cayleyR (version 0.1.0)

find_best_random_combinations: Find Best Random Operation Sequences

Description

Generates random sequences of operations and evaluates their cycle lengths to find sequences that produce the longest cycles in the Cayley graph. Useful for discovering interesting operation sequences in permutation puzzles.

Usage

find_best_random_combinations(
  moves,
  combo_length,
  n_samples,
  n_top,
  start_state,
  k
)

Value

Data frame with columns:

combination

String representation of the operation sequence

total_moves

Cycle length for this sequence

unique_states_count

Number of unique states visited in the cycle

Arguments

moves

Character vector of allowed operation symbols (e.g., c("1", "2", "3") or c("L", "R", "X"))

combo_length

Integer, length of each operation sequence to test

n_samples

Integer, number of random sequences to generate and test

n_top

Integer, number of top results to return (sorted by cycle length)

start_state

Integer vector, initial permutation state

k

Integer, parameter for reverse operations

Details

The returned data frame reachable_states_df has the following structure:

step | state           | operation
-----|-----------------|----------
1    | 1 2 3 4 5...    | 1         <- INITIAL, operation="1" (next operation)
2    | 2 3 4 5 6...    | 1         <- after applying op1 from row 1
3    | 3 4 5 6 7...    | 2         <- after applying op1 from row 2
4    | 4 5 6 7 8...    | 3         <- after applying op2 from row 3
5    | 5 6 7 8 9...    | 1         <- after applying op3 from row 4
...
20   | 20 1 2 3 4...   | 1         <- after applying all ops from rows 1-19
NA   | 1 2 3 4 5...    | NA        <- after applying op1 from row 20 = initial

Examples

# Find top 10 sequences from 100 random samples
best <- find_best_random_combinations(
  moves = c("1", "2", "3"),
  combo_length = 10,
  n_samples = 100,
  n_top = 10,
  start_state = 1:10,
  k = 4
)
print(best)

# Quick search with letter codes
top5 <- find_best_random_combinations(
  moves = c("L", "R", "X"),
  combo_length = 5,
  n_samples = 100,
  n_top = 5,
  start_state = 1:10,
  k = 3
)
print(top5)