An algorithm for finding the number of shortest routes on square lattices
Vites Longani · Journal of Discrete Mathematical Sciences and Cryptography · 2007
Given an m×n square lattice. The number of shortest routes from lower left corner of the lattice to the upper right corner is . Usually, when some line segments of the lattice are deleted, the number of shortest routes could be obtained by using inclusion-exclusion principle. However, when the number of deleted segments increases, the amount of calculation could be quite laborious. In this paper we propose a simple algorithm for obtaining the number of shortest routes that require much less calculation when the number of deleted segments increases.