Implements algorithms for analyzing Cayley graphs of permutation groups, with a focus on the TopSpin puzzle and similar combinatorial problems. Provides methods for cycle detection, state space exploration, and finding optimal operation sequences in permutation groups generated by shift and reverse operations.
library(cayleyR)# Basic operations
shift_left(1:5)
reverse_prefix(1:10, k = 4)
# Cycle analysis for TopSpin 20-4
result <- get_reachable_states(
start_state = 1:20,
allowed_positions = c("L", "X"),
k = 4
)
Yuri Baramykov lbsbmsu@mail.ru
Basic permutation operations: cyclic left/right shifts, prefix reversal
Cycle analysis: find cycles in Cayley graphs with detailed state information
Sequence optimization: search for operation sequences with maximum cycle length
Fast processing: lightweight version for batch testing of combinations
Basic Operations:
shift_left - Cyclic left shift
shift_right - Cyclic right shift
reverse_prefix - Reverse first k elements (turnstile operation)
Analysis Tools:
apply_operations - Apply sequence of operations
get_reachable_states - Full cycle analysis with state tracking
get_reachable_states_light - Lightweight cycle detection
Optimization:
find_best_random_combinations - Find best random sequences
After installation from GitHub, visit: https://github.com/Zabis13/cayleyR
TopSpin puzzle: https://www.jaapsch.net/puzzles/topspin.htm
Cayley graphs: https://en.wikipedia.org/wiki/Cayley_graph
Useful links: