Package: cayleyR 0.2.5

Basic Permutation Operations (C++) | shift_left(state, coords = NULL) | shift_right(state, coords = NULL) | reverse_prefix(state, k, coords = NULL) | shift_left_simple(state) | shift_right_simple(state) | reverse_prefix_simple(state, k) | apply_operations(state, operations, k, coords = NULL, compute_coords = TRUE) | openmp_threads() | Cycle Analysis | get_reachable_states(start_state, allowed_positions, k, verbose = FALSE) | get_reachable_states_light(start_state, allowed_positions, k) | analyze_top_combinations(top_combos, start_state, k) | Pathfinding | bidirectional_bfs(n, state1, state2, max_level, moves, k) | find_path_iterative(start_state, final_state, k, moves, combo_length, n_samples, n_top, max_iterations, potc, ptr, opd, reuse_combos, keep_states, one_sided, distance_method, sort_by, verbose) | find_path_bfs(start_state, final_state, k, ...) | sparse_bfs(start_state, k, n_hubs, n_random, max_levels) | reconstruct_bfs_path(bfs_result, target_key) | short_path_bfs(path, start_state, k, depth = 5) | cycle_shortcut(path, start_state, k, n_points = 20, moves, combo_length = 20, n_samples = 200, n_top = 5, sort_by, max_cycle_len = 20000, n_threads = NULL, verbose = FALSE) | human_algorithm(start_state, final_state = NULL, k = 4L, simplify = TRUE) | human_algorithm_cpp(start_state, k, max_ops, final_rotate) (internal) | human_algorithm_to(start_state, target_state = NULL, k = 4, simplify = TRUE) | human_phase1_rank(state, k = 4, sorted = TRUE) | human_phase1_navigate(state, k = 4, max_steps = 2000, trace = FALSE) | run_length(state) | find_best_match_human(states, target, k) | Combination Search | find_best_random_combinations(moves, combo_length, n_samples, n_top, start_state, k, sort_by) | Path Utilities | invert_path(path) | short_position(allowed_positions, n) | validate_and_simplify_path(path_candidate, start_state, final_state, k) | State Processing & Distance | calculate_differences(start_state, reachable_states_start, method, use_gpu) | select_unique(df) | check_duplicates(df1, df2) | manhattan_distance(start_state, target_state) | breakpoint_distance(start_state, target_state) | save_bridge_states(bridge_states, filename) | filter_middle_states(data, skip_first, skip_last) (internal) | find_best_match_state(target_state, reachable_states, method, use_gpu) (internal) | select_new_state(target_all, opposite_state, method) (internal) | cayley_distance_methods() | cayley_distance(method) | State Indexing | add_state_keys(states_df, new_states, v_cols) (internal) | create_hash_index(states_df) (internal) | State Store (C++ Backend) | create_state_store(perm_length, init_capacity) | state_store_size(xp) | state_store_unique_count(xp) | state_store_perm_length(xp) | store_add_from_df(store, df, cycle_val) | store_get_state(store, idx) | store_get_meta(store, idx) | store_find_intersections(store_a, store_b) | store_lookup(store, state) | store_find_best_match(store, target, candidate_indices) | store_filter_middle(store, target_cycle, skip_first, skip_last) | store_set_opd(store, target_cycle, combos) | store_clear_opd(store) | store_combos_for_state(store, state, target_cycle) | store_to_dataframe(store) | store_reconstruct_path(store, bridge_states, target_state, target_cycle, target_combo) | store_analyze_combos(store, top_combos, start_state, k, cycle_val) | store_analyze_combos_gpu(store, top_combos, start_state, k, cycle_val) | store_clear(store) | store_collect_ops(store, target_cycle, target_combo, end_step) | state_store_indices_for_cycle(xp, target_cycle) | Graph Metrics | cayley_bfs_full(start_state, k, moves = c("L", "R", "X")) | cayley_graph_diameter(start_state, k, moves, method = c("all_pairs", "from_start"), max_pairs = Inf, verbose = FALSE) | Celestial Coordinates | convert_LRX_to_celestial(nL, nR, nX) | calculate_angular_distance_z(result1, result2) | calculate_midpoint_z(coords1, coords2) | find_closest_to_coords(reachable_states, target_coords, v_cols) | GPU Acceleration (optional, requires ggmlR) | cayley_gpu_available() | cayley_gpu_init(device = 0, force = FALSE) | cayley_gpu_status() | cayley_gpu_free() | apply_operations_batch_gpu(states_matrix, operations, k) | manhattan_distance_matrix_gpu(states1, states2, batch_size = 256) | calculate_differences_gpu(start_state, states_matrix) (internal) | build_permutation_matrix(op, n, k) (internal) | compose_permutation_matrix(operations, n, k) (internal) | Utilities | convert_digits(s) | generate_state(n, k, n_moves, moves, max_attempts) | generate_unique_states_df(n, n_rows) | has_data_table() (internal) | Intersection Processing (internal) | reconstruct_full_path(reachable_states, start_state, target_state, target_cycle, target_combo, v_cols) | process_start_intersection(intersection_state, reachable_states_final, bridge_states_final, final_index, v_cols) | process_final_intersection(intersection_state, reachable_states_start, bridge_states_start, start_index, v_cols) | process_intermediate_intersection(intersection_state, reachable_states_start, reachable_states_final, bridge_states_start, bridge_states_final, start_index, final_index, v_cols) | State Search | find_combination_in_states(reachable_states_start, search_state)

Notation | Phase 1: build 1…12 | Why stop at 12 rather than 16 | Phase 2: sort the eight-tile tail (13…20) | Sequence A | Sequence B | Parity: why it sometimes refuses to finish | Finishing | Differences from the common description | Scope