cube-hs 0.4.0.1 → 0.5.0.0

raw patch · 7 files changed

+1868/−1668 lines, 7 filesPVP ok

version bump matches the API change (PVP)

API changes (from Hackage documentation)

Files

• CHANGELOG.md +3/−0
• README.md +1/−1
• cbits/cube_amalg.min.cpp +1837/−1659
• cube-hs.cabal +2/−2
• src/Data/Cube.hs +1/−0
• src/Data/Cube/FFI.hs +1/−2
• src/Data/Cube/Internal.hs +23/−4

@@ -1,5 +1,8 @@ # Revision history for cube-hs +0.5.0.0+- Upgrade underlying C++ library to improve performance + ## 0.3.0 -- YYYY-mm-dd  * First version. Released on an unsuspecting world.

@@ -2,7 +2,7 @@  [![Hackage](https://img.shields.io/hackage/v/cube-hs.svg)](https://hackage.haskell.org/package/cube-hs) [![License: MIT](https://img.shields.io/badge/License-MIT-yellow.svg)](LICENSE)-[![GitHub](https://img.shields.io/badge/github-coshz%2Fcube-blue?logo=github)](https://github.com/coshz/cube/tree/master/bindings/haskell)+[![GitHub](https://img.shields.io/badge/github-coshz%2Fcube-blue?logo=github)](https://github.com/coshz/cube/tree/HEAD/bindings/haskell)  A performant and type-safe Rubik's Cube manipulation and permutation library for Haskell. 

@@ -2,1664 +2,1842 @@  * File: cube_amalg.min.cpp  * Project: cube  * Author: coshz <fsinhx@gmail.com>- * Version: 0.4.0- * Date: 2026-09-17- * Homepage: https://github.com/coshz/cube- * License: MIT- *- * Copyright (c) 2026 coshz <fsinhx@gmail.com>. All rights reserved.- */--#include <iostream>-#include <vector>-#include <array>-#include <set>-#include <algorithm>-#include <utility>-#include <numeric>-#include <stdexcept>-#include <cassert>-#include <cstdlib>-#include <regex>-#include <string>-#include <sstream>-#include <filesystem>-#include <chrono>-#include <optional>-#include <type_traits>-#include <string_view>-#include <cmath>-#include <fstream>-#include <limits>-#include <tuple>-#include <stdbool.h>-#include <stdint.h>-#include <format>-#include <cstring>--enum Face       { U1,U2,U3,U4,U5,U6,U7,U8,U9,R1,R2,R3,R4,R5,R6,R7,R8,R9,F1,F2,F3,F4,F5,F6,F7,F8,F9,D1,D2,D3,D4,D5,D6,D7,D8,D9,L1,L2,L3,L4,L5,L6,L7,L8,L9,B1,B2,B3,B4,B5,B6,B7,B8,B9 };-enum Layer      { U,R,F,D,L,B };-enum TurnMove   { Ux1,Ux2,Ux3,Rx1,Rx2,Rx3,Fx1,Fx2,Fx3,Dx1,Dx2,Dx3,Lx1,Lx2,Lx3,Bx1,Bx2,Bx3 };-enum Symmetry   { S_URF3,S_F2,S_U4,S_LR2 };-enum ColorIndex { UCol,RCol,FCol,DCol,LCol,BCol,NoCol };-enum Corner     { URF,UFL,ULB,UBR,DFR,DLF,DBL,DRB };-enum Edge       { UR,UF,UL,UB,DR,DF,DL,DB,FR,FL,BL,BR };-struct OrientedCorner   { Corner c; unsigned o; };-struct OrientedEdge     { Edge e;   unsigned o; };-typedef ColorIndex      SingleFace[9];-typedef ColorIndex      CornerColorIndex[8][3];-typedef ColorIndex      EdgeColorIndex[12][2];-typedef ColorIndex      FaceletColor[54];-typedef Face            CentreFacelet[6];-typedef Face            CornerFacelet[8][3];-typedef Face            EdgeFacelet[12][2];-typedef Face            Facelet[54];-typedef OrientedCorner  CornerCubie[8];-typedef OrientedEdge    EdgeCubie[12];-typedef Corner          EdgeNeighbour[12][2];-const CornerColorIndex  CCI = {{UCol,RCol,FCol},{UCol,FCol,LCol},{UCol,LCol,BCol},{UCol,BCol,RCol},{DCol,FCol,RCol},{DCol,LCol,FCol},{DCol,BCol,LCol},{DCol,RCol,BCol}};-const EdgeColorIndex    ECI = {{UCol,RCol},{UCol,FCol},{UCol,LCol},{UCol,BCol},{DCol,RCol},{DCol,FCol}, {DCol,LCol},{DCol,BCol},{FCol,RCol},{FCol,LCol},{BCol,LCol},{BCol,RCol}};-const CentreFacelet     CC  = {U5,R5,F5,D5,L5,B5};-const CornerFacelet     CF  = {{U9,R1,F3},{U7,F1,L3},{U1,L1,B3},{U3,B1,R3},{D3,F9,R7},{D1,L9,F7},{D7,B9,L7},{D9,R9,B7}};-const EdgeFacelet       EF  = {{U6,R2},{U8,F2},{U4,L2},{U2,B2},{D6,R8},{D2,F8}, {D4,L8},{D8,B8},{F6,R4},{F4,L6},{B6,L4},{B4,R6}};-const EdgeNeighbour     EN  = {{URF,UBR},{UFL,URF},{ULB,UFL},{UBR,ULB},{DRB,DFR},{DFR,DLF}, {DLF,DBL},{DBL,DRB},{URF,DFR},{DLF,UFL},{DBL,ULB},{UBR,DRB}};-const Facelet FaceletMove[6] = {-    {U3,U6,U9,U2,U5,U8,U1,U4,U7,F1,F2,F3,R4,R5,R6,R7,R8,R9,L1,L2,L3,F4,F5,F6,F7,F8,F9,D1,D2,D3,D4,D5,D6,D7,D8,D9,B1,B2,B3,L4,L5,L6,L7,L8,L9,R1,R2,R3,B4,B5,B6,B7,B8,B9},-    {U1,U2,B7,U4,U5,B4,U7,U8,B1,R3,R6,R9,R2,R5,R8,R1,R4,R7,F1,F2,U3,F4,F5,U6,F7,F8,U9,D1,D2,F3,D4,D5,F6,D7,D8,F9,L1,L2,L3,L4,L5,L6,L7,L8,L9,D9,B2,B3,D6,B5,B6,D3,B8,B9},-    {U1,U2,U3,U4,U5,U6,R1,R4,R7,D3,R2,R3,D2,R5,R6,D1,R8,R9,F3,F6,F9,F2,F5,F8,F1,F4,F7,L3,L6,L9,D4,D5,D6,D7,D8,D9,L1,L2,U9,L4,L5,U8,L7,L8,U7,B1,B2,B3,B4,B5,B6,B7,B8,B9},-    {U1,U2,U3,U4,U5,U6,U7,U8,U9,R1,R2,R3,R4,R5,R6,B7,B8,B9,F1,F2,F3,F4,F5,F6,R7,R8,R9,D3,D6,D9,D2,D5,D8,D1,D4,D7,L1,L2,L3,L4,L5,L6,F7,F8,F9,B1,B2,B3,B4,B5,B6,L7,L8,L9},-    {F1,U2,U3,F4,U5,U6,F7,U8,U9,R1,R2,R3,R4,R5,R6,R7,R8,R9,D1,F2,F3,D4,F5,F6,D7,F8,F9,B9,D2,D3,B6,D5,D6,B3,D8,D9,L3,L6,L9,L2,L5,L8,L1,L4,L7,B1,B2,U7,B4,B5,U4,B7,B8,U1},-    {L7,L4,L1,U4,U5,U6,U7,U8,U9,R1,R2,U1,R4,R5,U2,R7,R8,U3,F1,F2,F3,F4,F5,F6,F7,F8,F9,D1,D2,D3,D4,D5,D6,R9,R6,R3,D7,L2,L3,D8,L5,L6,D9,L8,L9,B3,B6,B9,B2,B5,B8,B1,B4,B7}-};-const Facelet FaceletSym[4] = {-    {R9,R8,R7,R6,R5,R4,R3,R2,R1,F3,F6,F9,F2,F5,F8,F1,F4,F7,U3,U6,U9,U2,U5,U8,U1,U4,U7,L1,L2,L3,L4,L5,L6,L7,L8,L9,B7,B4,B1,B8,B5,B2,B9,B6,B3,D3,D6,D9,D2,D5,D8,D1,D4,D7},-    {D9,D8,D7,D6,D5,D4,D3,D2,D1,L9,L8,L7,L6,L5,L4,L3,L2,L1,F9,F8,F7,F6,F5,F4,F3,F2,F1,U9,U8,U7,U6,U5,U4,U3,U2,U1,R9,R8,R7,R6,R5,R4,R3,R2,R1,B9,B8,B7,B6,B5,B4,B3,B2,B1},-    {U3,U6,U9,U2,U5,U8,U1,U4,U7,F1,F2,F3,F4,F5,F6,F7,F8,F9,L1,L2,L3,L4,L5,L6,L7,L8,L9,D7,D4,D1,D8,D5,D2,D9,D6,D3,B1,B2,B3,B4,B5,B6,B7,B8,B9,R1,R2,R3,R4,R5,R6,R7,R8,R9},-    {U3,U2,U1,U6,U5,U4,U9,U8,U7,L3,L2,L1,L6,L5,L4,L9,L8,L7,F3,F2,F1,F6,F5,F4,F9,F8,F7,D3,D2,D1,D6,D5,D4,D9,D8,D7,R3,R2,R1,R6,R5,R4,R9,R8,R7,B3,B2,B1,B6,B5,B4,B9,B8,B7}-};-const CornerCubie CornerCubieMove[6] = {-    {{UBR,0},{URF,0},{UFL,0},{ULB,0},{DFR,0},{DLF,0},{DBL,0},{DRB,0}},-    {{DFR,2},{UFL,0},{ULB,0},{URF,1},{DRB,1},{DLF,0},{DBL,0},{UBR,2}},-    {{UFL,1},{DLF,2},{ULB,0},{UBR,0},{URF,2},{DFR,1},{DBL,0},{DRB,0}},-    {{URF,0},{UFL,0},{ULB,0},{UBR,0},{DLF,0},{DBL,0},{DRB,0},{DFR,0}},-    {{URF,0},{ULB,1},{DBL,2},{UBR,0},{DFR,0},{UFL,2},{DLF,1},{DRB,0}},-    {{URF,0},{UFL,0},{UBR,1},{DRB,2},{DFR,0},{DLF,0},{ULB,2},{DBL,1}}-};-const EdgeCubie EdgeCubieMove[6] = {-    {{UB,0},{UR,0},{UF,0},{UL,0},{DR,0},{DF,0},{DL,0},{DB,0},{FR,0},{FL,0},{BL,0},{BR,0}},-    {{FR,0},{UF,0},{UL,0},{UB,0},{BR,0},{DF,0},{DL,0},{DB,0},{DR,0},{FL,0},{BL,0},{UR,0}},-    {{UR,0},{FL,1},{UL,0},{UB,0},{DR,0},{FR,1},{DL,0},{DB,0},{UF,1},{DF,1},{BL,0},{BR,0}},-    {{UR,0},{UF,0},{UL,0},{UB,0},{DF,0},{DL,0},{DB,0},{DR,0},{FR,0},{FL,0},{BL,0},{BR,0}},-    {{UR,0},{UF,0},{BL,0},{UB,0},{DR,0},{DF,0},{FL,0},{DB,0},{FR,0},{UL,0},{DL,0},{BR,0}},-    {{UR,0},{UF,0},{UL,0},{BR,1},{DR,0},{DF,0},{DL,0},{BL,1},{FR,0},{FL,0},{UB,1},{DB,1}}-};-const CornerCubie CornerCubieSym[4] = {-    {{URF,1},{DFR,2},{DLF,1},{UFL,2},{UBR,2},{DRB,1},{DBL,2},{ULB,1}},-    {{DLF,0},{DFR,0},{DRB,0},{DBL,0},{UFL,0},{URF,0},{UBR,0},{ULB,0}},-    {{UBR,0},{URF,0},{UFL,0},{ULB,0},{DRB,0},{DFR,0},{DLF,0},{DBL,0}},-    {{UFL,3},{URF,3},{UBR,3},{ULB,3},{DLF,3},{DFR,3},{DRB,3},{DBL,3}}-};-const EdgeCubie EdgeCubieSym[4] = {-    {{UF,1},{FR,0},{DF,1},{FL,0},{UB,1},{BR,0},{DB,1},{BL,0},{UR,1},{DR,1},{DL,1},{UL,1}},-    {{DL,0},{DF,0},{DR,0},{DB,0},{UL,0},{UF,0},{UR,0},{UB,0},{FL,0},{FR,0},{BR,0},{BL,0}},-    {{UB,0},{UR,0},{UF,0},{UL,0},{DB,0},{DR,0},{DF,0},{DL,0},{BR,1},{FR,1},{FL,1},{BL,1}},-    {{UL,0},{UF,0},{UR,0},{UB,0},{DL,0},{DF,0},{DR,0},{DB,0},{FL,0},{FR,0},{BR,0},{BL,0}}-};-enum Constant {-    GN_HTM      = 20,-    GN_QTM      = 26,-    N_MOVE      = 18,-    N_TWIST     = 2187,-    N_FLIP      = 2048,-    N_SLICE     = 495,-    N_CORNER    = 40320,-    N_EDGE8     = 40320,-    N_EDGE4     = 24,-    N_SYM       = 48,-    N_SYM_D4h   = 16,-    EQ_FLIPSLICE= 64430,-    EQ_CORNER   = 2768,-};-namespace cube::math {-using std::size_t;-template<typename VectorLike>-auto decomposite(const VectorLike &xs) -> std::pair<std::vector<typename VectorLike::value_type>,std::vector<std::vector<typename VectorLike::value_type>>>;-template<typename T, size_t N>-size_t orderOf(const std::array<T,N> &xs);-template<typename T, size_t N>-constexpr size_t rankOf(const std::array<T,N> &xs);-template<typename T, size_t N>-constexpr std::array<T,N> fromRank(size_t r);-template<typename F, typename T, size_t N>-constexpr std::array<T,N+1> nestList(F &&f, T &&x);-template<size_t Begin, size_t End, typename T, size_t N>-constexpr auto takeByRange(const std::array<T,N>&) -> std::array<T,End-Begin+1>;-template<size_t B, typename Int, size_t N>-constexpr auto fromDigits(const std::array<Int,N> &xs) -> size_t;-template<size_t B, size_t N, typename Int>-constexpr auto toDigits(size_t i) -> std::array<Int,N>;-constexpr size_t factorial(size_t n);-constexpr size_t binomial(size_t n, size_t k);-template<size_t N, size_t M>-constexpr auto lexicalOrderFromIndices(const std::array<size_t,M> &X) -> int;-template<size_t N, size_t M>-constexpr auto lexicalOrderToIndices(int rank) -> std::array<size_t,M>;-template<size_t N, typename ArrayLike>-constexpr bool isValidPermutation(const ArrayLike& xs);-template<typename Array, typename Perm>-constexpr Array backpermute(const Array& src, const Perm& P);-template<typename Array, typename Perm>-constexpr Array forepermute(const Array& src, const Perm& P);-template<typename VectorLike>-auto decomposite(const VectorLike &xs) -> std::pair<std::vector<typename VectorLike::value_type>,std::vector<std::vector<typename VectorLike::value_type>>>-{-    using T = typename VectorLike::value_type;-    std::vector<T> fixed;-    std::vector<std::vector<T>> cycles;-    std::vector<bool> visited(xs.size(),false);-    for(int i = 0; i < xs.size(); ++i) {-        if(visited[i]) continue;-        std::vector<T> cycle;-        for(int j = xs[i]; j != i; j = xs[j]) {-            visited[j] = true;-            cycle.push_back(static_cast<T>(j));-        }-        visited[i] = true;-        cycle.push_back(static_cast<T>(i));-        if(cycle.size() > 1) cycles.push_back(cycle);-        else fixed.push_back(cycle[0]);-    }-    std::sort(cycles.begin(), cycles.end(), [](auto &v1, auto &v2){-        return v1.size() > v2.size();-    });-    return std::make_pair(fixed,cycles);-}-template<typename T, size_t N>-size_t orderOf(const std::array<T,N> &xs)-{-    size_t m = 1;-    auto cs = decomposite(xs);-    for(size_t i = 1; i < cs.size(); i++) { m = std::lcm(m, cs[i].size()); }-    return m;-}-template<typename T, size_t N>-constexpr size_t rankOf(const std::array<T,N> &xs)-{-    size_t r = 0;-    std::array<bool,N> used {false};-    for(size_t i = 0; i < N; i++)-    {-        int cnt = 0;-        for(int j=0; j < xs[i]; j++) if(!used[j]) cnt++;-        r += cnt * factorial(N - i - 1);-        used[xs[i]] = true;-    }-    return r;-}-template<typename T, size_t N>-constexpr std::array<T,N> fromRank(size_t r)-{-    std::array<T,N> A{};-    std::array<bool,N> used {false};-    for(size_t i = 0; i < N; i++)-    {-        size_t f = factorial(N - i - 1);-        size_t cnt = r / f;-        r %= f;-        for(size_t j = 0; j < N; j++)-        {-            if(used[j]) continue;-            if(cnt-- == 0) {-                A[i] = j;-                used[j] = true;-                break;-            }-        }-    }-    return A;-}-template<typename F, typename T, size_t N>-constexpr std::array<T,N+1> nestList(F &&f, T &&x)-{-    std::array<T,N+1> r;-    r[0] = x;-    for(auto i = 1; i <= N; i++) r[i] = f(r[i-1]);-    return r;-}-template<size_t Begin, size_t End, typename T, size_t N>-constexpr auto takeByRange(const std::array<T,N> &xs) -> std::array<T,End-Begin+1>-{-    static_assert(Begin <= End && End < N);-    std::array<T,End-Begin+1> ys;-    std::copy(xs.begin()+Begin,xs.begin()+End+1,ys.begin());-    return ys;-}-template<size_t B, typename Int, size_t N>-constexpr auto fromDigits(const std::array<Int,N> &xs) -> size_t-{-    auto pow = [](size_t base, size_t exp) -> size_t {-        size_t prod = 1;-        for(size_t i = 0; i < exp; i++) prod *= base;-        return prod;-    };-    size_t res = 0;-    for(size_t i = 0; i < N; i++) res += static_cast<size_t>(xs[i]) * pow(B, N-i-1);-    return res;-}-template<size_t B, size_t N, typename Int>-constexpr auto toDigits(size_t i) -> std::array<Int,N>-{-    auto pow = [](size_t base, size_t exp) -> size_t {-        size_t prod = 1;-        for(size_t i = 0; i < exp; i++) prod *= base;-        return prod;-    };-    std::array<Int,N> a {};-    for(size_t k = 0; k < N; k++) {-        size_t z = pow(B, N-1-k);-        a[k] = static_cast<Int>(i / z);-        i = i % z;-    }-    return a;-}-constexpr size_t binomial(size_t n, size_t k)-{-    if(n < k)   return 0;-    if(n == k)  return 1;-    size_t r = 1, m = std::min(k, n-k);-    for(size_t i = 1; i <= m; i++) r *= n-i+1;-    for(size_t i = 1; i <= m; i++) r /= i;-    return r;-};-constexpr size_t factorial(size_t n)-{-    if(n>=21) throw std::invalid_argument("factorial(n) overflows for n >= 21");-    return n == 0 ? 1 : n * factorial(n-1);-}-template<size_t N, size_t M>-constexpr auto lexicalOrderFromIndices(const std::array<size_t,M> &X) -> int-{-    static_assert(M<=N);-    int rank = 0;-    for(size_t i = 0; i < M; i++) rank += binomial(N-1-X[i],M-i);-    return rank;-}-template<size_t N, size_t M>-constexpr auto lexicalOrderToIndices(int rank) -> std::array<size_t,M>-{-    static_assert(M<=N);-    std::array<size_t,M> X {};-    size_t n=rank, k=0;-    for(size_t i = 0; i < M; i++) {-        while(binomial(N-1-k,M-i) > n || n >= binomial(N-k,M-i)) k++;-        X[i] = k;-        n -= binomial(N-1-k,M-i);-        k += 1;-    }-    return X;-}-template<size_t N, typename ArrayLike>-constexpr bool isValidPermutation(const ArrayLike& xs)-{-    if(xs.size() != N) return false;-    std::array<bool,N> visited{};-    for(auto i = 0; i < N; ++i) {-        size_t val = static_cast<size_t>(xs[i]);-        if(xs[i] < 0 || xs[i] >= N) return false;-        if(visited[val]) return false;-        visited[val] = true;-    }-    return true;-}-template<typename Array, typename Perm>-constexpr Array backpermute(const Array& src, const Perm& P)-{-    Array out{src};-    for (size_t i = 0; i < P.size(); ++i) { out[i] = src[P[i]]; }-    return out;-}-template<typename Array, typename Perm>-constexpr Array forepermute(const Array& src, const Perm& P)-{-    Array out{src};-    for (size_t i = 0; i < P.size(); ++i) { out[P[i]] = src[i]; }-    return out;-}-}-namespace cube::utils {-inline auto get_cache_dir() -> std::filesystem::path-{-#ifdef _WIN32-    const char* localAppData = std::getenv("LOCALAPPDATA");-    if (localAppData) return std::filesystem::path(localAppData);-#elif __APPLE__-    const char* home = std::getenv("HOME");-    if (home) return std::filesystem::path(home) / "Library" / "Caches";-#else-    const char* xdgCache = std::getenv("XDG_CACHE_HOME");-    if (xdgCache) return std::filesystem::path(xdgCache);-    const char* home = std::getenv("HOME");-    if (home) return std::filesystem::path(home) / ".cache";-#endif-    throw std::runtime_error("Unable to determine cache path");-}-template<typename F, typename... Args>-inline auto time_execution(F&& f, Args&&... args)-{-    using Rf = std::invoke_result_t<F, Args...>;-    auto start = std::chrono::high_resolution_clock::now();-    auto duration_from_start = [start](){-        auto end = std::chrono::high_resolution_clock::now();-        return std::chrono::duration_cast<std::chrono::microseconds>(end-start);-    };-    if constexpr (std::is_void_v<Rf>) {-        std::forward<F>(f)(std::forward<Args>(args)...);-        return std::make_pair(-            duration_from_start(),-            std::nullopt-        );-    } else {-        auto result = std::forward<F>(f)(std::forward<Args>(args)...);-        return std::make_pair(-            duration_from_start(),-            std::make_optional(result)-        );-    }-}-template<typename VectorLike>-bool is_valid_config(const VectorLike &cfg)-{-    if(cfg.size() != 54) return false;-    std::set<char> vs { cfg[CC[0]],cfg[CC[1]],cfg[CC[2]],cfg[CC[3]],cfg[CC[4]],cfg[CC[5]] };-    if(vs.size() != 6) return false;-    for(size_t i = 0, x = 0; i < 8; i++) {-        for(x = 0; x < 24; x++) {-            if(cfg[CC[CCI[i][0]]] == cfg[CF[x/3][x%3]]-               && cfg[CC[CCI[i][1]]] == cfg[CF[x/3][(x+1)%3]]-               && cfg[CC[CCI[i][2]]] == cfg[CF[x/3][(x+2)%3]]) break;-        }-        if(x >= 24) return false;-    }-    for(size_t i = 0, y = 0; i < 12; i++) {-        for(y = 0; y < 24; y++) {-            if(cfg[CC[ECI[i][0]]] == cfg[EF[y/2][y%2]]-               && cfg[CC[ECI[i][1]]] == cfg[EF[y/2][(y+1)%2]]) break;-        }-        if(y >= 24) return false;-    }-    return true;-}-inline bool is_valid_maneuver(std::string_view s)-{-    static const std::regex pat(-        R"(\s*(([UDLRFB]['23]?|\(([UDLRFB]['23]?\s*)+\)(\{\d+\})?)\s*)*)"-    );-    return std::regex_match(s.begin(), s.end(), pat);-}-inline auto parse_manuever(std::string_view s) -> std::vector<TurnMove>-{-    assert(is_valid_maneuver(s) && "invalid maneuver");-    auto expand = [](std::string_view in) -> std::string {-        static const std::regex group_re(R"(\(([^)]+)\)(?:\{(\d+)\})?)");-        std::string res;-        auto start = in.cbegin();-        std::match_results<std::string_view::const_iterator> m;-        while (std::regex_search(start, in.cend(), m, group_re)) {-            res.append(start, m[0].first);-            int repeat = m[2].matched ? std::stoi(m[2].str()) : 1;-            for (int i = 0; i < repeat; ++i) res += m[1].str();-            start = m[0].second;-        }-        res.append(start, in.cend());-        return res;-    };-    auto char_to_move = [](char c) -> TurnMove {-        switch(c) {-        case 'U': return Ux1;-        case 'R': return Rx1;-        case 'F': return Fx1;-        case 'D': return Dx1;-        case 'L': return Lx1;-        case 'B': return Bx1;-        default: throw std::invalid_argument("char_to_move: ???");-        }-    };-    std::string in = expand(s);-    std::vector<TurnMove> ms;-    ms.reserve(in.size());-    for (char c : in)-    {-        switch (c) {-        case ' ': break;-        case '2':-            ms.back() = static_cast<TurnMove>(ms.back() + 1);-            break;-        case '\'':-            ms.back() = static_cast<TurnMove>(ms.back() + 2);-            break;-        default:-            ms.push_back(char_to_move(c));-            break;-        }-    }-    return ms;-}-inline std::vector<TurnMove> operator""_Tm(const char* ts, size_t n)-{-    return parse_manuever(std::string(ts,n));-}-}-namespace cube::data {-using std::size_t;-using namespace cube::math;-template<size_t N,typename T=int>-struct Perm-{-    using value_type = T;-    static constexpr size_t size() { return N; }-    constexpr Perm() noexcept-    {-        for(size_t i = 0; i < N; ++i) X[i] = static_cast<T>(i);-    }-    constexpr Perm(const std::array<T,N>& xs) noexcept-    :X{xs}-    {-        assert(isValidPermutation<N>(xs) && "array must be a valid permutation");-    }-    constexpr Perm(std::initializer_list<T> xs) noexcept-    {-        assert(xs.size() == N && "size mismatch");-        auto dit = X.begin();-        for(auto it = xs.begin(); it != xs.end(); it++, dit++) { *dit = *it; }-        assert(isValidPermutation<N>(X) && "invalid permutation list");-    }-    template<typename ArrayLike>-    constexpr ArrayLike act_right(const ArrayLike& src) const noexcept-    {-        return backpermute(src,this->X);-    }-    friend constexpr Perm operator*(const Perm &P, const Perm& Q) noexcept-    {-        return Q.act_right(P);-    }-    constexpr Perm& operator*=(const Perm& rhs) noexcept-    {-        return *this = *this * rhs;-    }-    friend constexpr bool operator==(const Perm &lhs, const Perm& rhs) noexcept-    {-        return lhs.X == rhs.X;-    }-    constexpr Perm operator~() const-    {-        return { forepermute(Perm::id.X, this->X) };-    }-    constexpr T& operator[](size_t idx)             { return X[idx]; }-    constexpr const T& operator[](size_t idx) const { return X[idx]; }-    bool parity() const-    {-        const auto [fixed, cs] = decomposite(this->X);-        int s = 1;-        for(auto &c:cs) s *= (c.size() % 2 == 0) ? -1 : 1;-        return s == 1;-    }-    size_t order() const { return orderOf(X); }-    constexpr size_t rank() const { return rankOf(X); }-    static constexpr Perm<N,T> fromRank(size_t i)-    { return { cube::math::fromRank<T,N>(i) }; }-    static const Perm id;-    std::array<T,N> X{};-};-template<size_t N,typename T>-inline constexpr Perm<N,T> Perm<N,T>::id{};-template<size_t N, size_t L, typename T=int>-struct CArray-{-    using value_type = T;-    static constexpr size_t period = N;-    static constexpr size_t size() noexcept { return L; }-    constexpr CArray() noexcept {}-    constexpr CArray(const std::array<T,L> &arr) noexcept-    :xs{arr}-    {-        auto n = static_cast<T>(N);-        for(size_t i = 0; i < L; i++) { xs[i] = (xs[i] % n + n) % n; }-    }-    constexpr CArray(std::initializer_list<T> list) noexcept-    {-        auto n = static_cast<T>(N);-        std::size_t i = 0;-        for(T val : list) { if(i < L) { xs[i++] = (val % n + n) % n; } }-    }-    constexpr T& operator[](size_t idx) noexcept             { return xs[idx]; }-    constexpr const T& operator[](size_t idx) const noexcept { return xs[idx]; }-    friend constexpr bool operator==(const CArray& lhs, const CArray& rhs) noexcept-    {-        return lhs.xs == rhs.xs;-    }-    constexpr CArray& operator+=(const CArray& rhs)-    {-        for(size_t i = 0; i < L; i++) xs[i] = (xs[i] + rhs.xs[i]) % N;-        return *this;-    }-    friend constexpr CArray operator+(CArray lhs, const CArray& rhs)-    {-        return lhs += rhs;-    }-    constexpr CArray operator~() const noexcept-    {-        CArray<N,L,T> inv {};-        auto n = static_cast<T>(N);-        for(size_t i = 0; i < L; i++) inv[i] = (n - xs[i]) % n;-        return inv;-    }-    constexpr T sum() const noexcept-    {-        T s = 0;-        for(size_t i = 0; i < L; i++) s += xs[i];-        return s % N;-    }-    static const CArray id;-    std::array<T,L> xs {};-};-template<size_t N, size_t L, typename T>-inline constexpr CArray<N,L,T> CArray<N,L,T>::id{};-template<size_t N, size_t L, typename T>-constexpr CArray<N,L,T> operator*(const CArray<N,L,T> &xs, const Perm<L,T> &P)-{-    return P.act_right(xs);-}-template<size_t N, size_t L, typename T>-constexpr CArray<N,L,T>& operator*=(CArray<N,L,T> &xs, const Perm<L,T> &P)-{-    return xs = P.act_right(xs);-}-template<typename T, size_t N, size_t... Ns>-struct ArrayHelper {-    using type = std::array<typename ArrayHelper<T,Ns...>::type,N>;-};-template<typename T, size_t N>-struct ArrayHelper<T,N> {-    using type = std::array<T,N>;-};-template<typename T, size_t... Ns>-struct NArray-{-    using value_type = T;-    static constexpr size_t size = (Ns * ...);-    static constexpr size_t dim = sizeof...(Ns);-    static constexpr std::array<size_t,dim> shape { Ns... };-    typename ArrayHelper<T,Ns...>::type data;-    auto & operator[](size_t i) {-        return data[i];-    }-    const auto & operator[](size_t i) const {-        return data[i];-    }-};-}-namespace cube {-using namespace cube::data;-using namespace cube::utils;-typedef int8_t cube_value_t;-typedef Perm<54,    cube_value_t>   FacePerm;-typedef Perm<8,     cube_value_t>   CornerPerm;-typedef Perm<12,    cube_value_t>   EdgePerm;-typedef CArray<3, 8,cube_value_t>   CornerOri;-typedef CArray<2,12,cube_value_t>   EdgeOri;-struct ColorState;-struct FaceCube;-struct CubieCube;-constexpr CornerPerm operator*(const CornerPerm &cp, const CubieCube &cc);-constexpr CornerOri  operator*(const CornerOri  &co, const CubieCube &cc);-constexpr EdgePerm   operator*(const EdgePerm   &ep, const CubieCube &cc);-constexpr EdgeOri    operator*(const EdgeOri    &eo, const CubieCube &cc);-struct ColorState-{-    std::array<Layer,54> s;-    Layer & operator[](size_t i) noexcept           { return s[i]; }-    const Layer operator[](size_t i) const noexcept { return s[i]; }-    static ColorState fromString(std::string_view cube);-    FaceCube  toFaceCube() const;-    CubieCube toCubieCube() const;-    static const ColorState id;-};-inline const ColorState ColorState::id = {{U,U,U,U,U,U,U,U,U,R,R,R,R,R,R,R,R,R,F,F,F,F,F,F,F,F,F,D,D,D,D,D,D,D,D,D,L,L,L,L,L,L,L,L,L,B,B,B,B,B,B,B,B,B}};-struct FaceCube-{-    FacePerm f;-    CubieCube toCubieCube() const;-    friend constexpr FaceCube operator*(const FaceCube &lhs, const FaceCube &rhs)-    { return { lhs.f * rhs.f }; }-    constexpr FaceCube& operator*=(const FaceCube &rhs)-    { return *this = *this * rhs; }-    constexpr FaceCube operator~() const-    { return { ~f }; }-    friend bool operator==(const FaceCube &lhs, const FaceCube &rhs)-    { return lhs.f == rhs.f; }-    static const FaceCube id;-};-struct CubieCube-{-    CornerPerm  cp;-    CornerOri   co;-    EdgePerm    ep;-    EdgeOri     eo;-    FaceCube toFaceCube() const;-    bool isSolvable() const-    {  return cp.parity() == ep.parity() && co.sum() == 0 && eo.sum() == 0; }-    friend constexpr CubieCube operator*(const CubieCube &a, const CubieCube &b)-    { return { a.cp*b, a.co*b, a.ep*b, a.eo*b }; }-    constexpr CubieCube& operator*=(const CubieCube &rhs)-    { return *this = *this * rhs; }-    constexpr CubieCube operator~() const-    {-        auto cp_inv = ~cp;-        auto ep_inv = ~ep;-        return { cp_inv, ~(co*cp_inv), ep_inv, ~(eo*ep_inv) };-    }-    friend bool operator==(const CubieCube &lhs, const CubieCube &rhs)-    { return lhs.cp == rhs.cp && lhs.co == rhs.co && lhs.ep == rhs.ep && lhs.eo == rhs.eo; }-    static const CubieCube id;-};-inline constexpr CornerPerm operator*(const CornerPerm &cp, const CubieCube &cc) { return cp * cc.cp;}-inline constexpr CornerOri  operator*(const CornerOri &co,  const CubieCube &cc) { return co * cc.cp + cc.co; }-inline constexpr EdgePerm   operator*(const EdgePerm &ep,   const CubieCube &cc) { return ep * cc.ep; }-inline constexpr EdgeOri    operator*(const EdgeOri &eo,    const CubieCube &cc) { return eo * cc.ep + cc.eo; }-inline constexpr CornerPerm    eCP = {0,1,2,3,4,5,6,7};-inline constexpr EdgePerm      eEP = {0,1,2,3,4,5,6,7,8,9,10,11};-inline constexpr CornerOri     eCO = {0,0,0,0,0,0,0,0};-inline constexpr EdgeOri       eEO = {0,0,0,0,0,0,0,0,0,0,0,0};-inline constexpr FacePerm      eFP = {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53};-inline const FaceCube   FaceCube::id = FaceCube{eFP};-inline const CubieCube  CubieCube::id = CubieCube{eCP,eCO,eEP,eEO};-inline constexpr CubieCube mU = {{3,0,1,2,4,5,6,7},{0,0,0,0,0,0,0,0},{3,0,1,2,4,5,6,7,8,9,10,11},{0,0,0,0,0,0,0,0,0,0,0,0}};-inline constexpr CubieCube mR = {{4,1,2,0,7,5,6,3},{2,0,0,1,1,0,0,2},{8,1,2,3,11,5,6,7,4,9,10,0},{0,0,0,0,0,0,0,0,0,0,0,0}};-inline constexpr CubieCube mF = {{1,5,2,3,0,4,6,7},{1,2,0,0,2,1,0,0},{0,9,2,3,4,8,6,7,1,5,10,11},{0,1,0,0,0,1,0,0,1,1,0,0}};-inline constexpr CubieCube mD = {{0,1,2,3,5,6,7,4},{0,0,0,0,0,0,0,0},{0,1,2,3,5,6,7,4,8,9,10,11},{0,0,0,0,0,0,0,0,0,0,0,0}};-inline constexpr CubieCube mL = {{0,2,6,3,4,1,5,7},{0,1,2,0,0,2,1,0},{0,1,10,3,4,5,9,7,8,2,6,11},{0,0,0,0,0,0,0,0,0,0,0,0}};-inline constexpr CubieCube mB = {{0,1,3,7,4,5,2,6},{0,0,1,2,0,0,2,1},{0,1,2,11,4,5,6,10,8,9,3,7},{0,0,0,1,0,0,0,1,0,0,1,1}};-inline constexpr std::array<CubieCube,18>-    ElementaryMove = { mU,mU*mU,mU*mU*mU,mR,mR*mR,mR*mR*mR,mF,mF*mF,mF*mF*mF,mD,mD*mD,mD*mD*mD,mL,mL*mL,mL*mL*mL,mB,mB*mB,mB*mB*mB };-inline constexpr FaceCube pU = {{6,3,0,7,4,1,8,5,2,45,46,47,12,13,14,15,16,17,9,10,11,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20,39,40,41,42,43,44,36,37,38,48,49,50,51,52,53}};-inline constexpr FaceCube pR = {{0,1,20,3,4,23,6,7,26,15,12,9,16,13,10,17,14,11,18,19,29,21,22,32,24,25,35,27,28,51,30,31,48,33,34,45,36,37,38,39,40,41,42,43,44,8,46,47,5,49,50,2,52,53}};-inline constexpr FaceCube pF = {{0,1,2,3,4,5,44,41,38,6,10,11,7,13,14,8,16,17,24,21,18,25,22,19,26,23,20,15,12,9,30,31,32,33,34,35,36,37,27,39,40,28,42,43,29,45,46,47,48,49,50,51,52,53}};-inline constexpr FaceCube pD = {{0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,24,25,26,18,19,20,21,22,23,42,43,44,33,30,27,34,31,28,35,32,29,36,37,38,39,40,41,51,52,53,45,46,47,48,49,50,15,16,17}};-inline constexpr FaceCube pL = {{53,1,2,50,4,5,47,7,8,9,10,11,12,13,14,15,16,17,0,19,20,3,22,23,6,25,26,18,28,29,21,31,32,24,34,35,42,39,36,43,40,37,44,41,38,45,46,33,48,49,30,51,52,27}};-inline constexpr FaceCube pB = {{11,14,17,3,4,5,6,7,8,9,10,35,12,13,34,15,16,33,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,36,39,42,2,37,38,1,40,41,0,43,44,51,48,45,52,49,46,53,50,47}};-inline constexpr std::array<FaceCube,18>-    ElementaryPerm = { pU,pU*pU,pU*pU*pU,pR,pR*pR,pR*pR*pR,pF,pF*pF,pF*pF*pF,pD,pD*pD,pD*pD*pD,pL,pL*pL,pL*pL*pL,pB,pB*pB,pB*pB*pB };-inline FaceCube operator*(const FaceCube &c, const std::vector<TurnMove> &ms)-{-    FaceCube fc = c;-    for (auto m : ms) fc = fc * ElementaryPerm[m];-    return fc;-}-inline CubieCube operator*(const CubieCube &c, const std::vector<TurnMove> &ms)-{-    CubieCube cc = c;-    for (auto m : ms) cc = cc * ElementaryMove[m];-    return cc;-}-inline ColorState operator*(const ColorState &c, const std::vector<TurnMove> &ms)-{-    ColorState cs = c;-    for (auto m : ms) cs = ElementaryPerm[m].f.act_right(cs);-    return cs;-}-}-namespace cube {-ColorState ColorState::fromString(std::string_view cube)-{-    assert(is_valid_config(cube) && "invalid cube config");-    std::array<Layer,54> xs{};-    std::transform(cube.cbegin(), cube.cend(), xs.begin(), [](char c) {-        switch(c) {-        case 'U': return U;-        case 'R': return R;-        case 'F': return F;-        case 'D': return D;-        case 'L': return L;-        case 'B': return B;-        default: throw std::invalid_argument("invalid cube config");-        }-    });-    return { xs };-}-FaceCube ColorState::toFaceCube() const-{-    FacePerm fp{};-    for(int i = 0; i < 6; ++i) {-        fp[CC[i]] = s[CC[i]];-    }-    for(int i = 0; i < 8; i++) {-        for(int x = 0; x < 24; x++) {-            if(s[CC[CCI[i][0]]] == s[CF[x/3][x%3]]-            && s[CC[CCI[i][1]]] == s[CF[x/3][(x+1)%3]]-            && s[CC[CCI[i][2]]] == s[CF[x/3][(x+2)%3]])-            {-                fp[CF[x/3][x%3]]      = CF[i][0];-                fp[CF[x/3][(x+1)%3]]  = CF[i][1];-                fp[CF[x/3][(x+2)%3]]  = CF[i][2];-                break;-            }-        }-    }-    for(int i = 0; i < 12; i++) {-        for(int y = 0; y < 24; y++) {-            if(s[CC[ECI[i][0]]] == s[EF[y/2][y%2]]-            && s[CC[ECI[i][1]]] == s[EF[y/2][(y+1)%2]])-            {-                fp[EF[y/2][y%2]]      = EF[i][0];-                fp[EF[y/2][(y+1)%2]]  = EF[i][1];-                break;-            }-        }-    }-    return { fp };-}-CubieCube ColorState::toCubieCube() const-{-    return toFaceCube().toCubieCube();-}-CubieCube FaceCube::toCubieCube() const-{-    CubieCube cc{};-    const FaceCube &fc = *this;-    for(int i = 0; i < 8; i++) {-        for(int x = 0; x < 24; x++) {-            if(fc.f[CF[i][0]] == CF[x/3][x%3]) {-                cc.cp[i] = x/3, cc.co[i] = (3-x%3)%3;-                break;-            }-        }-    }-    for(int i = 0; i < 12; i++){-        for(int y = 0; y < 24; y++){-            if(fc.f[EF[i][0]] == EF[y/2][y%2]) {-                cc.ep[i] = y/2, cc.eo[i] = (2-y%2)%2;-                break;-            }-        }-    }-    return cc;-}-FaceCube CubieCube::toFaceCube() const-{-    FaceCube fc{};-    const CubieCube &cc = *this;-    for(int i = 0; i < 6; i++) {-        fc.f[CC[i]] = CC[i];-    }-    for(int i = 0; i < 8; i++) for(int j = 0; j < 3; j++) {-        fc.f[CF[i][j]] = CF[cc.cp[i]][(j-cc.co[i]+3)%3];-    }-    for(int i = 0; i < 12; i++) for(int j = 0; j < 2; j++) {-        fc.f[EF[i][j]] = EF[cc.ep[i]][(j-cc.eo[i]+2)%2];-    }-    return fc;-}-}-namespace cube::pdb {-struct Coord-{-    int twist, flip, slice;-    int corner, edge4, edge8;-    static const Coord id;-    static CornerOri    twist2co(int);-    static int          co2twist(const CornerOri &);-    static EdgeOri      flip2eo(int);-    static int          eo2flip(const EdgeOri &);-    static CornerPerm   corner2cp(int);-    static int          cp2corner(const CornerPerm &);-    static int          ep2slice(const EdgePerm &);-    static int          ep2edge4(const EdgePerm &);-    static int          ep2edge8(const EdgePerm &);-    static EdgePerm     slice2ep(int);-    static EdgePerm     edge42ep(int);-    static EdgePerm     edge82ep(int);-    static EdgePerm     see2ep(int,int,int);-    static Coord        CubieCube2Coord(const CubieCube &);-    static CubieCube    Coord2CubieCube(const Coord &);-};-constexpr bool operator==(const Coord &c1, const Coord &c2)-{-    return c1.twist == c2.twist && c1.flip == c2.flip && c1.slice == c2.slice-        && c1.corner == c2.corner && c1.edge4 == c2.edge4 && c1.edge8 == c2.edge8;-}-inline constexpr Coord Coord::id = { 0,0,0,0,0,0 };-}-namespace cube::pdb {-using namespace cube::math;-using namespace cube::data;-inline bool isSliceEdge(size_t idx)-{-    return FR <= idx && idx <= BR;-}-int Coord::co2twist(const CornerOri &co)-{-    return static_cast<int>(fromDigits<3>(takeByRange<1,7>(co.xs)));-}-CornerOri Coord::twist2co(int i)-{-    CornerOri co;-    auto sub1to7 = CArray<3,7,CornerOri::value_type>{toDigits<3,7,CornerOri::value_type>(i)};-    std::copy(sub1to7.xs.begin(),sub1to7.xs.end(),co.xs.begin()+1);-    co[0] = (3 - sub1to7.sum()) % 3;-    return co;-}-int Coord::eo2flip(const EdgeOri &eo)-{-    return static_cast<int>(fromDigits<2>(takeByRange<1,11>(eo.xs)));-}-EdgeOri Coord::flip2eo(int i)-{-    EdgeOri eo;-    auto sub1to11 = CArray<2,11,CornerOri::value_type>{toDigits<2,11,CornerOri::value_type>(i)};-    std::copy(sub1to11.xs.begin(),sub1to11.xs.end(),eo.xs.begin()+1);-    eo[0] = (2 - sub1to11.sum()) % 2;-    return eo;-}-int Coord::ep2slice(const EdgePerm &ep)-{-    int x[4],slice=0,N=12;-    for(int i = 0, j = 0; i < N; i++) {-        if(isSliceEdge(ep[i])) x[j++] = i;-    }-    for(int i = 0; i < 4; i++) slice += binomial(N-1-x[i],4-i);-    return slice;-}-int Coord::ep2edge4(const EdgePerm &ep)-{-    Perm<4,EdgePerm::value_type> edge4_perm;-    for(int i = 0, j = 0; i < 4; i++, j++) {-        while(!isSliceEdge(ep[j])) j++;-        edge4_perm[i] = ep[j] - 8;-    }-    return static_cast<int>(edge4_perm.rank());-}-int Coord::ep2edge8(const EdgePerm &ep)-{-    Perm<8,EdgePerm::value_type> edge8_perm;-    for(size_t i = 0, j = 0; i < 8; i++, j++) {-        while(isSliceEdge(ep[j]) || ep[j] == (EdgePerm::value_type) ~0UL) j++;-        edge8_perm[i] = ep[j] - 0;-    }-    return static_cast<int>(edge8_perm.rank());-}-int Coord::cp2corner(const CornerPerm &cp)-{-    return static_cast<int>(cp.rank());-}-CornerPerm Coord::corner2cp(int i)-{-    return CornerPerm::fromRank(i);-}-EdgePerm Coord::slice2ep(int i)-{-    auto si = lexicalOrderToIndices<12,4>(i);-    EdgePerm ep;-    for(size_t i = 0, j = 0; i < 12; i++){-        ep[i] = (i == si[j]) ? 8 + j++ : (EdgePerm::value_type) ~0UL;-    }-    return ep;-}-EdgePerm Coord::edge42ep(int i)-{-    EdgePerm ep;-    auto e4 = Perm<4,EdgePerm::value_type>::fromRank(i);-    for(size_t i = 0; i < 12; i++){-        ep[i] = (i < 8) ? (EdgePerm::value_type) ~0UL : e4[i-8] + 8;-    }-    return ep;-}-EdgePerm Coord::edge82ep(int i)-{-    EdgePerm ep;-    auto e8 = Perm<8,EdgePerm::value_type>::fromRank(i);-    for(size_t i = 0; i < 12; i++){-        ep[i] = (i < 8) ? e8[i] + 0 : (EdgePerm::value_type) ~0UL;-    }-    return ep;-}-EdgePerm Coord::see2ep(int slice, int edge4, int edge8)-{-    auto e4 = Perm<4,EdgePerm::value_type>::fromRank(edge4);-    auto e8 = Perm<8,EdgePerm::value_type>::fromRank(edge8);-    auto slice_indices = lexicalOrderToIndices<12,4>(slice);-    EdgePerm ep;-    for(size_t i = 0, j = 0, x = 0, y = 0; i < 12; i++) {-        ep[i] = (i == slice_indices[j] && ++j) ? e4[x++]+8: e8[y++]+0;-    }-    return ep;-}-Coord Coord::CubieCube2Coord(const CubieCube &cc)-{-    return {-        Coord::co2twist(cc.co),-        Coord::eo2flip(cc.eo),-        Coord::ep2slice(cc.ep),-        Coord::cp2corner(cc.cp),-        Coord::ep2edge4(cc.ep),-        Coord::ep2edge8(cc.ep)-    };-}-CubieCube Coord::Coord2CubieCube(const Coord &c)-{-    return {-        Coord::corner2cp(c.corner),-        Coord::twist2co(c.twist),-        Coord::see2ep(c.slice,c.edge4,c.edge8),-        Coord::flip2eo(c.flip)-    };-}-}-namespace cube::internal-{-void set_table_dir(std::string_view dir);-auto get_table_dir() -> std::filesystem::path;-bool is_table_ready();-void preload_tables();-}-namespace cube::pdb {-#define TABLE_DIR_DEFAULT cube::internal::get_table_dir()-typedef uint16_t    mt_value_t;-typedef uint8_t     pt_value_t;-template <typename Table> void save_to(const Table &table, std::filesystem::path path);-template <typename Table> void load_from(Table &table, std::filesystem::path path);-template<class T>-class Singleton-{-public:-    Singleton(const Singleton&) = delete;-    Singleton(Singleton&&) = delete;-    Singleton& operator=(const Singleton&) = delete;-    Singleton& operator=(Singleton&&) = delete;-    static T& instance() {-        static T obj {};-        return obj;-    }-protected:-    Singleton() = default;-    ~Singleton() = default;-};-template<typename T=mt_value_t>-struct TableMove-{-    static_assert(std::is_integral<T>::value);-    static_assert(std::numeric_limits<T>::digits >= 16);-    using value_t = T;-    TableMove(std::filesystem::path dir = TABLE_DIR_DEFAULT);-    TableMove(const TableMove &) = delete;-    ~TableMove();-    TableMove& operator=(const TableMove &) = delete;-    template<typename Table, typename F1, typename F2>-    std::enable_if_t<Table::shape[0] == N_MOVE, void>-    buildMoveTable(Table &t, F1&& coord2i, F2&& i2coord, std::string filename="");-    const std::filesystem::path tdir;-    NArray<T,N_MOVE,N_TWIST>   *pTMTwist;-    NArray<T,N_MOVE,N_FLIP>    *pTMFlip;-    NArray<T,N_MOVE,N_SLICE>   *pTMSlice;-    NArray<T,N_MOVE,N_CORNER>  *pTMCorner;-    NArray<T,N_MOVE,N_EDGE4>   *pTMEdge4;-    NArray<T,N_MOVE,N_EDGE8>   *pTMEdge8;-};-template<typename T=pt_value_t>-struct TablePrunning-{-    using value_type = T;-    TablePrunning(std::filesystem::path dir = TABLE_DIR_DEFAULT);-    TablePrunning(const TablePrunning &) = delete;-    ~TablePrunning();-    TablePrunning operator=(const TablePrunning &) = delete;-    template<typename Table, typename MT1, typename MT2>-    std::enable_if_t<Table::shape[0] == MT1::shape[1] && Table::shape[1] == MT2::shape[1]>-    buildPrunningTable(Table &t, const MT1 &mt1, const MT2 &mt2, std::string filename);-    const std::filesystem::path tdir;-    NArray<T,N_SLICE,N_FLIP>   *pTPSliceFlip;-    NArray<T,N_SLICE,N_TWIST>  *pTPSliceTwist;-    NArray<T,N_EDGE4,N_EDGE8>  *pTPEdge4Edge8;-    NArray<T,N_EDGE4,N_CORNER> *pTPEdge4Corner;-};-inline const auto &get_TM() { return Singleton<TableMove<mt_value_t>>::instance(); }-inline const auto &get_TP() { return Singleton<TablePrunning<pt_value_t>>::instance(); }-}-#if defined(VERBOSE) && VERBOSE-#define VPRINT(...) printf(__VA_ARGS__)-#else-#define VPRINT(...)-#endif-namespace cube::pdb {-namespace fs = std::filesystem;-template <typename Table>-void save_to(const Table &table, fs::path path)-{-    std::ofstream f(path, std::ios::binary);-    if(f.is_open()) {-        f.write(reinterpret_cast<const char*>(&table.data), sizeof(table.data));-        f.close();-    }-}-template <typename Table>-void load_from(Table &table, fs::path path)-{-    VPRINT("loading table from %s...", path.c_str());-    std::ifstream f(path,std::ios::binary);-    f.read(reinterpret_cast<char*>(&table.data), sizeof(table.data));-    f.close();-    VPRINT("done.\n");-}-template<typename T>-template<typename Table, typename F1, typename F2>-std::enable_if_t<Table::shape[0] == N_MOVE>-TableMove<T>::buildMoveTable(Table &t, F1&& coord2i, F2&& i2coord, std::string filename)-{-    VPRINT("creating move table %s of shape (%zu,%zu)... ",-           filename.c_str(), t.shape[0], t.shape[1]);-    for(size_t i = 0; i < t.shape[0]; i++) for(size_t j = 0; j < t.shape[1]; j++) {-        t[i][j] = coord2i(i2coord(j) * ElementaryMove[i]);-    }-    if(filename != "") save_to(t, tdir/filename);-    VPRINT("done.\n");-}-template<typename T>-TableMove<T>::TableMove(std::filesystem::path dir)-:tdir(dir)-{-    VPRINT("INIT MOVE TABLES -- \n");-    pTMTwist     = new NArray<T,N_MOVE,N_TWIST>;-    pTMFlip      = new NArray<T,N_MOVE,N_FLIP>;-    pTMSlice     = new NArray<T,N_MOVE,N_SLICE>;-    pTMCorner    = new NArray<T,N_MOVE,N_CORNER>;-    pTMEdge4     = new NArray<T,N_MOVE,N_EDGE4>;-    pTMEdge8     = new NArray<T,N_MOVE,N_EDGE8>;-    if(!fs::exists(tdir/"tm_twist.dat")) {-        if(!fs::exists(tdir)) fs::create_directories(tdir);-        buildMoveTable(*pTMTwist, Coord::co2twist, Coord::twist2co, "tm_twist.dat");-        buildMoveTable(*pTMFlip, Coord::eo2flip, Coord::flip2eo, "tm_flip.dat");-        buildMoveTable(*pTMSlice, Coord::ep2slice, Coord::slice2ep, "tm_slice.dat");-        buildMoveTable(*pTMCorner, Coord::cp2corner, Coord::corner2cp, "tm_corner.dat");-        buildMoveTable(*pTMEdge4, Coord::ep2edge4, Coord::edge42ep, "tm_edge4.dat");-        buildMoveTable(*pTMEdge8, Coord::ep2edge8, Coord::edge82ep, "tm_edge8.dat");-    } else {-        load_from(*pTMTwist, tdir/"tm_twist.dat");-        load_from(*pTMFlip, tdir/"tm_flip.dat");-        load_from(*pTMSlice, tdir/"tm_slice.dat");-        load_from(*pTMCorner, tdir/"tm_corner.dat");-        load_from(*pTMEdge4, tdir/"tm_edge4.dat");-        load_from(*pTMEdge8, tdir/"tm_edge8.dat");-    }-    VPRINT("-- DONE.\n");-}-template<typename T>-TableMove<T>::~TableMove()-{-    delete pTMTwist;-    delete pTMFlip;-    delete pTMSlice;-    delete pTMCorner;-    delete pTMEdge4;-    delete pTMEdge8;-}-template<typename T>-template<typename Table, typename MT1, typename MT2>-std::enable_if_t<Table::shape[0] == MT1::shape[1] && Table::shape[1] == MT2::shape[1]>-TablePrunning<T>::buildPrunningTable(-    Table &t, const MT1 &mt1, const MT2 &mt2, std::string filename)-{-    VPRINT("creating prunning table %s of shape (%zu,%zu):\n",-           filename.c_str(), mt1.shape[1], mt2.shape[1]);-    std::fill_n(&t.data[0][0], t.size, (typename Table::value_type) ~0UL);-    t[0][0] = 0;-    typename Table::value_type depth = 0;-    size_t count = 1;-    VPRINT("\tdepth %2d: %10zu / %-10zu.\n", depth, count, t.size);-    while(count < t.size)-    {-        for(size_t i = 0; i < t.shape[0]; i++)-        for(size_t j = 0; j < t.shape[1]; j++)-        if(t[i][j] == depth) {-            for(auto k = 0; k < N_MOVE; k++) {-                auto ii = mt1[k][i], jj = mt2[k][j];-                if(t[ii][jj] == (typename Table::value_type)~0UL) { t[ii][jj] = depth + 1; count++; }-            }-        }-        depth++;-        VPRINT("\tdepth %2d: %10zu / %-10zu.\n", depth, count, t.size);-    }-    if(filename != "") save_to(t, tdir/filename);-    VPRINT("done.\n");-}-template<typename T>-TablePrunning<T>::TablePrunning(std::filesystem::path dir)-:tdir(dir)-{-    VPRINT("INIT PRUNNING TABLES -- \n");-    pTPSliceFlip     = new NArray<T,N_SLICE,N_FLIP>;-    pTPSliceTwist    = new NArray<T,N_SLICE,N_TWIST>;-    pTPEdge4Edge8    = new NArray<T,N_EDGE4,N_EDGE8>;-    pTPEdge4Corner   = new NArray<T,N_EDGE4,N_CORNER>;-    if(!fs::exists(tdir/"tp_slicetwist.dat")) {-        const auto &TM = get_TM();-        buildPrunningTable(*pTPSliceTwist, *TM.pTMSlice, *TM.pTMTwist, "tp_slicetwist.dat");-        buildPrunningTable(*pTPSliceFlip, *TM.pTMSlice, *TM.pTMFlip, "tp_sliceflip.dat");-        buildPrunningTable(*pTPEdge4Corner, *TM.pTMEdge4, *TM.pTMCorner, "tp_edge4corner.dat");-        buildPrunningTable(*pTPEdge4Edge8, *TM.pTMEdge4, *TM.pTMEdge8, "tp_edge4edge8.dat");-    } else {-        load_from(*pTPSliceTwist, tdir/"tp_slicetwist.dat");-        load_from(*pTPSliceFlip, tdir/"tp_sliceflip.dat");-        load_from(*pTPEdge4Corner,tdir/"tp_edge4corner.dat");-        load_from(*pTPEdge4Edge8, tdir/"tp_edge4edge8.dat");-    }-    VPRINT("-- DONE.\n");-}-template<typename T>-TablePrunning<T>::~TablePrunning()-{-    delete pTPSliceFlip;-    delete pTPSliceTwist;-    delete pTPEdge4Edge8;-    delete pTPEdge4Corner;-}-template struct TableMove<>;-template struct TablePrunning<>;-}-namespace cube::solver {-using namespace cube::pdb;-class TwoPhaseSolver-{-public:-    auto solve(const Coord &c, int step, bool best)-        -> std::tuple<bool,std::vector<TurnMove>,std::vector<TurnMove>>;-protected:-    enum enum_phase { Ph1=0, Ph2=1 };-    template<enum_phase PhX> bool search_phase(const Coord &c, size_t togo);-    template<enum_phase PhX> static Coord transform(const Coord &c, const TurnMove &m);-    template<enum_phase PhX> static size_t distance(const Coord &c);-    static constexpr int D0 = 12, D1 = 18, DS = D0+D1;-    template<enum_phase PhX> static constexpr auto& D = std::get<PhX>(std::tie(D0,D1));-    static constexpr std::array<TurnMove,18> EM0-        = { Ux1,Ux2,Ux3,Rx1,Rx2,Rx3,Fx1,Fx2,Fx3,Dx1,Dx2,Dx3,Lx1,Lx2,Lx3,Bx1,Bx2,Bx3 };-    static constexpr std::array<TurnMove,10> EM1-        = { Ux1,Ux2,Ux3,Rx2,Fx2,Dx1,Dx2,Dx3,Lx2,Bx2 };-    template<enum_phase PhX>-    static constexpr auto& EM = std::get<PhX>(std::tie(EM0,EM1));-private:-    template<enum_phase PhX>-    void reset_ph_sofar_()  { sofar_[PhX].fill(-1); }-    template<enum_phase PhX>-    void set_ph_solution_(size_t L)-    {-        rsolution_[PhX].first = L;-        std::copy(sofar_[PhX].begin(), sofar_[PhX].begin()+L, rsolution_[PhX].second.begin());-    }-    template<enum_phase PhX>-    auto get_ph_solution_() const -> std::vector<TurnMove>-    {-        size_t n = rsolution_[PhX].first;-        if(n == 0) return {};-        std::vector<TurnMove> sol(n);-        for(auto i = 0; i < n; i++) {-            sol[i] = static_cast<TurnMove>(rsolution_[PhX].second[n-1-i]);-        }-        return sol;-    }-    Coord ph2_origin_(Coord c) const;-    std::array<std::array<int,DS+2>,2>                  sofar_;-    std::array<std::pair<size_t,std::array<int,DS>>,2>  rsolution_;-};-}-#define TM get_TM()-#define TP get_TP()-namespace cube::solver {-inline bool is_dull_triple(const TurnMove A, const int B, const int C)-{-    return ( B>=Ux1 && B<=Bx3 ) &&-           ( (A/3==B/3) || ((C>=Ux1&&C<=Bx3) && A/3==C/3 && (3+A/3-B/3)%3==0) )-    ;-}-template<TwoPhaseSolver::enum_phase I>-Coord TwoPhaseSolver::transform(const Coord &c, const TurnMove &m)-{-    if constexpr (I == Ph1)-    return Coord {-        (*TM.pTMTwist)[m][c.twist], (*TM.pTMFlip)[m][c.flip], (*TM.pTMSlice)[m][c.slice],-        -1,-1,-1-    };-    else-    return Coord {-        0,0,0,-        (*TM.pTMCorner)[m][c.corner], (*TM.pTMEdge4)[m][c.edge4], (*TM.pTMEdge8)[m][c.edge8]-    };-}-template<TwoPhaseSolver::enum_phase I>-size_t TwoPhaseSolver::distance(const Coord &c)-{-    if constexpr (I == Ph1)-    return std::max((*TP.pTPSliceTwist)[c.slice][c.twist],-                    (*TP.pTPSliceFlip)[c.slice][c.flip]);-    else-    return std::max((*TP.pTPEdge4Corner)[c.edge4][c.corner],-                    (*TP.pTPEdge4Edge8)[c.edge4][c.edge8]);-}-template<TwoPhaseSolver::enum_phase PhX>-bool TwoPhaseSolver::search_phase(const Coord &c, size_t togo)-{-    if(togo == 0) return distance<PhX>(c) == 0;-    if(togo < distance<PhX>(c)) return false;-    for(auto m: EM<PhX>)-    {-        if(is_dull_triple(m,sofar_[PhX][togo],sofar_[PhX][togo+1])) continue;-        sofar_[PhX][togo-1] = m;-        bool ret = search_phase<PhX>(transform<PhX>(c,m), togo-1);-        if(ret) return true;-    }-    return false;-}-Coord TwoPhaseSolver::ph2_origin_(Coord c) const-{-    int corner = c.corner, edge4, edge8;-    auto ep = Coord::see2ep(c.slice,c.edge4,c.edge8);-    for(auto &m : get_ph_solution_<Ph1>())-    {-        corner = (*TM.pTMCorner)[m][corner];-        ep = ep * ElementaryMove[m].ep;-    }-    edge4 = Coord::ep2edge4(ep);-    edge8 = Coord::ep2edge8(ep);-    return Coord { 0,0,0,corner,edge4,edge8 };-}-auto TwoPhaseSolver::solve(const Coord &c, int step, bool best)-    -> std::tuple<bool,std::vector<TurnMove>,std::vector<TurnMove>>-{-    const size_t maxL = std::clamp(step,0,DS);-    size_t solL = maxL + 1;-    std::array<std::vector<TurnMove>,2> solution;-    reset_ph_sofar_<Ph1>();-    reset_ph_sofar_<Ph2>();-    for(auto d1 = distance<Ph1>(c); d1 <= maxL; d1++)-    {-        bool ret1 = search_phase<Ph1>(c,d1);-        if(!ret1) continue;-        set_ph_solution_<Ph1>(d1);-        auto c2 = ph2_origin_(c);-        size_t togo = (solL > rsolution_[Ph1].first) ? solL - rsolution_[Ph1].first : 0;-        for(auto d2 = distance<Ph2>(c2); d2 < togo; d2++)-        {-            bool ret2 = search_phase<Ph2>(c2,d2);-            if(!ret2) continue;-            set_ph_solution_<Ph2>(d2);-            solution[Ph1] = get_ph_solution_<Ph1>();-            solution[Ph2] = get_ph_solution_<Ph2>();-            solL = solution[1].size() + solution[0].size();-            if(!best) goto found;-            if(d2==0) goto found; else break;-        }-    }-    if(solL > maxL)-        return {false, {}, {}};-    found:-    return std::make_tuple(true, solution[0], solution[1]);-}-}-#ifndef CUBE_EXPORT_H-#define CUBE_EXPORT_H-#ifdef CUBE_STATIC_DEFINE-#  define CUBE_EXPORT-#  define CUBE_NO_EXPORT-#else-#  ifndef CUBE_EXPORT-#    ifdef cube_EXPORTS-#      define CUBE_EXPORT __attribute__((visibility("default")))-#    else-#      define CUBE_EXPORT __attribute__((visibility("default")))-#    endif-#  endif-#  ifndef CUBE_NO_EXPORT-#    define CUBE_NO_EXPORT __attribute__((visibility("hidden")))-#  endif-#endif-#ifndef CUBE_DEPRECATED-#  define CUBE_DEPRECATED __attribute__ ((__deprecated__))-#endif-#ifndef CUBE_DEPRECATED_EXPORT-#  define CUBE_DEPRECATED_EXPORT CUBE_EXPORT CUBE_DEPRECATED-#endif-#ifndef CUBE_DEPRECATED_NO_EXPORT-#  define CUBE_DEPRECATED_NO_EXPORT CUBE_NO_EXPORT CUBE_DEPRECATED-#endif-#if 0-#  ifndef CUBE_NO_DEPRECATED-#    define CUBE_NO_DEPRECATED-#  endif-#endif-#endif-#define CUBE_VERSION_FULL  v0.4.0-alpha-#define CUBE_VERSION_MAJOR 0-#define CUBE_VERSION_MINOR 4-#define CUBE_VERSION_PATCH 0-#define CUBE_VERSION_BUILD alpha-#if defined(__GNUC__) || defined(__clang__)-    #define CUBE_EXPORT_FORCE CUBE_EXPORT __attribute__((used))-#else-    #define CUBE_EXPORT_FORCE CUBE_EXPORT-#endif-#ifdef __cplusplus-    #define Default(x) = x-#else-    #define Default(x)-#endif-#define CUBE_BS 128-#define CUBE_ID "UUUUUUUUURRRRRRRRRFFFFFFFFFDDDDDDDDDLLLLLLLLLBBBBBBBBB"-#ifndef CF_ENUM-    #if defined(__cplusplus)-        #define CF_ENUM(_type, _name) \-            int __CF_ENUM_##_name; \-            enum _name : _type-    #elif defined(__clang__) || defined(__OBJC__)-        #define CF_ENUM(_type, _name) \-            enum _name : _type _name; \-            enum _name: _type-    #else-        #define CF_ENUM(_type, _name) \-            _type _name; \-            enum-    #endif-#endif-typedef CF_ENUM(int32_t,SolveResult) {-    SolveResultSuccess = 0,-    SolveResultUnsolvable = 1,-    SolveResultNotFound = 2,-    SolveResultInvalidSrc = 3,-    SolveResultInvalidTgt = 4,-    SolveResultUnknownErr = 5-};-#ifdef __cplusplus-extern "C" {-#endif-CUBE_EXPORT_FORCE inline const char *solve_result_to_string(SolveResult sr) {-    switch(sr) {-        case SolveResultSuccess:    return "Success.";-        case SolveResultUnsolvable: return "The cube configuration is unsolvable.";-        case SolveResultNotFound:   return "No solution found within the step limit.";-        case SolveResultInvalidSrc: return "Invalid source color configuration.";-        case SolveResultInvalidTgt: return "Invalid target color configuration.";-        case SolveResultUnknownErr: return "Unknown error.";-        default:                    return "???";-    }-}-CUBE_EXPORT SolveResult solve(-    char*       buf,-    const char* src         Default(CUBE_ID),-    const char* tgt         Default(CUBE_ID),-    int         step        Default(30),-    bool        best        Default(true)-);-CUBE_EXPORT bool solvable(-    const char* color_cube  Default(CUBE_ID)-);-CUBE_EXPORT bool facecube(-    char* buf,-    const char* maneuver    Default(""),-    const char *cube        Default(CUBE_ID)-);-CUBE_EXPORT bool permutation(-    char*       buf,-    const char* ms_or_cube  Default(CUBE_ID),-    int         format      Default(2)-);-#ifdef __cplusplus-}-#endif-namespace cube::show {-template<size_t N>-using StringArr = std::array<std::string_view,N>;-inline constexpr StringArr< 8> CornerToString       = { "urf", "ufl", "ulb", "ubr", "dfr", "dlf", "dbl", "drb" };-inline constexpr StringArr<12> EdgeToString         = { "ur","uf","ul","ub","dr","df","dl","db","fr","fl","bl","br" };-inline constexpr StringArr< 6> CenterToString       = { "u", "r", "f", "d", "l", "b" };-inline constexpr StringArr< 3> OrientationToString  = { "", "+", "-" };-inline constexpr StringArr<18> Move2Str             = { "U","U2","U'","R","R2","R'","F","F2","F'","D","D2","D'","L","L2","L'","B","B2","B'" };-inline constexpr StringArr<54> Face2Str             = { "U1","U2","U3","U4","U5","U6","U7","U8","U9","R1","R2","R3","R4","R5","R6","R7","R8","R9","F1","F2","F3","F4","F5","F6","F7","F8","F9","D1","D2","D3","D4","D5","D6","D7","D8","D9","L1","L2","L3","L4","L5","L6","L7","L8","L9","B1","B2","B3","B4","B5","B6","B7","B8","B9" };-inline constexpr std::string_view ColorSet          = "URFDLB";-inline constexpr std::string_view CornerSet         = "ABCDEFGH";-inline constexpr std::string_view EdgeSet           = "opqrstuvwxyz";-enum class CubeFormat {-    Face,-    Cubie,-    Cycle-};-template<typename Array, typename Formatter>-inline std::string seq2str_fmt(const Array &xs,-                           Formatter && fmt,-                           std::string_view sep="",-                           std::string_view pre="",-                           std::string_view suf="")-{-    const size_t len = xs.size();-    if(len == 0) { return std::string(pre) + std::string(suf); }-    std::stringstream ss;-    ss << pre << fmt(xs[0]);-    for(size_t i = 1; i < len; ++i) ss << sep << fmt(xs[i]);-    ss << suf;-    return ss.str();-}-template<typename Container>-inline std::string seq2str(const Container &xs,-                           std::string_view sep="",-                           std::string_view pre="",-                           std::string_view suf="")-{-    auto default_formatter = [](const auto& val) {-        using T = std::decay_t<decltype(val)>;-        if constexpr (std::is_same_v<T,uint8_t> || std::is_same_v<T,int8_t>) {-            return static_cast<int>(val);-        } else {-            return val;-        }-    };-    return seq2str_fmt(xs, default_formatter, sep, pre, suf);-}-std::string to_string(const ColorState& cs)-{-    return seq2str_fmt(cs.s, [](auto v) {-        switch(v){-        case U: return 'U';-        case R: return 'R';-        case F: return 'F';-        case D: return 'D';-        case L: return 'L';-        case B: return 'B';-        default: throw std::invalid_argument("to_string(ColorState): ???");-        }-    });-}-std::string to_string(const FaceCube& fc, bool use_digit=true)-{-    if(use_digit){-        return seq2str(fc.f);-    } else {-        return seq2str_fmt(fc.f, [](auto v) { return Face2Str[v]; });-    }-}-std::string to_string(const CubieCube& cc, CubeFormat fmt)-{-    switch(fmt){-    case CubeFormat::Face:-        return to_string(cc.toFaceCube(), false);-    case CubeFormat::Cubie:-        return seq2str_fmt(cc.cp, [](auto v) { return CornerSet[v]; }) +-               seq2str_fmt(cc.co, [](auto v) { return static_cast<char>('0'+v); }) +-               seq2str_fmt(cc.ep, [](auto v) { return EdgeSet[v]; }) +-               seq2str_fmt(cc.eo, [](auto v) { return static_cast<char>('0'+v);});-    default:-        const auto [fixed_corner,cycles_corner] = decomposite(cc.cp);-        const auto [fixed_edge, cycles_edge ]   = decomposite(cc.ep);-        std::string s1, s2;-        s1.reserve(64);-        s2.reserve(64);-        auto append_fixed = [&](std::string& out, const auto& fixed, const auto& ori_arr, auto name_table) {-            for(auto idx: fixed) {-                if(ori_arr[idx] == 0) continue;-                out += '(';-                out += OrientationToString[ori_arr[idx]];-                out += name_table[idx];-                out += ')';-            }-        };-        auto append_cycles = [&](std::string& out, const auto& cycles, const auto& ori_arr, auto name_table) {-            for(const auto& cycle: cycles) {-                const size_t N = cycle.size();-                if(N == 0) continue;-                out += '(';-                for(int i = 0; i < N; i++) {-                    if(i > 0) out += ',';-                    size_t prev_idx = cycle[(N-1+i)%N];-                    out += OrientationToString[ori_arr[prev_idx]];-                    out += name_table[cycle[i]];-                }-                out += ')';-            }-        };-        append_fixed(s1, fixed_corner, cc.co, CornerToString);-        append_cycles(s1, cycles_corner, cc.co, CornerToString);-        append_fixed(s2, fixed_edge, cc.eo, EdgeToString);-        append_cycles(s2, cycles_edge, cc.eo, EdgeToString);-        return s1.empty() && s2.empty() ? "id" : s1 + s2;-    }-}-std::string to_string(const std::vector<TurnMove>& ms)-{-    return seq2str_fmt(ms, [](auto v){-        return Move2Str[v];-    }, " ");-}-}-using namespace cube;-const std::string_view cid = CUBE_ID;-cube::solver::TwoPhaseSolver TPS;-std::string apply_moves(std::string_view s, const std::vector<TurnMove> &ms)-{-    assert(s.size() == 54 && "invalid cube length");-    char buf[2][54];-    std::memcpy(buf[0], s.data(), 54);-    size_t curr = 0;-    for(const auto &m : ms)-    {-        const auto& p   = ElementaryPerm[m].f;-        const char* src = buf[curr];-        char*       dst = buf[1-curr];-        for(int i = 0; i < 54; ++i) dst[i] = src[p[i]];-        curr = 1-curr;-    }-    return std::string(buf[curr],54);-}-SolveResult solve(-    char* buf, const char *src, const char* tgt, int step, bool best)-{-    auto s_src = src == NULL ? cid : std::string_view(src);-    auto s_tgt = tgt == NULL ? cid : std::string_view(tgt);-    if(s_src != cid && !cube::utils::is_valid_config(s_src)) return SolveResultInvalidSrc;-    if(s_tgt != cid && !cube::utils::is_valid_config(s_tgt)) return SolveResultInvalidTgt;-    if(s_src == s_tgt) { buf[0] = '\0'; return SolveResultSuccess; }-    auto cc_src = ColorState::fromString(s_src).toCubieCube();-    auto cc_tgt = ColorState::fromString(s_tgt).toCubieCube();-    CubieCube cc = ~cc_tgt*cc_src;-    if(!cc.isSolvable()) return SolveResultUnsolvable;-    const auto & [found, s1, s2] = TPS.solve(cube::pdb::Coord::CubieCube2Coord(cc), step, best);-    if(!found) return SolveResultNotFound;-    std::vector<TurnMove> sol = [](const auto &s1, const auto &s2) {-        std::vector<TurnMove> solution;-        size_t n1 = s1.size(), n2 = s2.size();-        if(!s1.empty() && !s2.empty() && s1[n1-1]/3 == s2[0]/3) {-            std::copy(s1.begin(), s1.end()-1, std::back_inserter(solution));-            int m = (s1[n1-1] + s2[0]- s2[0]/3 *6 +2) %4;-            if(m!=0) solution.push_back(static_cast<TurnMove>(s2[0]/3*3+m-1));-            std::copy(s2.begin()+1, s2.end(), std::back_inserter(solution));-        } else {-            std::copy(s1.begin(), s1.end(), std::back_inserter(solution));-            std::copy(s2.begin(), s2.end(), std::back_inserter(solution));-        }-        return solution;-    }(s1,s2);-    auto s = show::to_string(sol);-    std::copy(s.cbegin(), s.cend(), buf);-    buf[s.length()] = '\0';-    return SolveResultSuccess;-}-bool solvable(const char* cube)-{-    return cube::utils::is_valid_config<std::string_view>(cube)-           && ColorState::fromString(cube).toCubieCube().isSolvable();-}-bool facecube(char* buf, const char *maneuver, const char *cube)-{-    if(!buf) return false;-    std::string cube_str = cube ? std::string(cube) : std::string(CUBE_ID);-    std::string maneuver_str = maneuver ? std::string(maneuver) : std::string("");-    if(cube_str.size()!= 54 || !cube::utils::is_valid_maneuver(maneuver_str)) {-        buf[0] = '\0';-        return false;-    }-    const auto ms = cube::utils::parse_manuever(maneuver_str);-    const auto color = apply_moves(cube_str, ms);-    std::copy(color.cbegin(), color.cend(), buf);-    buf[color.length()] = '\0';-    return true;-}-bool permutation(char* buf, const char* ms_or_cube, int format)-{-    if(!buf) return false;-    std::string cube_str{};-    if(ms_or_cube) {-        if(cube::utils::is_valid_config<std::string_view>(ms_or_cube)) {-            cube_str = std::string(ms_or_cube);-        } else if(cube::utils::is_valid_maneuver(ms_or_cube)) {-            auto ms = cube::utils::parse_manuever(ms_or_cube);-            cube_str = apply_moves(cid,ms);-        } else {-            buf[0] = '\0';-            return false;-        }-    } else {-        cube_str = cid;-    }-    std::string perm_str{};-    auto cc = ColorState::fromString(cube_str).toCubieCube();-    perm_str = show::to_string(cc, show::CubeFormat(format));-    std::copy(perm_str.cbegin(), perm_str.cend(), buf);-    buf[perm_str.length()] = '\0';-    return true;-}-namespace cube::internal {-namespace fs = std::filesystem;-static std::string& get_custom_dir_storage()-{-    static std::string custom_dir = "";-    return custom_dir;-}-void set_table_dir(std::string_view dir)-{-    get_custom_dir_storage() = dir;-}-fs::path get_table_dir()-{-    std::string user_dir = get_custom_dir_storage();-    if(!user_dir.empty()) return fs::path(user_dir);-    if(const char *env = std::getenv("CUBE_TABLE_DIR")) {-        if(env[0] != '\0') return fs::path(env);-    }-    try {-        return cube::utils::get_cache_dir() / "cube" / "tables";-    } catch (...) {}-    return fs::current_path() / "tables";-}-bool is_table_ready()-{-    return fs::exists(get_table_dir() / "tm_twist.dat");-}-void preload_tables()-{-    (void)pdb::get_TM();-    (void)pdb::get_TP();+ * Version: v0.5.0+ * Date: 2026-10-10+ * Homepage: https://github.com/coshz/cube+ * License: MIT+ *+ * Copyright (c) 2026 coshz <fsinhx@gmail.com>. All rights reserved.+ */++#include <cstddef>+#include <vector>+#include <array>+#include <algorithm>+#include <utility>+#include <numeric>+#include <stdexcept>+#include <initializer_list>+#include <cassert>+#include <cstdint>+#include <string_view>+#include <set>+#include <filesystem>+#include <type_traits>+#include <limits>+#include <fstream>+#include <ios>+#include <tuple>+#include <cstdlib>+#include <chrono>+#include <optional>+#include <string>+#include <cstring>+#include <regex>+#include <sstream>+#include <stdbool.h>+#include <stdint.h>++namespace cube::math {+using std::size_t;+template<typename VectorLike>+auto decomposite(const VectorLike &xs) -> std::pair<+    std::vector<typename VectorLike::value_type>,+    std::vector<std::vector<typename VectorLike::value_type>>+>+{+    using T = typename VectorLike::value_type;+    std::vector<T> fixed;+    std::vector<std::vector<T>> cycles;+    std::vector<bool> visited(xs.size(),false);+    for(int i = 0; i < xs.size(); ++i) {+        if(visited[i]) continue;+        std::vector<T> cycle;+        for(int j = xs[i]; j != i; j = xs[j]) {+            visited[j] = true;+            cycle.push_back(static_cast<T>(j));+        }+        visited[i] = true;+        cycle.push_back(static_cast<T>(i));+        if(cycle.size() > 1) cycles.push_back(cycle);+        else fixed.push_back(cycle[0]);+    }+    std::sort(cycles.begin(), cycles.end(), [](auto &v1, auto &v2){+        return v1.size() > v2.size();+    });+    return std::make_pair(fixed,cycles);+}+constexpr size_t factorial(size_t n)+{+    if(n>=21) throw std::invalid_argument("factorial(n) overflows for n >= 21");+    return n == 0 ? 1 : n * factorial(n-1);+}+constexpr size_t binomial(size_t n, size_t k)+{+    if(n < k)   return 0;+    if(n == k)  return 1;+    size_t r = 1, m = std::min(k, n-k);+    for(size_t i = 1; i <= m; i++) r *= n-i+1;+    for(size_t i = 1; i <= m; i++) r /= i;+    return r;+};+template<typename T, size_t N>+size_t orderOf(const std::array<T,N> &xs)+{+    size_t m = 1;+    auto cs = decomposite(xs);+    for(size_t i = 1; i < cs.size(); i++) { m = std::lcm(m, cs[i].size()); }+    return m;+}+template<typename T, size_t N>+constexpr size_t rankOf(const std::array<T,N> &xs)+{+    size_t r = 0;+    std::array<bool,N> used {false};+    for(size_t i = 0; i < N; i++)+    {+        int cnt = 0;+        for(int j=0; j < xs[i]; j++) if(!used[j]) cnt++;+        r += cnt * factorial(N - i - 1);+        used[xs[i]] = true;+    }+    return r;+}+template<typename T, size_t N>+constexpr std::array<T,N> fromRank(size_t r)+{+    std::array<T,N> A{};+    std::array<bool,N> used {false};+    for(size_t i = 0; i < N; i++)+    {+        size_t f = factorial(N - i - 1);+        size_t cnt = r / f;+        r %= f;+        for(size_t j = 0; j < N; j++)+        {+            if(used[j]) continue;+            if(cnt-- == 0) {+                A[i] = j;+                used[j] = true;+                break;+            }+        }+    }+    return A;+}+template<typename F, typename T, size_t N>+constexpr std::array<T,N+1> nestList(F &&f, T &&x)+{+    std::array<T,N+1> r;+    r[0] = x;+    for(auto i = 1; i <= N; i++) r[i] = f(r[i-1]);+    return r;+}+template<size_t Begin, size_t End, typename T, size_t N>+constexpr auto takeByRange(const std::array<T,N>& xs) -> std::array<T,End-Begin+1>+{+    static_assert(Begin <= End && End < N);+    std::array<T,End-Begin+1> ys;+    std::copy(xs.begin()+Begin,xs.begin()+End+1,ys.begin());+    return ys;+}+template<size_t B, typename Int, size_t N>+constexpr auto fromDigits(const std::array<Int,N> &xs) -> size_t+{+    auto pow = [](size_t base, size_t exp) -> size_t {+        size_t prod = 1;+        for(size_t i = 0; i < exp; i++) prod *= base;+        return prod;+    };+    size_t res = 0;+    for(size_t i = 0; i < N; i++) res += static_cast<size_t>(xs[i]) * pow(B, N-i-1);+    return res;+}+template<size_t B, size_t N, typename Int>+constexpr auto toDigits(size_t i) -> std::array<Int,N>+{+    auto pow = [](size_t base, size_t exp) -> size_t {+        size_t prod = 1;+        for(size_t i = 0; i < exp; i++) prod *= base;+        return prod;+    };+    std::array<Int,N> a {};+    for(size_t k = 0; k < N; k++) {+        size_t z = pow(B, N-1-k);+        a[k] = static_cast<Int>(i / z);+        i = i % z;+    }+    return a;+}+template<size_t N, size_t M>+constexpr auto lexicalOrderFromIndices(const std::array<size_t,M> &X) -> int+{+    static_assert(M<=N);+    int rank = 0;+    for(size_t i = 0; i < M; i++) rank += binomial(N-1-X[i],M-i);+    return rank;+}+template<size_t N, size_t M>+constexpr auto lexicalOrderToIndices(int rank) -> std::array<size_t,M>+{+    static_assert(M<=N);+    std::array<size_t,M> X {};+    size_t n=rank, k=0;+    for(size_t i = 0; i < M; i++) {+        while(binomial(N-1-k,M-i) > n || n >= binomial(N-k,M-i)) k++;+        X[i] = k;+        n -= binomial(N-1-k,M-i);+        k += 1;+    }+    return X;+}+template<size_t N, typename ArrayLike>+constexpr bool isValidPermutation(const ArrayLike& xs)+{+    if(xs.size() != N) return false;+    std::array<bool,N> visited{};+    for(auto i = 0; i < N; ++i) {+        size_t val = static_cast<size_t>(xs[i]);+        if(xs[i] < 0 || xs[i] >= N) return false;+        if(visited[val]) return false;+        visited[val] = true;+    }+    return true;+}+template<typename Array, typename Perm>+constexpr Array backpermute(const Array& src, const Perm& P)+{+    Array out{src};+    for (size_t i = 0; i < P.size(); ++i) { out[i] = src[P[i]]; }+    return out;+}+template<typename Array, typename Perm>+constexpr Array forepermute(const Array& src, const Perm& P)+{+    Array out{src};+    for (size_t i = 0; i < P.size(); ++i) { out[P[i]] = src[i]; }+    return out;+}+}+namespace cube::data {+enum Face       { U1,U2,U3,U4,U5,U6,U7,U8,U9,R1,R2,R3,R4,R5,R6,R7,R8,R9,F1,F2,F3,F4,F5,F6,F7,F8,F9,D1,D2,D3,D4,D5,D6,D7,D8,D9,L1,L2,L3,L4,L5,L6,L7,L8,L9,B1,B2,B3,B4,B5,B6,B7,B8,B9 };+enum Layer      { U,R,F,D,L,B };+enum TurnMove   { Ux1,Ux2,Ux3,Rx1,Rx2,Rx3,Fx1,Fx2,Fx3,Dx1,Dx2,Dx3,Lx1,Lx2,Lx3,Bx1,Bx2,Bx3 };+enum Symmetry   { S_URF3,S_F2,S_U4,S_LR2 };+enum ColorIndex { UCol,RCol,FCol,DCol,LCol,BCol,NoCol };+enum Corner     { URF,UFL,ULB,UBR,DFR,DLF,DBL,DRB };+enum Edge       { UR,UF,UL,UB,DR,DF,DL,DB,FR,FL,BL,BR };+struct OrientedCorner   { Corner c; unsigned o; };+struct OrientedEdge     { Edge e;   unsigned o; };+typedef ColorIndex      SingleFace[9];+typedef ColorIndex      CornerColorIndex[8][3];+typedef ColorIndex      EdgeColorIndex[12][2];+typedef ColorIndex      FaceletColor[54];+typedef Face            CentreFacelet[6];+typedef Face            CornerFacelet[8][3];+typedef Face            EdgeFacelet[12][2];+typedef Face            Facelet[54];+typedef OrientedCorner  CornerCubie[8];+typedef OrientedEdge    EdgeCubie[12];+typedef Corner          EdgeNeighbour[12][2];+const CornerColorIndex  CCI = {{UCol,RCol,FCol},{UCol,FCol,LCol},{UCol,LCol,BCol},{UCol,BCol,RCol},{DCol,FCol,RCol},{DCol,LCol,FCol},{DCol,BCol,LCol},{DCol,RCol,BCol}};+const EdgeColorIndex    ECI = {{UCol,RCol},{UCol,FCol},{UCol,LCol},{UCol,BCol},{DCol,RCol},{DCol,FCol}, {DCol,LCol},{DCol,BCol},{FCol,RCol},{FCol,LCol},{BCol,LCol},{BCol,RCol}};+const CentreFacelet     CC  = {U5,R5,F5,D5,L5,B5};+const CornerFacelet     CF  = {{U9,R1,F3},{U7,F1,L3},{U1,L1,B3},{U3,B1,R3},{D3,F9,R7},{D1,L9,F7},{D7,B9,L7},{D9,R9,B7}};+const EdgeFacelet       EF  = {{U6,R2},{U8,F2},{U4,L2},{U2,B2},{D6,R8},{D2,F8}, {D4,L8},{D8,B8},{F6,R4},{F4,L6},{B6,L4},{B4,R6}};+const EdgeNeighbour     EN  = {{URF,UBR},{UFL,URF},{ULB,UFL},{UBR,ULB},{DRB,DFR},{DFR,DLF}, {DLF,DBL},{DBL,DRB},{URF,DFR},{DLF,UFL},{DBL,ULB},{UBR,DRB}};+const Facelet FaceletMove[6] = {+    {U3,U6,U9,U2,U5,U8,U1,U4,U7,F1,F2,F3,R4,R5,R6,R7,R8,R9,L1,L2,L3,F4,F5,F6,F7,F8,F9,D1,D2,D3,D4,D5,D6,D7,D8,D9,B1,B2,B3,L4,L5,L6,L7,L8,L9,R1,R2,R3,B4,B5,B6,B7,B8,B9},+    {U1,U2,B7,U4,U5,B4,U7,U8,B1,R3,R6,R9,R2,R5,R8,R1,R4,R7,F1,F2,U3,F4,F5,U6,F7,F8,U9,D1,D2,F3,D4,D5,F6,D7,D8,F9,L1,L2,L3,L4,L5,L6,L7,L8,L9,D9,B2,B3,D6,B5,B6,D3,B8,B9},+    {U1,U2,U3,U4,U5,U6,R1,R4,R7,D3,R2,R3,D2,R5,R6,D1,R8,R9,F3,F6,F9,F2,F5,F8,F1,F4,F7,L3,L6,L9,D4,D5,D6,D7,D8,D9,L1,L2,U9,L4,L5,U8,L7,L8,U7,B1,B2,B3,B4,B5,B6,B7,B8,B9},+    {U1,U2,U3,U4,U5,U6,U7,U8,U9,R1,R2,R3,R4,R5,R6,B7,B8,B9,F1,F2,F3,F4,F5,F6,R7,R8,R9,D3,D6,D9,D2,D5,D8,D1,D4,D7,L1,L2,L3,L4,L5,L6,F7,F8,F9,B1,B2,B3,B4,B5,B6,L7,L8,L9},+    {F1,U2,U3,F4,U5,U6,F7,U8,U9,R1,R2,R3,R4,R5,R6,R7,R8,R9,D1,F2,F3,D4,F5,F6,D7,F8,F9,B9,D2,D3,B6,D5,D6,B3,D8,D9,L3,L6,L9,L2,L5,L8,L1,L4,L7,B1,B2,U7,B4,B5,U4,B7,B8,U1},+    {L7,L4,L1,U4,U5,U6,U7,U8,U9,R1,R2,U1,R4,R5,U2,R7,R8,U3,F1,F2,F3,F4,F5,F6,F7,F8,F9,D1,D2,D3,D4,D5,D6,R9,R6,R3,D7,L2,L3,D8,L5,L6,D9,L8,L9,B3,B6,B9,B2,B5,B8,B1,B4,B7}+};+const Facelet FaceletSym[4] = {+    {R9,R8,R7,R6,R5,R4,R3,R2,R1,F3,F6,F9,F2,F5,F8,F1,F4,F7,U3,U6,U9,U2,U5,U8,U1,U4,U7,L1,L2,L3,L4,L5,L6,L7,L8,L9,B7,B4,B1,B8,B5,B2,B9,B6,B3,D3,D6,D9,D2,D5,D8,D1,D4,D7},+    {D9,D8,D7,D6,D5,D4,D3,D2,D1,L9,L8,L7,L6,L5,L4,L3,L2,L1,F9,F8,F7,F6,F5,F4,F3,F2,F1,U9,U8,U7,U6,U5,U4,U3,U2,U1,R9,R8,R7,R6,R5,R4,R3,R2,R1,B9,B8,B7,B6,B5,B4,B3,B2,B1},+    {U3,U6,U9,U2,U5,U8,U1,U4,U7,F1,F2,F3,F4,F5,F6,F7,F8,F9,L1,L2,L3,L4,L5,L6,L7,L8,L9,D7,D4,D1,D8,D5,D2,D9,D6,D3,B1,B2,B3,B4,B5,B6,B7,B8,B9,R1,R2,R3,R4,R5,R6,R7,R8,R9},+    {U3,U2,U1,U6,U5,U4,U9,U8,U7,L3,L2,L1,L6,L5,L4,L9,L8,L7,F3,F2,F1,F6,F5,F4,F9,F8,F7,D3,D2,D1,D6,D5,D4,D9,D8,D7,R3,R2,R1,R6,R5,R4,R9,R8,R7,B3,B2,B1,B6,B5,B4,B9,B8,B7}+};+const CornerCubie CornerCubieMove[6] = {+    {{UBR,0},{URF,0},{UFL,0},{ULB,0},{DFR,0},{DLF,0},{DBL,0},{DRB,0}},+    {{DFR,2},{UFL,0},{ULB,0},{URF,1},{DRB,1},{DLF,0},{DBL,0},{UBR,2}},+    {{UFL,1},{DLF,2},{ULB,0},{UBR,0},{URF,2},{DFR,1},{DBL,0},{DRB,0}},+    {{URF,0},{UFL,0},{ULB,0},{UBR,0},{DLF,0},{DBL,0},{DRB,0},{DFR,0}},+    {{URF,0},{ULB,1},{DBL,2},{UBR,0},{DFR,0},{UFL,2},{DLF,1},{DRB,0}},+    {{URF,0},{UFL,0},{UBR,1},{DRB,2},{DFR,0},{DLF,0},{ULB,2},{DBL,1}}+};+const EdgeCubie EdgeCubieMove[6] = {+    {{UB,0},{UR,0},{UF,0},{UL,0},{DR,0},{DF,0},{DL,0},{DB,0},{FR,0},{FL,0},{BL,0},{BR,0}},+    {{FR,0},{UF,0},{UL,0},{UB,0},{BR,0},{DF,0},{DL,0},{DB,0},{DR,0},{FL,0},{BL,0},{UR,0}},+    {{UR,0},{FL,1},{UL,0},{UB,0},{DR,0},{FR,1},{DL,0},{DB,0},{UF,1},{DF,1},{BL,0},{BR,0}},+    {{UR,0},{UF,0},{UL,0},{UB,0},{DF,0},{DL,0},{DB,0},{DR,0},{FR,0},{FL,0},{BL,0},{BR,0}},+    {{UR,0},{UF,0},{BL,0},{UB,0},{DR,0},{DF,0},{FL,0},{DB,0},{FR,0},{UL,0},{DL,0},{BR,0}},+    {{UR,0},{UF,0},{UL,0},{BR,1},{DR,0},{DF,0},{DL,0},{BL,1},{FR,0},{FL,0},{UB,1},{DB,1}}+};+const CornerCubie CornerCubieSym[4] = {+    {{URF,1},{DFR,2},{DLF,1},{UFL,2},{UBR,2},{DRB,1},{DBL,2},{ULB,1}},+    {{DLF,0},{DFR,0},{DRB,0},{DBL,0},{UFL,0},{URF,0},{UBR,0},{ULB,0}},+    {{UBR,0},{URF,0},{UFL,0},{ULB,0},{DRB,0},{DFR,0},{DLF,0},{DBL,0}},+    {{UFL,3},{URF,3},{UBR,3},{ULB,3},{DLF,3},{DFR,3},{DRB,3},{DBL,3}}+};+const EdgeCubie EdgeCubieSym[4] = {+    {{UF,1},{FR,0},{DF,1},{FL,0},{UB,1},{BR,0},{DB,1},{BL,0},{UR,1},{DR,1},{DL,1},{UL,1}},+    {{DL,0},{DF,0},{DR,0},{DB,0},{UL,0},{UF,0},{UR,0},{UB,0},{FL,0},{FR,0},{BR,0},{BL,0}},+    {{UB,0},{UR,0},{UF,0},{UL,0},{DB,0},{DR,0},{DF,0},{DL,0},{BR,1},{FR,1},{FL,1},{BL,1}},+    {{UL,0},{UF,0},{UR,0},{UB,0},{DL,0},{DF,0},{DR,0},{DB,0},{FL,0},{FR,0},{BR,0},{BL,0}}+};+enum Constant {+    GN_HTM      = 20,+    GN_QTM      = 26,+    N_MOVE      = 18,+    N_TWIST     = 2187,+    N_FLIP      = 2048,+    N_SLICE     = 495,+    N_CORNER    = 40320,+    N_EDGE8     = 40320,+    N_EDGE4     = 24,+    N_SYM       = 48,+    N_SYM_D4h   = 16,+    EQ_FLIPSLICE= 64430,+    EQ_CORNER   = 2768,+};+using std::size_t;+using namespace cube::math;+template<size_t N,typename T=int>+struct Perm+{+    using value_type = T;+    static constexpr size_t size() { return N; }+    constexpr Perm() noexcept+    {+        for(size_t i = 0; i < N; ++i) X[i] = static_cast<T>(i);+    }+    constexpr Perm(const std::array<T,N>& xs) noexcept+    :X{xs}+    {+        assert(isValidPermutation<N>(xs) && "array must be a valid permutation");+    }+    constexpr Perm(std::initializer_list<T> xs) noexcept+    {+        assert(xs.size() == N && "size mismatch");+        auto dit = X.begin();+        for(auto it = xs.begin(); it != xs.end(); it++, dit++) { *dit = *it; }+        assert(isValidPermutation<N>(X) && "invalid permutation list");+    }+    template<typename ArrayLike>+    constexpr ArrayLike act_right(const ArrayLike& src) const noexcept+    {+        return backpermute(src,this->X);+    }+    friend constexpr Perm operator*(const Perm &P, const Perm& Q) noexcept+    {+        return Q.act_right(P);+    }+    constexpr Perm& operator*=(const Perm& rhs) noexcept+    {+        return *this = *this * rhs;+    }+    friend constexpr bool operator==(const Perm &lhs, const Perm& rhs) noexcept+    {+        return lhs.X == rhs.X;+    }+    constexpr Perm operator~() const+    {+        return { forepermute(Perm::id.X, this->X) };+    }+    constexpr T& operator[](size_t idx)             { return X[idx]; }+    constexpr const T& operator[](size_t idx) const { return X[idx]; }+    bool parity() const+    {+        const auto [fixed, cs] = decomposite(this->X);+        int s = 1;+        for(auto &c:cs) s *= (c.size() % 2 == 0) ? -1 : 1;+        return s == 1;+    }+    size_t order() const { return orderOf(X); }+    constexpr size_t rank() const { return rankOf(X); }+    static constexpr Perm<N,T> fromRank(size_t i)+    { return { cube::math::fromRank<T,N>(i) }; }+    static const Perm id;+    std::array<T,N> X{};+};+template<size_t N,typename T>+inline constexpr Perm<N,T> Perm<N,T>::id{};+template<size_t N, size_t L, typename T=int>+struct CArray+{+    using value_type = T;+    static constexpr size_t period = N;+    static constexpr size_t size() noexcept { return L; }+    constexpr CArray() noexcept {}+    constexpr CArray(const std::array<T,L> &arr) noexcept+    :xs{arr}+    {+        auto n = static_cast<T>(N);+        for(size_t i = 0; i < L; i++) { xs[i] = (xs[i] % n + n) % n; }+    }+    constexpr CArray(std::initializer_list<T> list) noexcept+    {+        auto n = static_cast<T>(N);+        std::size_t i = 0;+        for(T val : list) { if(i < L) { xs[i++] = (val % n + n) % n; } }+    }+    constexpr T& operator[](size_t idx) noexcept             { return xs[idx]; }+    constexpr const T& operator[](size_t idx) const noexcept { return xs[idx]; }+    friend constexpr bool operator==(const CArray& lhs, const CArray& rhs) noexcept+    {+        return lhs.xs == rhs.xs;+    }+    constexpr CArray& operator+=(const CArray& rhs)+    {+        for(size_t i = 0; i < L; i++) xs[i] = (xs[i] + rhs.xs[i]) % N;+        return *this;+    }+    friend constexpr CArray operator+(CArray lhs, const CArray& rhs)+    {+        return lhs += rhs;+    }+    constexpr CArray operator~() const noexcept+    {+        CArray<N,L,T> inv {};+        auto n = static_cast<T>(N);+        for(size_t i = 0; i < L; i++) inv[i] = (n - xs[i]) % n;+        return inv;+    }+    constexpr T sum() const noexcept+    {+        T s = 0;+        for(size_t i = 0; i < L; i++) s += xs[i];+        return s % N;+    }+    static const CArray id;+    std::array<T,L> xs {};+};+template<size_t N, size_t L, typename T>+inline constexpr CArray<N,L,T> CArray<N,L,T>::id{};+template<size_t N, size_t L, typename T>+constexpr CArray<N,L,T> operator*(const CArray<N,L,T> &xs, const Perm<L,T> &P)+{+    return P.act_right(xs);+}+template<size_t N, size_t L, typename T>+constexpr CArray<N,L,T>& operator*=(CArray<N,L,T> &xs, const Perm<L,T> &P)+{+    return xs = P.act_right(xs);+}+template<typename T, size_t N, size_t... Ns>+struct ArrayHelper {+    using type = std::array<typename ArrayHelper<T,Ns...>::type,N>;+};+template<typename T, size_t N>+struct ArrayHelper<T,N> {+    using type = std::array<T,N>;+};+template<typename T, size_t... Ns>+struct NArray+{+    using value_type = T;+    static constexpr size_t size = (Ns * ...);+    static constexpr size_t dim = sizeof...(Ns);+    static constexpr std::array<size_t,dim> shape { Ns... };+    typename ArrayHelper<T,Ns...>::type data;+    auto & operator[](size_t i) {+        return data[i];+    }+    const auto & operator[](size_t i) const {+        return data[i];+    }+};+}+namespace cube {+using namespace cube::data;+typedef std::int8_t cube_value_t;+typedef Perm<54,    cube_value_t>   FacePerm;+typedef Perm<8,     cube_value_t>   CornerPerm;+typedef Perm<12,    cube_value_t>   EdgePerm;+typedef CArray<3, 8,cube_value_t>   CornerOri;+typedef CArray<2,12,cube_value_t>   EdgeOri;+struct ColorState;+struct FaceCube;+struct CubieCube;+constexpr CornerPerm operator*(const CornerPerm &cp, const CubieCube &cc);+constexpr CornerOri  operator*(const CornerOri  &co, const CubieCube &cc);+constexpr EdgePerm   operator*(const EdgePerm   &ep, const CubieCube &cc);+constexpr EdgeOri    operator*(const EdgeOri    &eo, const CubieCube &cc);+struct ColorState+{+    std::array<Layer,54> s;+    Layer & operator[](size_t i) noexcept           { return s[i]; }+    const Layer operator[](size_t i) const noexcept { return s[i]; }+    static ColorState fromString(std::string_view cube);+    static bool is_valid_config(std::string_view cube);+    FaceCube  toFaceCube() const;+    CubieCube toCubieCube() const;+    static const ColorState id;+};+inline const ColorState ColorState::id = {{U,U,U,U,U,U,U,U,U,R,R,R,R,R,R,R,R,R,F,F,F,F,F,F,F,F,F,D,D,D,D,D,D,D,D,D,L,L,L,L,L,L,L,L,L,B,B,B,B,B,B,B,B,B}};+struct FaceCube+{+    FacePerm f;+    CubieCube toCubieCube() const;+    friend constexpr FaceCube operator*(const FaceCube &lhs, const FaceCube &rhs)+    { return { lhs.f * rhs.f }; }+    constexpr FaceCube& operator*=(const FaceCube &rhs)+    { return *this = *this * rhs; }+    constexpr FaceCube operator~() const+    { return { ~f }; }+    friend bool operator==(const FaceCube &lhs, const FaceCube &rhs)+    { return lhs.f == rhs.f; }+    static const FaceCube id;+};+struct CubieCube+{+    CornerPerm  cp;+    CornerOri   co;+    EdgePerm    ep;+    EdgeOri     eo;+    FaceCube toFaceCube() const;+    bool isSolvable() const+    {  return cp.parity() == ep.parity() && co.sum() == 0 && eo.sum() == 0; }+    friend constexpr CubieCube operator*(const CubieCube &a, const CubieCube &b)+    { return { a.cp*b, a.co*b, a.ep*b, a.eo*b }; }+    constexpr CubieCube& operator*=(const CubieCube &rhs)+    { return *this = *this * rhs; }+    constexpr CubieCube operator~() const+    {+        auto cp_inv = ~cp;+        auto ep_inv = ~ep;+        return { cp_inv, ~(co*cp_inv), ep_inv, ~(eo*ep_inv) };+    }+    friend bool operator==(const CubieCube &lhs, const CubieCube &rhs)+    { return lhs.cp == rhs.cp && lhs.co == rhs.co && lhs.ep == rhs.ep && lhs.eo == rhs.eo; }+    static const CubieCube id;+};+inline constexpr CornerPerm operator*(const CornerPerm &cp, const CubieCube &cc) { return cp * cc.cp;}+inline constexpr CornerOri  operator*(const CornerOri &co,  const CubieCube &cc) { return co * cc.cp + cc.co; }+inline constexpr EdgePerm   operator*(const EdgePerm &ep,   const CubieCube &cc) { return ep * cc.ep; }+inline constexpr EdgeOri    operator*(const EdgeOri &eo,    const CubieCube &cc) { return eo * cc.ep + cc.eo; }+inline constexpr CornerPerm    eCP = {0,1,2,3,4,5,6,7};+inline constexpr EdgePerm      eEP = {0,1,2,3,4,5,6,7,8,9,10,11};+inline constexpr CornerOri     eCO = {0,0,0,0,0,0,0,0};+inline constexpr EdgeOri       eEO = {0,0,0,0,0,0,0,0,0,0,0,0};+inline constexpr FacePerm      eFP = {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53};+inline const FaceCube   FaceCube::id = FaceCube{eFP};+inline const CubieCube  CubieCube::id = CubieCube{eCP,eCO,eEP,eEO};+inline constexpr CubieCube mU = {{3,0,1,2,4,5,6,7},{0,0,0,0,0,0,0,0},{3,0,1,2,4,5,6,7,8,9,10,11},{0,0,0,0,0,0,0,0,0,0,0,0}};+inline constexpr CubieCube mR = {{4,1,2,0,7,5,6,3},{2,0,0,1,1,0,0,2},{8,1,2,3,11,5,6,7,4,9,10,0},{0,0,0,0,0,0,0,0,0,0,0,0}};+inline constexpr CubieCube mF = {{1,5,2,3,0,4,6,7},{1,2,0,0,2,1,0,0},{0,9,2,3,4,8,6,7,1,5,10,11},{0,1,0,0,0,1,0,0,1,1,0,0}};+inline constexpr CubieCube mD = {{0,1,2,3,5,6,7,4},{0,0,0,0,0,0,0,0},{0,1,2,3,5,6,7,4,8,9,10,11},{0,0,0,0,0,0,0,0,0,0,0,0}};+inline constexpr CubieCube mL = {{0,2,6,3,4,1,5,7},{0,1,2,0,0,2,1,0},{0,1,10,3,4,5,9,7,8,2,6,11},{0,0,0,0,0,0,0,0,0,0,0,0}};+inline constexpr CubieCube mB = {{0,1,3,7,4,5,2,6},{0,0,1,2,0,0,2,1},{0,1,2,11,4,5,6,10,8,9,3,7},{0,0,0,1,0,0,0,1,0,0,1,1}};+inline constexpr std::array<CubieCube,18>+    ElementaryMove = { mU,mU*mU,mU*mU*mU,mR,mR*mR,mR*mR*mR,mF,mF*mF,mF*mF*mF,mD,mD*mD,mD*mD*mD,mL,mL*mL,mL*mL*mL,mB,mB*mB,mB*mB*mB };+inline constexpr FaceCube pU = {{6,3,0,7,4,1,8,5,2,45,46,47,12,13,14,15,16,17,9,10,11,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20,39,40,41,42,43,44,36,37,38,48,49,50,51,52,53}};+inline constexpr FaceCube pR = {{0,1,20,3,4,23,6,7,26,15,12,9,16,13,10,17,14,11,18,19,29,21,22,32,24,25,35,27,28,51,30,31,48,33,34,45,36,37,38,39,40,41,42,43,44,8,46,47,5,49,50,2,52,53}};+inline constexpr FaceCube pF = {{0,1,2,3,4,5,44,41,38,6,10,11,7,13,14,8,16,17,24,21,18,25,22,19,26,23,20,15,12,9,30,31,32,33,34,35,36,37,27,39,40,28,42,43,29,45,46,47,48,49,50,51,52,53}};+inline constexpr FaceCube pD = {{0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,24,25,26,18,19,20,21,22,23,42,43,44,33,30,27,34,31,28,35,32,29,36,37,38,39,40,41,51,52,53,45,46,47,48,49,50,15,16,17}};+inline constexpr FaceCube pL = {{53,1,2,50,4,5,47,7,8,9,10,11,12,13,14,15,16,17,0,19,20,3,22,23,6,25,26,18,28,29,21,31,32,24,34,35,42,39,36,43,40,37,44,41,38,45,46,33,48,49,30,51,52,27}};+inline constexpr FaceCube pB = {{11,14,17,3,4,5,6,7,8,9,10,35,12,13,34,15,16,33,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,36,39,42,2,37,38,1,40,41,0,43,44,51,48,45,52,49,46,53,50,47}};+inline constexpr std::array<FaceCube,18>+    ElementaryPerm = { pU,pU*pU,pU*pU*pU,pR,pR*pR,pR*pR*pR,pF,pF*pF,pF*pF*pF,pD,pD*pD,pD*pD*pD,pL,pL*pL,pL*pL*pL,pB,pB*pB,pB*pB*pB };+inline FaceCube operator*(const FaceCube &c, const std::vector<TurnMove> &ms)+{+    FaceCube fc = c;+    for (auto m : ms) fc = fc * ElementaryPerm[m];+    return fc;+}+inline CubieCube operator*(const CubieCube &c, const std::vector<TurnMove> &ms)+{+    CubieCube cc = c;+    for (auto m : ms) cc = cc * ElementaryMove[m];+    return cc;+}+inline ColorState operator*(const ColorState &c, const std::vector<TurnMove> &ms)+{+    ColorState cs = c;+    for (auto m : ms) cs = ElementaryPerm[m].f.act_right(cs);+    return cs;+}+}+namespace cube {+using namespace cube::data;+ColorState ColorState::fromString(std::string_view cube)+{+    assert(is_valid_config(cube) && "invalid cube config");+    std::array<Layer,54> xs{};+    std::transform(cube.cbegin(), cube.cend(), xs.begin(), [](char c) {+        switch(c) {+        case 'U': return U;+        case 'R': return R;+        case 'F': return F;+        case 'D': return D;+        case 'L': return L;+        case 'B': return B;+        default: throw std::invalid_argument("invalid cube config");+        }+    });+    return { xs };+}+bool ColorState::is_valid_config(std::string_view cfg)+{+    if(cfg.size() != 54) return false;+    std::set<char> vs { cfg[CC[0]],cfg[CC[1]],cfg[CC[2]],cfg[CC[3]],cfg[CC[4]],cfg[CC[5]] };+    if(vs.size() != 6) return false;+    for(size_t i = 0, x = 0; i < 8; i++) {+        for(x = 0; x < 24; x++) {+            if(cfg[CC[CCI[i][0]]] == cfg[CF[x/3][x%3]]+               && cfg[CC[CCI[i][1]]] == cfg[CF[x/3][(x+1)%3]]+               && cfg[CC[CCI[i][2]]] == cfg[CF[x/3][(x+2)%3]]) break;+        }+        if(x >= 24) return false;+    }+    for(size_t i = 0, y = 0; i < 12; i++) {+        for(y = 0; y < 24; y++) {+            if(cfg[CC[ECI[i][0]]] == cfg[EF[y/2][y%2]]+               && cfg[CC[ECI[i][1]]] == cfg[EF[y/2][(y+1)%2]]) break;+        }+        if(y >= 24) return false;+    }+    return true;+}+FaceCube ColorState::toFaceCube() const+{+    FacePerm fp{};+    for(int i = 0; i < 6; ++i) {+        fp[CC[i]] = s[CC[i]];+    }+    for(int i = 0; i < 8; i++) {+        for(int x = 0; x < 24; x++) {+            if(s[CC[CCI[i][0]]] == s[CF[x/3][x%3]]+            && s[CC[CCI[i][1]]] == s[CF[x/3][(x+1)%3]]+            && s[CC[CCI[i][2]]] == s[CF[x/3][(x+2)%3]])+            {+                fp[CF[x/3][x%3]]      = CF[i][0];+                fp[CF[x/3][(x+1)%3]]  = CF[i][1];+                fp[CF[x/3][(x+2)%3]]  = CF[i][2];+                break;+            }+        }+    }+    for(int i = 0; i < 12; i++) {+        for(int y = 0; y < 24; y++) {+            if(s[CC[ECI[i][0]]] == s[EF[y/2][y%2]]+            && s[CC[ECI[i][1]]] == s[EF[y/2][(y+1)%2]])+            {+                fp[EF[y/2][y%2]]      = EF[i][0];+                fp[EF[y/2][(y+1)%2]]  = EF[i][1];+                break;+            }+        }+    }+    return { fp };+}+CubieCube ColorState::toCubieCube() const+{+    return toFaceCube().toCubieCube();+}+CubieCube FaceCube::toCubieCube() const+{+    CubieCube cc{};+    const FaceCube &fc = *this;+    for(int i = 0; i < 8; i++) {+        for(int x = 0; x < 24; x++) {+            if(fc.f[CF[i][0]] == CF[x/3][x%3]) {+                cc.cp[i] = x/3, cc.co[i] = (3-x%3)%3;+                break;+            }+        }+    }+    for(int i = 0; i < 12; i++){+        for(int y = 0; y < 24; y++){+            if(fc.f[EF[i][0]] == EF[y/2][y%2]) {+                cc.ep[i] = y/2, cc.eo[i] = (2-y%2)%2;+                break;+            }+        }+    }+    return cc;+}+FaceCube CubieCube::toFaceCube() const+{+    FaceCube fc{};+    const CubieCube &cc = *this;+    for(int i = 0; i < 6; i++) {+        fc.f[CC[i]] = CC[i];+    }+    for(int i = 0; i < 8; i++) for(int j = 0; j < 3; j++) {+        fc.f[CF[i][j]] = CF[cc.cp[i]][(j-cc.co[i]+3)%3];+    }+    for(int i = 0; i < 12; i++) for(int j = 0; j < 2; j++) {+        fc.f[EF[i][j]] = EF[cc.ep[i]][(j-cc.eo[i]+2)%2];+    }+    return fc;+}+}+namespace cube::pdb {+struct Coord+{+    int twist, flip, slice;+    int corner, edge4, edge8;+    static const Coord id;+    static CornerOri    twist2co(int);+    static int          co2twist(const CornerOri &);+    static EdgeOri      flip2eo(int);+    static int          eo2flip(const EdgeOri &);+    static CornerPerm   corner2cp(int);+    static int          cp2corner(const CornerPerm &);+    static int          ep2slice(const EdgePerm &);+    static int          ep2edge4(const EdgePerm &);+    static int          ep2edge8(const EdgePerm &);+    static EdgePerm     slice2ep(int);+    static EdgePerm     edge42ep(int);+    static EdgePerm     edge82ep(int);+    static EdgePerm     see2ep(int,int,int);+    static Coord        CubieCube2Coord(const CubieCube &);+    static CubieCube    Coord2CubieCube(const Coord &);+};+constexpr bool operator==(const Coord &c1, const Coord &c2)+{+    return c1.twist == c2.twist && c1.flip == c2.flip && c1.slice == c2.slice+        && c1.corner == c2.corner && c1.edge4 == c2.edge4 && c1.edge8 == c2.edge8;+}+inline constexpr Coord Coord::id = { 0,0,0,0,0,0 };+}+namespace cube::pdb {+using namespace cube::math;+using namespace cube::data;+inline bool isSliceEdge(size_t idx)+{+    return FR <= idx && idx <= BR;+}+int Coord::co2twist(const CornerOri &co)+{+    return static_cast<int>(fromDigits<3>(takeByRange<1,7>(co.xs)));+}+CornerOri Coord::twist2co(int i)+{+    CornerOri co;+    auto sub1to7 = CArray<3,7,CornerOri::value_type>{toDigits<3,7,CornerOri::value_type>(i)};+    std::copy(sub1to7.xs.begin(),sub1to7.xs.end(),co.xs.begin()+1);+    co[0] = (3 - sub1to7.sum()) % 3;+    return co;+}+int Coord::eo2flip(const EdgeOri &eo)+{+    return static_cast<int>(fromDigits<2>(takeByRange<1,11>(eo.xs)));+}+EdgeOri Coord::flip2eo(int i)+{+    EdgeOri eo;+    auto sub1to11 = CArray<2,11,CornerOri::value_type>{toDigits<2,11,CornerOri::value_type>(i)};+    std::copy(sub1to11.xs.begin(),sub1to11.xs.end(),eo.xs.begin()+1);+    eo[0] = (2 - sub1to11.sum()) % 2;+    return eo;+}+int Coord::ep2slice(const EdgePerm &ep)+{+    int x[4],slice=0,N=12;+    for(int i = 0, j = 0; i < N; i++) {+        if(isSliceEdge(ep[i])) x[j++] = i;+    }+    for(int i = 0; i < 4; i++) slice += binomial(N-1-x[i],4-i);+    return slice;+}+int Coord::ep2edge4(const EdgePerm &ep)+{+    Perm<4,EdgePerm::value_type> edge4_perm;+    for(int i = 0, j = 0; i < 4; i++, j++) {+        while(!isSliceEdge(ep[j])) j++;+        edge4_perm[i] = ep[j] - 8;+    }+    return static_cast<int>(edge4_perm.rank());+}+int Coord::ep2edge8(const EdgePerm &ep)+{+    Perm<8,EdgePerm::value_type> edge8_perm;+    for(size_t i = 0, j = 0; i < 8; i++, j++) {+        while(isSliceEdge(ep[j]) || ep[j] == (EdgePerm::value_type) ~0UL) j++;+        edge8_perm[i] = ep[j] - 0;+    }+    return static_cast<int>(edge8_perm.rank());+}+int Coord::cp2corner(const CornerPerm &cp)+{+    return static_cast<int>(cp.rank());+}+CornerPerm Coord::corner2cp(int i)+{+    return CornerPerm::fromRank(i);+}+EdgePerm Coord::slice2ep(int i)+{+    auto si = lexicalOrderToIndices<12,4>(i);+    EdgePerm ep;+    for(size_t i = 0, j = 0; i < 12; i++){+        ep[i] = (i == si[j]) ? 8 + j++ : (EdgePerm::value_type) ~0UL;+    }+    return ep;+}+EdgePerm Coord::edge42ep(int i)+{+    EdgePerm ep;+    auto e4 = Perm<4,EdgePerm::value_type>::fromRank(i);+    for(size_t i = 0; i < 12; i++){+        ep[i] = (i < 8) ? (EdgePerm::value_type) ~0UL : e4[i-8] + 8;+    }+    return ep;+}+EdgePerm Coord::edge82ep(int i)+{+    EdgePerm ep;+    auto e8 = Perm<8,EdgePerm::value_type>::fromRank(i);+    for(size_t i = 0; i < 12; i++){+        ep[i] = (i < 8) ? e8[i] + 0 : (EdgePerm::value_type) ~0UL;+    }+    return ep;+}+EdgePerm Coord::see2ep(int slice, int edge4, int edge8)+{+    auto e4 = Perm<4,EdgePerm::value_type>::fromRank(edge4);+    auto e8 = Perm<8,EdgePerm::value_type>::fromRank(edge8);+    auto slice_indices = lexicalOrderToIndices<12,4>(slice);+    EdgePerm ep;+    for(size_t i = 0, j = 0, x = 0, y = 0; i < 12; i++) {+        ep[i] = (i == slice_indices[j] && ++j) ? e4[x++]+8: e8[y++]+0;+    }+    return ep;+}+Coord Coord::CubieCube2Coord(const CubieCube &cc)+{+    return {+        Coord::co2twist(cc.co),+        Coord::eo2flip(cc.eo),+        Coord::ep2slice(cc.ep),+        Coord::cp2corner(cc.cp),+        Coord::ep2edge4(cc.ep),+        Coord::ep2edge8(cc.ep)+    };+}+CubieCube Coord::Coord2CubieCube(const Coord &c)+{+    return {+        Coord::corner2cp(c.corner),+        Coord::twist2co(c.twist),+        Coord::see2ep(c.slice,c.edge4,c.edge8),+        Coord::flip2eo(c.flip)+    };+}+}+namespace cube::config {+void set_table_dir(std::filesystem::path dir);+auto get_table_dir() -> std::filesystem::path;+}+namespace cube::pdb {+using namespace cube::data;+namespace fs = std::filesystem;+typedef uint16_t    mt_value_t;+typedef uint8_t     pt_value_t;+template <typename Table> void save_to(const Table &table, fs::path path);+template <typename Table> void load_from(Table &table, fs::path path);+template<class T>+class Singleton+{+public:+    Singleton(const Singleton&) = delete;+    Singleton(Singleton&&) = delete;+    Singleton& operator=(const Singleton&) = delete;+    Singleton& operator=(Singleton&&) = delete;+    static T& instance() {+        static T obj {};+        return obj;+    }+protected:+    Singleton() = default;+    ~Singleton() = default;+};+template<typename T=mt_value_t>+struct TableMove+{+    static_assert(std::is_integral<T>::value);+    static_assert(std::numeric_limits<T>::digits >= 16);+    using value_t = T;+    TableMove(fs::path dir = {});+    TableMove(const TableMove &) = delete;+    ~TableMove();+    TableMove& operator=(const TableMove &) = delete;+    template<typename Table, typename F1, typename F2>+    std::enable_if_t<Table::shape[0] == N_MOVE, void>+    buildMoveTable(Table &t, F1&& coord2i, F2&& i2coord, fs::path filename);+    static bool is_ready(fs::path);+    const fs::path tdir;+    NArray<T,N_MOVE,N_TWIST>   *pTMTwist;+    NArray<T,N_MOVE,N_FLIP>    *pTMFlip;+    NArray<T,N_MOVE,N_SLICE>   *pTMSlice;+    NArray<T,N_MOVE,N_CORNER>  *pTMCorner;+    NArray<T,N_MOVE,N_EDGE4>   *pTMEdge4;+    NArray<T,N_MOVE,N_EDGE8>   *pTMEdge8;+};+template<typename T=pt_value_t>+struct TablePrunning+{+    using value_type = T;+    TablePrunning(fs::path dir = {});+    TablePrunning(const TablePrunning &) = delete;+    ~TablePrunning();+    TablePrunning operator=(const TablePrunning &) = delete;+    template<typename Table, typename MT1, typename MT2>+    std::enable_if_t<Table::shape[0] == MT1::shape[1] && Table::shape[1] == MT2::shape[1]>+    buildPrunningTable(Table &t, const MT1 &mt1, const MT2 &mt2, fs::path filename);+    static bool is_ready(fs::path);+    const fs::path tdir;+    NArray<T,N_SLICE,N_FLIP>   *pTPSliceFlip;+    NArray<T,N_SLICE,N_TWIST>  *pTPSliceTwist;+    NArray<T,N_EDGE4,N_EDGE8>  *pTPEdge4Edge8;+    NArray<T,N_EDGE4,N_CORNER> *pTPEdge4Corner;+};+template<typename T=mt_value_t>+using SingletonTM = Singleton<TableMove<T>>;+template<typename T=pt_value_t>+using SingletonTP = Singleton<TablePrunning<T>>;+inline const auto &get_TM() { return SingletonTM<>::instance(); }+inline const auto &get_TP() { return SingletonTP<>::instance(); }+inline bool tables_ready(fs::path dir = {})+{+    return TableMove<>::is_ready(dir) && TablePrunning<>::is_ready(dir);+}+inline void preload_tables()+{+    (void) get_TM();+    (void) get_TP();+}+}+#if defined(VERBOSE) && VERBOSE+#define VPRINT(...) printf(__VA_ARGS__)+#else+#define VPRINT(...)+#endif+namespace cube::pdb {+using namespace cube::data;+auto table_dir_or_default(fs::path dir) -> fs::path+{+    return dir.empty() ? cube::config::get_table_dir() : dir;+}+template <typename Table>+void save_to(const Table &table, fs::path path)+{+    std::ofstream f(path, std::ios::binary);+    if(f.is_open()) {+        f.write(reinterpret_cast<const char*>(&table.data), sizeof(table.data));+        f.close();+    }+}+template <typename Table>+void load_from(Table &table, fs::path path)+{+    VPRINT("loading table from %s...", path.c_str());+    std::ifstream f(path,std::ios::binary);+    f.read(reinterpret_cast<char*>(&table.data), sizeof(table.data));+    f.close();+    VPRINT("done.\n");+}+template<typename T>+template<typename Table, typename F1, typename F2>+std::enable_if_t<Table::shape[0] == N_MOVE>+TableMove<T>::buildMoveTable(Table &t, F1&& coord2i, F2&& i2coord, fs::path filename)+{+    VPRINT("creating move table %s of shape (%zu,%zu)... ",+           filename.c_str(), t.shape[0], t.shape[1]);+    for(size_t i = 0; i < t.shape[0]; i++) for(size_t j = 0; j < t.shape[1]; j++) {+        t[i][j] = coord2i(i2coord(j) * ElementaryMove[i]);+    }+    if(filename != "") save_to(t, tdir/filename);+    VPRINT("done.\n");+}+template<typename T>+TableMove<T>::TableMove(fs::path dir)+:tdir{table_dir_or_default(dir)}+{+    VPRINT("INIT MOVE TABLES -- \n");+    pTMTwist     = new NArray<T,N_MOVE,N_TWIST>;+    pTMFlip      = new NArray<T,N_MOVE,N_FLIP>;+    pTMSlice     = new NArray<T,N_MOVE,N_SLICE>;+    pTMCorner    = new NArray<T,N_MOVE,N_CORNER>;+    pTMEdge4     = new NArray<T,N_MOVE,N_EDGE4>;+    pTMEdge8     = new NArray<T,N_MOVE,N_EDGE8>;+    if(!is_ready(tdir)) {+        if(!fs::exists(tdir)) fs::create_directories(tdir);+        buildMoveTable(*pTMTwist, Coord::co2twist, Coord::twist2co, "tm_twist.dat");+        buildMoveTable(*pTMFlip, Coord::eo2flip, Coord::flip2eo, "tm_flip.dat");+        buildMoveTable(*pTMSlice, Coord::ep2slice, Coord::slice2ep, "tm_slice.dat");+        buildMoveTable(*pTMCorner, Coord::cp2corner, Coord::corner2cp, "tm_corner.dat");+        buildMoveTable(*pTMEdge4, Coord::ep2edge4, Coord::edge42ep, "tm_edge4.dat");+        buildMoveTable(*pTMEdge8, Coord::ep2edge8, Coord::edge82ep, "tm_edge8.dat");+    } else {+        load_from(*pTMTwist, tdir/"tm_twist.dat");+        load_from(*pTMFlip, tdir/"tm_flip.dat");+        load_from(*pTMSlice, tdir/"tm_slice.dat");+        load_from(*pTMCorner, tdir/"tm_corner.dat");+        load_from(*pTMEdge4, tdir/"tm_edge4.dat");+        load_from(*pTMEdge8, tdir/"tm_edge8.dat");+    }+    VPRINT("-- DONE.\n");+}+template<typename T>+TableMove<T>::~TableMove()+{+    delete pTMTwist;+    delete pTMFlip;+    delete pTMSlice;+    delete pTMCorner;+    delete pTMEdge4;+    delete pTMEdge8;+}+template<typename T>+bool TableMove<T>::is_ready(fs::path tdir)+{+    tdir = table_dir_or_default(tdir);+    return fs::exists(tdir/"tm_twist.dat") &&+           fs::exists(tdir/"tm_flip.dat") &&+           fs::exists(tdir/"tm_slice.dat") &&+           fs::exists(tdir/"tm_corner.dat") &&+           fs::exists(tdir/"tm_edge4.dat") &&+           fs::exists(tdir/"tm_edge8.dat");+}+template<typename T>+template<typename Table, typename MT1, typename MT2>+std::enable_if_t<Table::shape[0] == MT1::shape[1] && Table::shape[1] == MT2::shape[1]>+TablePrunning<T>::buildPrunningTable(+    Table &t, const MT1 &mt1, const MT2 &mt2, fs::path filename)+{+    VPRINT("creating prunning table %s of shape (%zu,%zu):\n",+           filename.c_str(), mt1.shape[1], mt2.shape[1]);+    std::fill_n(&t.data[0][0], t.size, (typename Table::value_type) ~0UL);+    t[0][0] = 0;+    typename Table::value_type depth = 0;+    size_t count = 1;+    VPRINT("\tdepth %2d: %10zu / %-10zu.\n", depth, count, t.size);+    while(count < t.size)+    {+        for(size_t i = 0; i < t.shape[0]; i++) for(size_t j = 0; j < t.shape[1]; j++)+        if(t[i][j] == depth) {+            for(auto k = 0; k < N_MOVE; k++) {+                auto ii = mt1[k][i], jj = mt2[k][j];+                if(t[ii][jj] == (typename Table::value_type)~0UL) { t[ii][jj] = depth + 1; count++; }+            }+        }+        depth++;+        VPRINT("\tdepth %2d: %10zu / %-10zu.\n", depth, count, t.size);+    }+    if(filename != "") save_to(t, tdir/filename);+    VPRINT("done.\n");+}+template<typename T>+TablePrunning<T>::TablePrunning(fs::path dir)+:tdir{table_dir_or_default(dir)}+{+    VPRINT("INIT PRUNNING TABLES -- \n");+    pTPSliceFlip     = new NArray<T,N_SLICE,N_FLIP>;+    pTPSliceTwist    = new NArray<T,N_SLICE,N_TWIST>;+    pTPEdge4Edge8    = new NArray<T,N_EDGE4,N_EDGE8>;+    pTPEdge4Corner   = new NArray<T,N_EDGE4,N_CORNER>;+    if(!is_ready(tdir)) {+        const auto &TM = get_TM();+        buildPrunningTable(*pTPSliceTwist, *TM.pTMSlice, *TM.pTMTwist, "tp_slicetwist.dat");+        buildPrunningTable(*pTPSliceFlip, *TM.pTMSlice, *TM.pTMFlip, "tp_sliceflip.dat");+        buildPrunningTable(*pTPEdge4Corner, *TM.pTMEdge4, *TM.pTMCorner, "tp_edge4corner.dat");+        buildPrunningTable(*pTPEdge4Edge8, *TM.pTMEdge4, *TM.pTMEdge8, "tp_edge4edge8.dat");+    } else {+        load_from(*pTPSliceTwist, tdir/"tp_slicetwist.dat");+        load_from(*pTPSliceFlip, tdir/"tp_sliceflip.dat");+        load_from(*pTPEdge4Corner,tdir/"tp_edge4corner.dat");+        load_from(*pTPEdge4Edge8, tdir/"tp_edge4edge8.dat");+    }+    VPRINT("-- DONE.\n");+}+template<typename T>+TablePrunning<T>::~TablePrunning()+{+    delete pTPSliceFlip;+    delete pTPSliceTwist;+    delete pTPEdge4Edge8;+    delete pTPEdge4Corner;+}+template<typename T>+bool TablePrunning<T>::is_ready(fs::path tdir)+{+    tdir = table_dir_or_default(tdir);+    return fs::exists(tdir/"tp_slicetwist.dat") &&+           fs::exists(tdir/"tp_sliceflip.dat") &&+           fs::exists(tdir/"tp_edge4corner.dat") &&+           fs::exists(tdir/"tp_edge4edge8.dat");+}+template struct TableMove<>;+template struct TablePrunning<>;+}+namespace cube::solver {+using namespace cube::data;+using namespace cube::pdb;+enum enum_phase { Ph1=0, Ph2=1 };+struct solve_session+{+    const Coord root;+    const size_t good_enough;+    const size_t max_step;+};+class TwoPhaseSolver+{+public:+    auto solve(const Coord &c, int max_step = DS)+        -> std::tuple<bool,std::vector<TurnMove>,std::vector<TurnMove>>;+protected:+    template<enum_phase PhX>+    bool search_phase(const Coord &c, size_t togo);+    template<enum_phase PhX>+    static Coord transform(const Coord &c, const TurnMove &m);+    template<enum_phase PhX>+    static size_t distance(const Coord &c);+    static constexpr int D0 = 12, D1 = 18, DS = D0+D1;+    template<enum_phase PhX> static constexpr auto& D = std::get<PhX>(std::tie(D0,D1));+    static constexpr std::array<TurnMove,18> EM0+        = { Ux1,Ux2,Ux3,Rx1,Rx2,Rx3,Fx1,Fx2,Fx3,Dx1,Dx2,Dx3,Lx1,Lx2,Lx3,Bx1,Bx2,Bx3 };+    static constexpr std::array<TurnMove,10> EM1+        = { Ux1,Ux2,Ux3,Rx2,Fx2,Dx1,Dx2,Dx3,Lx2,Bx2 };+    template<enum_phase PhX>+    static constexpr auto& EM = std::get<PhX>(std::tie(EM0,EM1));+protected:+    template<enum_phase PhX>+    void reset_ph_sofar() { sofar_[PhX].fill(-1); }+    template<enum_phase PhX>+    void set_ph_sofar(int step, int move) { sofar_[PhX][step] = move; }+    template<enum_phase PhX>+    int get_ph_sofar(int step) { return sofar_[PhX][step]; }+    template<enum_phase PhX>+    void set_ph_solution(size_t L)+    {+        rsolution_[PhX].first = L;+        std::copy(sofar_[PhX].begin(), sofar_[PhX].begin()+L, rsolution_[PhX].second.begin());+    }+    template<enum_phase PhX>+    auto get_ph_solution() const -> std::vector<TurnMove>+    {+        size_t n = rsolution_[PhX].first;+        if(n == 0) return {};+        std::vector<TurnMove> sol(n);+        for(auto i = 0; i < n; i++) {+            sol[i] = static_cast<TurnMove>(rsolution_[PhX].second[n-1-i]);+        }+        return sol;+    }+    Coord ph2_origin(Coord c) const;+private:+    std::array<std::array<int,DS+2>,2>                  sofar_;+    std::array<std::pair<size_t,std::array<int,DS>>,2>  rsolution_;+};+class TwoPhaseOptimSolver: public TwoPhaseSolver+{+public:+    auto solve(const Coord &c, size_t good = 0)+        -> std::tuple<bool,std::vector<TurnMove>,std::vector<TurnMove>>;+    int start_search_ph1(const Coord& c, size_t d, size_t d_orig, size_t maxL);+    bool start_search_ph2(const Coord& c, size_t togo);+private:+    Coord root_;+    size_t good_;+};+}+namespace cube::solver {+#define TM cube::pdb::get_TM()+#define TP cube::pdb::get_TP()+inline bool is_dull_pair(const TurnMove A, const int B)+{+    if(!(B >= Ux1 && B <= Bx3)) return false;+    return (A/3 == B/3) || (A/3 == B/3+3);+}+template<enum_phase I>+Coord TwoPhaseSolver::transform(const Coord &c, const TurnMove &m)+{+    if constexpr (I == Ph1)+    return Coord {+        (*TM.pTMTwist)[m][c.twist], (*TM.pTMFlip)[m][c.flip], (*TM.pTMSlice)[m][c.slice],+        -1,-1,-1+    };+    else+    return Coord {+        0,0,0,+        (*TM.pTMCorner)[m][c.corner], (*TM.pTMEdge4)[m][c.edge4], (*TM.pTMEdge8)[m][c.edge8]+    };+}+template<enum_phase I>+size_t TwoPhaseSolver::distance(const Coord &c)+{+    if constexpr (I == Ph1)+    return std::max((*TP.pTPSliceTwist)[c.slice][c.twist],+                    (*TP.pTPSliceFlip)[c.slice][c.flip]);+    else+    return std::max((*TP.pTPEdge4Corner)[c.edge4][c.corner],+                    (*TP.pTPEdge4Edge8)[c.edge4][c.edge8]);+}+template<enum_phase PhX>+bool TwoPhaseSolver::search_phase(const Coord &c, size_t togo)+{+    if(togo < distance<PhX>(c)) return false;+    if(togo == 0) return distance<PhX>(c) == 0;+    for(auto m: EM<PhX>)+    {+        if(is_dull_pair(m,get_ph_sofar<PhX>(togo))) continue;+        set_ph_sofar<PhX>(togo-1,m);+        bool ret = search_phase<PhX>(transform<PhX>(c,m), togo-1);+        if(ret) return true;+    }+    return false;+}+Coord TwoPhaseSolver::ph2_origin(Coord c) const+{+    int corner = c.corner, edge4, edge8;+    auto ep = Coord::see2ep(c.slice,c.edge4,c.edge8);+    for(auto &m : get_ph_solution<Ph1>())+    {+        corner = (*TM.pTMCorner)[m][corner];+        ep = ep * ElementaryMove[m].ep;+    }+    edge4 = Coord::ep2edge4(ep);+    edge8 = Coord::ep2edge8(ep);+    return Coord { 0,0,0,corner,edge4,edge8 };+}+auto TwoPhaseSolver::solve(const Coord &c, int step)+    -> std::tuple<bool,std::vector<TurnMove>,std::vector<TurnMove>>+{+    reset_ph_sofar<Ph1>();+    reset_ph_sofar<Ph2>();+    const size_t maxL = std::clamp(step,0,DS);+    for(auto d1 = distance<Ph1>(c); d1 <= maxL; d1++)+    {+        bool ret1 = search_phase<Ph1>(c,d1);+        if(!ret1) continue;+        set_ph_solution<Ph1>(d1);+        auto c2 = ph2_origin(c);+        for(auto d2 = distance<Ph2>(c2); d2 <= maxL-d1; d2++)+        {+            bool ret2 = search_phase<Ph2>(c2,d2);+            if(!ret2) continue;+            set_ph_solution<Ph2>(d2);+            return {true, get_ph_solution<Ph1>(), get_ph_solution<Ph2>()};+        }+    }+    return {false, {}, {}};+}+auto TwoPhaseOptimSolver::solve(const Coord &c, size_t good)+    -> std::tuple<bool,std::vector<TurnMove>,std::vector<TurnMove>>+{+    good_ = good;+    root_ = c;+    size_t bestL = DS + 1;+    reset_ph_sofar<Ph1>();+    for(auto togo = distance<Ph1>(c); togo < bestL; ++togo)+    {+        int l = start_search_ph1(c,togo,togo,bestL-1);+        if(l >= 0) bestL = std::min(bestL,static_cast<size_t>(l));+        if(bestL <= good_) break;+    }+    if(bestL > DS) return {false, {}, {}};+    else return { true, get_ph_solution<Ph1>(), get_ph_solution<Ph2>() };+}+int TwoPhaseOptimSolver::start_search_ph1(const Coord& c, size_t d, size_t d_orig, size_t maxL)+{+    if(d < distance<Ph1>(c)) return -1;+    if(d == 0) {+        set_ph_solution<Ph1>(d_orig);+        auto c2 = ph2_origin(root_);+        reset_ph_sofar<Ph2>();+        for(auto togo = distance<Ph2>(c2); togo <= maxL; ++togo)+        {+            bool succ = start_search_ph2(c2,togo);+            if(succ) {+                set_ph_solution<Ph2>(togo);+                return togo;+            }+        }+        return -1;+    }+    int bestL = maxL + 1;+    for(auto m: EM<Ph1>)+    {+        if(is_dull_pair(m, get_ph_sofar<Ph1>(d))) continue;+        set_ph_sofar<Ph1>(d-1,m);+        auto l = start_search_ph1(transform<Ph1>(c,m), d-1, d_orig, bestL-2);+        if(l >= 0 && bestL > l+1) {+            bestL = l+1;+        }+        if(bestL + d_orig - d <= good_) break;+        if(d >= bestL) break;+    }+    return bestL > static_cast<int>(maxL) ? -1 : bestL;+}+bool TwoPhaseOptimSolver::start_search_ph2(const Coord& c, size_t togo)+{   if(togo < distance<Ph2>(c)) return false;+    if(togo == 0) return distance<Ph2>(c) == 0;+    for(auto m: EM<Ph2>)+    {+        if(is_dull_pair(m, get_ph_sofar<Ph2>(togo))) continue;+        set_ph_sofar<Ph2>(togo-1,m);+        bool ret = start_search_ph2(transform<Ph2>(c,m), togo-1);+        if(ret) return true;+    }+    return false;+}+}+namespace cube::utils {+inline auto get_cache_dir() -> std::filesystem::path+{+#ifdef _WIN32+    const char* localAppData = std::getenv("LOCALAPPDATA");+    if (localAppData) return std::filesystem::path(localAppData);+#elif __APPLE__+    const char* home = std::getenv("HOME");+    if (home) return std::filesystem::path(home) / "Library" / "Caches";+#else+    const char* xdgCache = std::getenv("XDG_CACHE_HOME");+    if (xdgCache) return std::filesystem::path(xdgCache);+    const char* home = std::getenv("HOME");+    if (home) return std::filesystem::path(home) / ".cache";+#endif+    throw std::runtime_error("Unable to determine cache path");+}+template<typename F, typename... Args>+inline auto time_execution(F&& f, Args&&... args)+{+    using Rf = std::invoke_result_t<F, Args...>;+    auto start = std::chrono::high_resolution_clock::now();+    auto duration_from_start = [start](){+        auto end = std::chrono::high_resolution_clock::now();+        return std::chrono::duration_cast<std::chrono::microseconds>(end-start);+    };+    if constexpr (std::is_void_v<Rf>) {+        std::forward<F>(f)(std::forward<Args>(args)...);+        return std::make_pair(+            duration_from_start(),+            std::nullopt+        );+    } else {+        auto result = std::forward<F>(f)(std::forward<Args>(args)...);+        return std::make_pair(+            duration_from_start(),+            std::make_optional(result)+        );+    }+}+}+namespace cube::config+{+namespace fs = std::filesystem;+static fs::path& get_custom_dir_storage()+{+    static fs::path custom_dir = "";+    return custom_dir;+}+void set_table_dir(fs::path dir)+{+    get_custom_dir_storage() = dir;+}+fs::path get_table_dir()+{+    const auto user_dir = get_custom_dir_storage();+    if(!user_dir.empty()) return user_dir;+    if(const char *env = std::getenv("CUBE_TABLE_DIR")) {+        if(env[0] != '\0') return fs::path(env);+    }+    try {+        return utils::get_cache_dir() / "cube.coshz" / "tables";+    } catch (...) {+        return fs::absolute("tables");+    }+}+}+namespace cube::internal+{+using namespace cube::data;+std::string apply_maneuver(std::string_view s, const std::vector<TurnMove>& ms);+auto parse_maneuver(std::string_view s) -> std::vector<TurnMove>;+inline auto operator""_Tm(const char* ts, size_t n) -> std::vector<TurnMove>+{+    return parse_maneuver(std::string(ts,n));+}+bool is_valid_maneuver(std::string_view);+}+namespace cube {+using namespace cube::data;+namespace internal {+std::string apply_maneuver(std::string_view s, const std::vector<TurnMove> &ms)+{+    assert(s.size() == 54 && "invalid cube length");+    char buf[2][54];+    std::memcpy(buf[0], s.data(), 54);+    size_t curr = 0;+    for(const auto &m : ms)+    {+        const auto& p   = ElementaryPerm[m].f;+        const char* src = buf[curr];+        char*       dst = buf[1-curr];+        for(int i = 0; i < 54; ++i) dst[i] = src[p[i]];+        curr = 1-curr;+    }+    return std::string(buf[curr],54);+}+auto parse_maneuver(std::string_view s) -> std::vector<TurnMove>+{+    assert(is_valid_maneuver(s) && "invalid maneuver");+    auto expand = [](std::string_view in) -> std::string {+        static const std::regex group_re(R"(\(([^)]+)\)(?:\{(\d+)\})?)");+        std::string res;+        auto start = in.cbegin();+        std::match_results<std::string_view::const_iterator> m;+        while (std::regex_search(start, in.cend(), m, group_re)) {+            res.append(start, m[0].first);+            int repeat = m[2].matched ? std::stoi(m[2].str()) : 1;+            for (int i = 0; i < repeat; ++i) res += m[1].str();+            start = m[0].second;+        }+        res.append(start, in.cend());+        return res;+    };+    auto char_to_move = [](char c) -> TurnMove {+        switch(c) {+        case 'U': return Ux1;+        case 'R': return Rx1;+        case 'F': return Fx1;+        case 'D': return Dx1;+        case 'L': return Lx1;+        case 'B': return Bx1;+        default: throw std::invalid_argument("char_to_move: ???");+        }+    };+    std::string in = expand(s);+    std::vector<TurnMove> ms;+    ms.reserve(in.size());+    for (char c : in)+    {+        switch (c) {+        case ' ': break;+        case '2':+            ms.back() = static_cast<TurnMove>(ms.back() + 1);+            break;+        case '\'':+            ms.back() = static_cast<TurnMove>(ms.back() + 2);+            break;+        default:+            ms.push_back(char_to_move(c));+            break;+        }+    }+    return ms;+}+bool is_valid_maneuver(std::string_view s)+{+    static const std::regex pat(+        R"(\s*(([UDLRFB]['23]?|\(([UDLRFB]['23]?\s*)+\)(\{\d+\})?)\s*)*)"+    );+    return std::regex_match(s.begin(), s.end(), pat);+}+}+}+#ifndef CUBE_EXPORT_H+#define CUBE_EXPORT_H+#ifdef CUBE_STATIC_DEFINE+#  define CUBE_EXPORT+#  define CUBE_NO_EXPORT+#else+#  ifndef CUBE_EXPORT+#    ifdef cube_shared_EXPORTS+#      define CUBE_EXPORT __attribute__((visibility("default")))+#    else+#      define CUBE_EXPORT __attribute__((visibility("default")))+#    endif+#  endif+#  ifndef CUBE_NO_EXPORT+#    define CUBE_NO_EXPORT __attribute__((visibility("hidden")))+#  endif+#endif+#ifndef CUBE_DEPRECATED+#  define CUBE_DEPRECATED __attribute__ ((__deprecated__))+#endif+#ifndef CUBE_DEPRECATED_EXPORT+#  define CUBE_DEPRECATED_EXPORT CUBE_EXPORT CUBE_DEPRECATED+#endif+#ifndef CUBE_DEPRECATED_NO_EXPORT+#  define CUBE_DEPRECATED_NO_EXPORT CUBE_NO_EXPORT CUBE_DEPRECATED+#endif+#if 0+#  ifndef CUBE_NO_DEPRECATED+#    define CUBE_NO_DEPRECATED+#  endif+#endif+#endif+#ifndef __cplusplus+#error "This is a C++ header; please use a C++ compiler OR include cube/cube.h instead"+#endif+namespace cube {+constexpr std::string_view cubeId = "UUUUUUUUURRRRRRRRRFFFFFFFFFDDDDDDDDDLLLLLLLLLBBBBBBBBB";+enum class SolveResult : int32_t {+    Success       = 0,+    Unsolvable    = 1,+    NotFound      = 2,+    InvalidSrc    = 3,+    InvalidTgt    = 4,+    UnknownErr    = 5+};+CUBE_EXPORT constexpr std::string_view to_string(SolveResult status) noexcept {+    switch (status) {+    case SolveResult::Success:      return "Success";+    case SolveResult::Unsolvable:   return "The cube configuration is unsolvable";+    case SolveResult::NotFound:     return "No solution found within the step limit";+    case SolveResult::InvalidSrc:   return "Invalid source color configuration";+    case SolveResult::InvalidTgt:   return "Invalid target color configuration";+    case SolveResult::UnknownErr:   return "Unknown error";+    }+}+enum class PermFormat : int {+    Face  = 0,+    Cubie = 1,+    Cycle = 2+};+struct Solution {+    SolveResult status;+    std::string maneuver;+    bool is_success() const noexcept+    {+        return status == SolveResult::Success;+    }+};+CUBE_EXPORT bool is_solvable(std::string_view color_cube);+[[nodiscard]] CUBE_EXPORT Solution solve(+    std::string_view src,+    std::string_view tgt = cubeId,+    int good = 22+);+[[nodiscard]] CUBE_EXPORT std::string apply_maneuver(+    std::string_view maneuver,+    std::string_view cube = cubeId+);+[[nodiscard]] CUBE_EXPORT std::string show_permutation(+    std::string_view ms_or_cube,+    PermFormat format = PermFormat::Cycle+);+}+namespace cube {+CUBE_EXPORT void set_table_dir(std::filesystem::path dir);+CUBE_EXPORT auto get_table_dir() -> std::filesystem::path;+CUBE_EXPORT bool tables_ready();+CUBE_EXPORT void preload_tables();+CUBE_EXPORT bool is_valid_config(std::string_view cube);+CUBE_EXPORT bool is_valid_maneuver(std::string_view maneuver);+}+namespace cube::show {+using std::size_t;+using namespace cube::data;+template<size_t N>+using StringArr = std::array<std::string_view,N>;+inline constexpr StringArr< 8> CornerToString       = { "urf", "ufl", "ulb", "ubr", "dfr", "dlf", "dbl", "drb" };+inline constexpr StringArr<12> EdgeToString         = { "ur","uf","ul","ub","dr","df","dl","db","fr","fl","bl","br" };+inline constexpr StringArr< 6> CenterToString       = { "u", "r", "f", "d", "l", "b" };+inline constexpr StringArr< 3> OrientationToString  = { "", "+", "-" };+inline constexpr StringArr<18> Move2Str             = { "U","U2","U'","R","R2","R'","F","F2","F'","D","D2","D'","L","L2","L'","B","B2","B'" };+inline constexpr StringArr<54> Face2Str             = { "U1","U2","U3","U4","U5","U6","U7","U8","U9","R1","R2","R3","R4","R5","R6","R7","R8","R9","F1","F2","F3","F4","F5","F6","F7","F8","F9","D1","D2","D3","D4","D5","D6","D7","D8","D9","L1","L2","L3","L4","L5","L6","L7","L8","L9","B1","B2","B3","B4","B5","B6","B7","B8","B9" };+inline constexpr std::string_view ColorSet          = "URFDLB";+inline constexpr std::string_view CornerSet         = "ABCDEFGH";+inline constexpr std::string_view EdgeSet           = "opqrstuvwxyz";+enum class CubeFormat {+    Face,+    Cubie,+    Cycle+};+template<typename Array, typename Formatter>+inline std::string seq2str_fmt(const Array &xs,+                           Formatter && fmt,+                           std::string_view sep="",+                           std::string_view pre="",+                           std::string_view suf="")+{+    const size_t len = xs.size();+    if(len == 0) { return std::string(pre) + std::string(suf); }+    std::stringstream ss;+    ss << pre << fmt(xs[0]);+    for(size_t i = 1; i < len; ++i) ss << sep << fmt(xs[i]);+    ss << suf;+    return ss.str();+}+template<typename Container>+inline std::string seq2str(const Container &xs,+                           std::string_view sep="",+                           std::string_view pre="",+                           std::string_view suf="")+{+    auto default_formatter = [](const auto& val) {+        using T = std::decay_t<decltype(val)>;+        if constexpr (std::is_same_v<T,uint8_t> || std::is_same_v<T,int8_t>) {+            return static_cast<int>(val);+        } else {+            return val;+        }+    };+    return seq2str_fmt(xs, default_formatter, sep, pre, suf);+}+inline std::string to_string(const ColorState& cs)+{+    return seq2str_fmt(cs.s, [](auto v) {+        switch(v){+        case U: return 'U';+        case R: return 'R';+        case F: return 'F';+        case D: return 'D';+        case L: return 'L';+        case B: return 'B';+        default: throw std::invalid_argument("to_string(ColorState): ???");+        }+    });+}+inline std::string to_string(const FaceCube& fc, bool use_digit=true)+{+    if(use_digit){+        return seq2str(fc.f);+    } else {+        return seq2str_fmt(fc.f, [](auto v) { return Face2Str[v]; });+    }+}+inline std::string to_string(const CubieCube& cc, CubeFormat fmt)+{+    switch(fmt){+    case CubeFormat::Face:+        return to_string(cc.toFaceCube(), false);+    case CubeFormat::Cubie:+        return seq2str_fmt(cc.cp, [](auto v) { return CornerSet[v]; }) ++               seq2str_fmt(cc.co, [](auto v) { return static_cast<char>('0'+v); }) ++               seq2str_fmt(cc.ep, [](auto v) { return EdgeSet[v]; }) ++               seq2str_fmt(cc.eo, [](auto v) { return static_cast<char>('0'+v);});+    default:+        const auto [fixed_corner,cycles_corner] = decomposite(cc.cp);+        const auto [fixed_edge, cycles_edge ]   = decomposite(cc.ep);+        std::string s1, s2;+        s1.reserve(64);+        s2.reserve(64);+        auto append_fixed = [&](std::string& out, const auto& fixed, const auto& ori_arr, auto name_table) {+            for(auto idx: fixed) {+                if(ori_arr[idx] == 0) continue;+                out += '(';+                out += OrientationToString[ori_arr[idx]];+                out += name_table[idx];+                out += ')';+            }+        };+        auto append_cycles = [&](std::string& out, const auto& cycles, const auto& ori_arr, auto name_table) {+            for(const auto& cycle: cycles) {+                const size_t N = cycle.size();+                if(N == 0) continue;+                out += '(';+                for(int i = 0; i < N; i++) {+                    if(i > 0) out += ',';+                    size_t prev_idx = cycle[(N-1+i)%N];+                    out += OrientationToString[ori_arr[prev_idx]];+                    out += name_table[cycle[i]];+                }+                out += ')';+            }+        };+        append_fixed(s1, fixed_corner, cc.co, CornerToString);+        append_cycles(s1, cycles_corner, cc.co, CornerToString);+        append_fixed(s2, fixed_edge, cc.eo, EdgeToString);+        append_cycles(s2, cycles_edge, cc.eo, EdgeToString);+        return s1.empty() && s2.empty() ? "id" : s1 + s2;+    }+}+inline std::string to_string(const std::vector<TurnMove>& ms)+{+    return seq2str_fmt(ms, [](auto v){+        return Move2Str[v];+    }, " ");+}+}+namespace cube {+using namespace cube::data;+namespace fs = std::filesystem;+void set_table_dir(fs::path dir) { config::set_table_dir(dir); }+auto get_table_dir() -> fs::path { return config::get_table_dir(); }+bool tables_ready() { return pdb::tables_ready(); }+void preload_tables() { pdb::preload_tables(); }+bool is_valid_config(std::string_view cube) { return ColorState::is_valid_config(cube); }+bool is_valid_maneuver(std::string_view maneuver) { return internal::is_valid_maneuver(maneuver); }+cube::solver::TwoPhaseOptimSolver TPS;+Solution solve(std::string_view src, std::string_view tgt, int good)+{+    if (src != cubeId && !is_valid_config(src)) return {SolveResult::InvalidSrc, ""};+    if (tgt != cubeId && !is_valid_config(tgt)) return {SolveResult::InvalidTgt, ""};+    if (src == tgt) return {SolveResult::Success, ""};+    auto cc_src = ColorState::fromString(src).toCubieCube();+    auto cc_tgt = ColorState::fromString(tgt).toCubieCube();+    CubieCube cc = ~cc_tgt * cc_src;+    if (!cc.isSolvable()) return {SolveResult::Unsolvable, ""};+    const auto& [found, s1, s2] = TPS.solve(pdb::Coord::CubieCube2Coord(cc), good < 0 ? 0 : good);+    if (!found) return {SolveResult::NotFound, ""};+    std::vector<TurnMove> sol;+    size_t n1 = s1.size(), n2 = s2.size();+    if (!s1.empty() && !s2.empty() && s1[n1 - 1] / 3 == s2[0] / 3) {+        sol.insert(sol.end(), s1.begin(), s1.end() - 1);+        int m = (s1[n1 - 1] + s2[0] - s2[0] / 3 * 6 + 2) % 4;+        if (m != 0) sol.push_back(static_cast<TurnMove>(s2[0] / 3 * 3 + m - 1));+        sol.insert(sol.end(), s2.begin() + 1, s2.end());+    } else {+        sol.insert(sol.end(), s1.begin(), s1.end());+        sol.insert(sol.end(), s2.begin(), s2.end());+    }+    return {SolveResult::Success, show::to_string(sol)};+}+bool is_solvable(std::string_view color_cube) {+    return is_valid_config(color_cube) &&+           ColorState::fromString(color_cube).toCubieCube().isSolvable();+}+std::string apply_maneuver(std::string_view maneuver, std::string_view cube_state) {+    if (cube_state.size() != 54 || !is_valid_maneuver(maneuver)) {+        throw std::invalid_argument("Invalid cube format or maneuver string.");+    }+    const auto ms = internal::parse_maneuver(maneuver);+    return internal::apply_maneuver(cube_state, ms);+}+std::string show_permutation(std::string_view ms_or_cube, PermFormat format) {+    std::string cube_str;+    if (is_valid_config(ms_or_cube)) {+        cube_str = ms_or_cube;+    } else if (is_valid_maneuver(ms_or_cube)) {+        auto ms = internal::parse_maneuver(ms_or_cube);+        cube_str = internal::apply_maneuver(cubeId, ms);+    } else {+        throw std::invalid_argument("Input is neither a valid configuration nor a valid maneuver.");+    }+    auto cc = ColorState::fromString(cube_str).toCubieCube();+    return show::to_string(cc, show::CubeFormat(static_cast<int>(format)));+}+}+#define CUBE_VERSION_FULL  v0.5.0+#define CUBE_VERSION_MAJOR 0+#define CUBE_VERSION_MINOR 5+#define CUBE_VERSION_PATCH 0+#define CUBE_VERSION_BUILD+#ifdef __cplusplus+    #define Default(x) = x+#else+    #define Default(x)+#endif+#define CUBE_BS 128+#define CUBE_ID "UUUUUUUUURRRRRRRRRFFFFFFFFFDDDDDDDDDLLLLLLLLLBBBBBBBBB"+#ifndef CF_ENUM+    #if defined(__cplusplus)+        #define CF_ENUM(_type, _name) \+            int __CF_ENUM_##_name; \+            enum _name : _type+    #elif defined(__clang__) || defined(__OBJC__)+        #define CF_ENUM(_type, _name) \+            enum _name : _type _name; \+            enum _name: _type+    #else+        #define CF_ENUM(_type, _name) \+            _type _name; \+            enum+    #endif+#endif+typedef CF_ENUM(int32_t,SolveResult) {+    SolveResultSuccess = 0,+    SolveResultUnsolvable = 1,+    SolveResultNotFound = 2,+    SolveResultInvalidSrc = 3,+    SolveResultInvalidTgt = 4,+    SolveResultUnknownErr = 5+};+static inline const char* solve_result_info(SolveResult sr)+{+    switch(sr) {+    case SolveResultSuccess:    return "Success.";+    case SolveResultUnsolvable: return "The cube configuration is unsolvable.";+    case SolveResultNotFound:   return "No solution found within the step limit.";+    case SolveResultInvalidSrc: return "Invalid source color configuration.";+    case SolveResultInvalidTgt: return "Invalid target color configuration.";+    case SolveResultUnknownErr: return "Unknown error.";+    default:                    return "???";+    }+}+#ifdef __cplusplus+extern "C" {+#endif+CUBE_EXPORT const char *solve_result_to_string(int32_t sr);+CUBE_EXPORT SolveResult solve(+    char*       buf,+    const char* src         Default(CUBE_ID),+    const char* tgt         Default(CUBE_ID),+    int         good        Default(22)+);+CUBE_EXPORT bool solvable(+    const char* color_cube  Default(CUBE_ID)+);+CUBE_EXPORT bool facecube(+    char* buf,+    const char* maneuver    Default(""),+    const char *cube        Default(CUBE_ID)+);+CUBE_EXPORT bool permutation(+    char*       buf,+    const char* ms_or_cube  Default(CUBE_ID),+    int         format      Default(2)+);+#ifdef __cplusplus+}+#endif+extern "C" {+const char* solve_result_to_string(int sr)+{+    return solve_result_info(static_cast<SolveResult>(sr));+}+SolveResult solve(+    char* buf, const char *src, const char* tgt, int good)+{+    if(!buf) return SolveResultUnknownErr;+    auto s_src = src == NULL ? cube::cubeId : std::string_view(src);+    auto s_tgt = tgt == NULL ? cube::cubeId : std::string_view(tgt);+    auto res = cube::solve(s_src, s_tgt, good);+    if(res.is_success()) {+        const auto& s = res.maneuver;+        std::memcpy(buf,s.c_str(),s.size()+1);+        return SolveResultSuccess;+    }+    return static_cast<SolveResult>(res.status);+}+bool solvable(const char* cube)+{+    return cube::is_solvable(cube ? cube : cube::cubeId);+}+bool facecube(char* buf, const char *maneuver, const char *cube)+{+    if(!buf) return false;+    try {+        auto s = cube::apply_maneuver(maneuver, cube);+        std::memcpy(buf, s.c_str(), s.size()+1);+        return true;+    } catch(...) {+        buf[0] = '\0';+        return false;+    }+}+bool permutation(char* buf, const char* ms_or_cube, int format)+{+    if(!buf) return false;+    try {+        auto s = cube::show_permutation(+            ms_or_cube ? ms_or_cube : cube::cubeId,+            static_cast<cube::PermFormat>(format)+        );+        std::memcpy(buf, s.c_str(), s.size()+1);+        return true;+    } catch(...) {+        buf[0] = '\0';+        return false;+    } } }

@@ -20,7 +20,7 @@ -- PVP summary:     +-+------- breaking API changes --                  | | +----- non-breaking API additions --                  | | | +--- code changes with no API change-version:            0.4.0.1+version:            0.5.0.0  -- A short (one-line) description of the package. synopsis:           High-performance, type-safe Rubik's Cube solver with C FFI bindings.@@ -88,7 +88,7 @@      cxx-sources:        cbits/cube_amalg.min.cpp     include-dirs:       cbits-    cxx-options:        -std=c++17+    cxx-options:        -std=c++17 -O3  test-suite cube-hs-test     -- Import common warning flags.

@@ -51,6 +51,7 @@ , showTurns , parseTurns   -- * Solving Interface (C FFI)+, rawSolve , solve , unsafeSolve , solveFrom

@@ -8,8 +8,7 @@         :: CString  -- buffer         -> CString  -- src color         -> CString  -- tgt color-        -> CInt     -- step-        -> CBool    -- best+        -> CInt     -- good enough         -> IO CInt  foreign import ccall "solvable"

@@ -23,6 +23,7 @@ , applyTurns , showTurns , parseTurns+, rawSolve , solve , unsafeSolve , solveFrom@@ -41,13 +42,15 @@ import Foreign.C.String (withCString) import Foreign.C.Types (CBool(..)) -+-- | The solved state of a Rubik's cube. cubeId :: Cube cubeId = Cube (fromMaybe (error "cId") (V.fromList (concatMap (replicate 9) [U .. B]))) +-- | Converts a cube into its 54-character string representation. showCube :: Cube -> String showCube (Cube v) = concatMap show (V.toList v) +-- | Parses a 54-character string into a `Cube`, returning `Nothing` if invalid. parseCube :: String -> Maybe Cube parseCube cubeStr     | isLegalCubeString cubeStr = do@@ -65,6 +68,7 @@             'B' -> Just B             _ -> Nothing +-- | Checks if a 54-character string represents a legal (solvable) cube state. isLegalCubeString :: String -> Bool isLegalCubeString str =      length str == 54 &&@@ -72,9 +76,11 @@         CBool res <- c_solvable c_str         return (res /= 0)) +-- | Applies a sequence of turns to a cube. applyTurns :: Cube -> [Turn] -> Cube applyTurns = foldl (&>) +-- | Parses a space-separated string of turns (e.g., "R U R' U'") into a list of `Turn`. parseTurns :: String -> Maybe [Turn] parseTurns str = mapM stringToTurn (words str) where      stringToTurn :: String -> Maybe Turn @@ -87,6 +93,7 @@         "B" -> Just Bx1; "B2" -> Just Bx2; "B'" -> Just Bx3         _ -> Nothing +-- | Converts a list of turns into a space-separated string representation. showTurns :: [Turn] -> String  showTurns ts = unwords (map turnToString ts) where      turnToString :: Turn -> String @@ -98,12 +105,16 @@         Lx1 -> "L"; Lx2 -> "L2"; Lx3 -> "L'"         Bx1 -> "B"; Bx2 -> "B2"; Bx3 -> "B'" -solve :: Cube -> Cube -> Either String [Turn]-solve src tgt = unsafePerformIO $+-- | Uses Kociemba's two-phase algorithm. The search stops as soon as any solution +-- of length at most `good` is found, trading optimality for speed. +-- If the returned maneuver is *longer* than `good`, no shorter solution exists+-- and the result is the two-phase optimum. +rawSolve :: Cube -> Cube -> Int -> Either String [Turn]+rawSolve src tgt good = unsafePerformIO $     withCString (showCube src) $ \c_src ->     withCString (showCube tgt) $ \c_tgt ->     allocaBytes 128 $ \c_buf -> do-        resCode <- c_solve c_buf c_src c_tgt 30 (CBool 1)+        resCode <- c_solve c_buf c_src c_tgt (fromIntegral good)         if resCode == 0             then parseCSolution c_buf             else handleErr resCode  @@ -119,14 +130,22 @@             errStr <- peekCString errPtr             return $ Left $ "Solver error (" ++ show code ++ "): "++ errStr +-- | Solves the cube using a default search depth limit of 22.+-- For fine-grained control over the search depth, use `rawSolve`.+solve :: Cube -> Cube -> Either String [Turn]+solve src tgt = rawSolve src tgt 22 +-- | Same as `solve`, but throws a runtime error if no solution is found +-- or if parsing fails. Use this only when Cube is known to be legal. unsafeSolve :: Cube -> Cube -> [Turn] unsafeSolve src tgt = case solve src tgt of      Left err -> error err     Right ts -> ts +-- | Solves the given cube back to the solved state (`cubeId`). solveFrom :: Cube -> Either String [Turn] solveFrom c = solve c cubeId  +-- | Same as `solveFrom`, but throws a runtime error on failure. unsafeSolveFrom :: Cube -> [Turn] unsafeSolveFrom c = unsafeSolve c cubeId