a rectangular obstacle area. The three-dimensional coordinate system was set up, and the calculating formulas of the shortest route between two points were generated under the conditions of having no barrier, having one or two barriers, and having one rectangular obstacle area.