gijs-pennings / kenken-solver

Fast backtracking solver for KenKen puzzles

KenKen solver

This is a (somewhat optimized) backtracking solver in C++11 for KenKen puzzles, also known as Calcudoku. It is licensed under the ISC license.

The puzzle input is read from a file (path given as argument) and its solution is printed to stdout. No validity or uniqueness checks are performed. The format is easily determined from the available examples, noting that cages with the subtraction or division operator must be of size 2.

Timing information is printed to stderr. Only the time spent backtracking is measured; I/O is ignored, for example. On my high-end machine from 2014, the running time ranges from <1μs to ~2.2s. 'Average' puzzles (6x6) are solved in ≪1ms.

Some implementation details

• Each cage stores its intermediate result (current), i.e. the result of the calculation involving all non-empty cells. This way, new values can be tested more efficiently, without querying other cage cells.
• Each column, row, and cage keeps a list of candidates, i.e. values that are not proven to be illegal. This list is stored as a bitset (a simple int suffices) where the ith bit is set if i is a possible value. This makes it possible to take intersections and find the 'next' candidate in O(1) time, using the & operator and __builtin_ctz intrinsic (count trailing zeros) respectively.
• Using candidates.py, bitsets for all cage configurations of size ≤5 are precomputed (larger cages are rare and therefore not worth the additional space). Here, a grid size of 9 and the 'worst' cage shape (i.e. a staircase, which permits the most duplicates) is assumed. For smaller grids, illegal candidates are simply ignored. Although this is sometimes suboptimal (e.g. in a *6 cage of size 2, the value 1 is possible in a grid of size 9, but not in a grid of size 3), grids of size ≤8 are solved almost instantly anyway.