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A C++ program for fast computation of the number of paths in a grid graph.

This program computes the number of corner-to-corner simple paths and the number of simple cycles in a grid graph. It have extended integer sequences A007764 and A140517 in November 2013. Technical details are shown in the following report:

H. Iwashita, Y. Nakazawa, J. Kawahara, T. Uno, and S. Minato, "Efficient Computation of the Number of Paths in a Grid Graph with Minimal Perfect Hash Functions", Technical Report TCS-TR-A-13-64, Division of Computer Science, Graduate School of Information Science and Technology, Hokkaido University, 2013. (pdf)


Modern Linux or Linux-like environment including:

  • GCC with C++11 and OpenMP features
  • GNU Make

This program is tested only on 64-bit Linux.


Just type make in the source directory to get both single-thread version (ggcount_single) and multi-thread version (ggcount_multi) of the executable program. Please check the Makefile if necessary.


$ ./ggcount_single [ -c ] [ -h ] columns [ rows ] [ %modulus ]

$ ./ggcount_multi [ -c ] [ -h ] columns [ rows ] [ %modulus ]

$ ./ [ -c ] [ -h ] size

Arguments columns and rows specify the horizontal and vertical sizes of a grid graph. The latter one can be ommited if they are the same.

When option -c is given, it computes the number of cycles in the graph; otherwise it computes the number of paths connecting opposite corners of the graph. Option -h is a switch to count Hamiltonian paths/cycles.

Optional argument %modulus makes the program use modular arithmetic rather than bignum arithmetic. The modulus value must not be greater than 64-bit unsigned integer. is the Perl utility that repeats executution of ./ggcount_multi with coprime %modulus values and computes the final answer from those results using Chinese remainder theorem. It only supports square grid graphs.

See also