6/4-6/10 CareerCup 8.2

Imagine a robot sitting on the upper left hand corner of an NxN grid. The robot can only move in two directions: right and down. How many possible paths are there for the robot?
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Imagine certain squares are “off limits”, such that the robot can not step on them. Design an algorithm to get all possible paths for the robot.

https://gist.github.com/3140349

楼上的方法只能解n*n的矩阵，第五版书9.2是求解X*Y的矩阵。我写了个小程序你们可以看一下。
https://gist.github.com/4052672

从（0,0）点到任意一点（m,n），
可以选择的路径数是：choose m from（m+n）items。

从（0,0）点到任意一点（m,n），
可以选择的路径数是：choose m from（m+n）items。