verify/utilities/dice.test.cpp

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Last update: 2026-10-06 01:57:24+09:00
Problem: https://onlinejudge.u-aizu.ac.jp/problems/ITP1_11_A

Depends on

Code

#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/ITP1_11_A"

#include "../../utilities/dice.hpp"

#include <array>
#include <cassert>
#include "../../utilities/fast_io.hpp"
#include <set>
#include <string>

namespace {

using m1une::utilities::Dice;
using m1une::utilities::DiceDirection;
using m1une::utilities::DiceFace;

void test_rolls() {
    Dice<int> original(1, 6, 5, 2, 3, 4);

    Dice<int> north = original;
    north.roll_north();
    std::array<int, 6> expected_north{2, 5, 1, 6, 3, 4};
    assert(north.faces() == expected_north);
    north.roll_south();
    assert(north == original);

    Dice<int> east = original;
    east.roll_east();
    std::array<int, 6> expected_east{4, 3, 5, 2, 1, 6};
    assert(east.faces() == expected_east);
    east.roll_west();
    assert(east == original);

    Dice<int> cycle = original;
    for (int step = 0; step < 4; ++step) cycle.roll(DiceDirection::north);
    assert(cycle == original);
    for (int step = 0; step < 4; ++step) cycle.rotate_clockwise();
    assert(cycle == original);
    cycle.rotate_clockwise().rotate_counterclockwise();
    assert(cycle == original);
}

void test_orientations() {
    Dice<int> die(0, 1, 2, 3, 4, 5);
    std::array<Dice<int>, 24> orientations = die.orientations();
    std::set<std::array<int, 6>> distinct;
    std::array<int, 6> top_count{};

    for (const Dice<int>& oriented : orientations) {
        distinct.insert(oriented.faces());
        ++top_count[static_cast<std::size_t>(oriented.top())];
        assert(oriented[DiceFace::bottom] == oriented.bottom());
    }
    assert(distinct.size() == 24);
    for (int count : top_count) assert(count == 4);

    for (int top = 0; top < 6; ++top) {
        for (int south = 0; south < 6; ++south) {
            bool are_opposite =
                (top == 0 && south == 1) ||
                (top == 1 && south == 0) ||
                (top == 2 && south == 3) ||
                (top == 3 && south == 2) ||
                (top == 4 && south == 5) ||
                (top == 5 && south == 4);
            auto oriented = die.orientation(top, south);
            assert(oriented.has_value() == (top != south && !are_opposite));
            if (oriented.has_value()) {
                assert(oriented->top() == top);
                assert(oriented->south() == south);
            }
        }
    }
}

void test_equivalence() {
    Dice<std::string> first("T", "B", "N", "S", "E", "W");
    Dice<std::string> rotated = first;
    rotated.roll_north().roll_east().rotate_clockwise();
    assert(first != rotated);
    assert(first.equivalent(rotated));

    Dice<std::string> reflected("T", "B", "N", "S", "W", "E");
    assert(!first.equivalent(reflected));

    Dice<int> repeated(1, 1, 2, 2, 3, 3);
    assert(repeated.orientations().size() == 24);
    assert(repeated.equivalent(repeated));
}

void test_opposites() {
    using m1une::utilities::opposite;
    for (DiceFace face : {
             DiceFace::top,
             DiceFace::bottom,
             DiceFace::north,
             DiceFace::south,
             DiceFace::east,
             DiceFace::west
         }) {
        assert(opposite(opposite(face)) == face);
    }
}

}  // namespace

int main() {
    m1une::utilities::FastInput fast_input;
    m1une::utilities::FastOutput fast_output;

    test_rolls();
    test_orientations();
    test_equivalence();
    test_opposites();

    std::array<int, 6> input;
    for (int& value : input) fast_input >> value;

    Dice<int> die(
        input[0],
        input[5],
        input[4],
        input[1],
        input[2],
        input[3]
    );

    std::string commands;
    fast_input >> commands;
    for (char command : commands) {
        if (command == 'N') die.roll_north();
        if (command == 'S') die.roll_south();
        if (command == 'E') die.roll_east();
        if (command == 'W') die.roll_west();
    }
    fast_output << die.top() << '\n';
}

#line 1 "verify/utilities/dice.test.cpp"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/ITP1_11_A"

#line 1 "utilities/dice.hpp"



#include <array>
#include <cstddef>
#include <optional>
#include <stdexcept>
#include <string>
#include <utility>
#include <vector>

namespace m1une {
namespace utilities {

enum class DiceFace : std::size_t {
    top,
    bottom,
    north,
    south,
    east,
    west
};

enum class DiceDirection {
    north,
    south,
    east,
    west
};

constexpr DiceFace opposite(DiceFace face) noexcept {
    switch (face) {
        case DiceFace::top:
            return DiceFace::bottom;
        case DiceFace::bottom:
            return DiceFace::top;
        case DiceFace::north:
            return DiceFace::south;
        case DiceFace::south:
            return DiceFace::north;
        case DiceFace::east:
            return DiceFace::west;
        case DiceFace::west:
            return DiceFace::east;
    }
    return DiceFace::top;
}

constexpr DiceFace rotate_direction(
    DiceFace direction,
    DiceDirection rotation
) noexcept {
    switch (rotation) {
        case DiceDirection::north:
            switch (direction) {
                case DiceFace::top:
                    return DiceFace::north;
                case DiceFace::north:
                    return DiceFace::bottom;
                case DiceFace::bottom:
                    return DiceFace::south;
                case DiceFace::south:
                    return DiceFace::top;
                default:
                    return direction;
            }
        case DiceDirection::south:
            switch (direction) {
                case DiceFace::top:
                    return DiceFace::south;
                case DiceFace::south:
                    return DiceFace::bottom;
                case DiceFace::bottom:
                    return DiceFace::north;
                case DiceFace::north:
                    return DiceFace::top;
                default:
                    return direction;
            }
        case DiceDirection::east:
            switch (direction) {
                case DiceFace::top:
                    return DiceFace::east;
                case DiceFace::east:
                    return DiceFace::bottom;
                case DiceFace::bottom:
                    return DiceFace::west;
                case DiceFace::west:
                    return DiceFace::top;
                default:
                    return direction;
            }
        case DiceDirection::west:
            switch (direction) {
                case DiceFace::top:
                    return DiceFace::west;
                case DiceFace::west:
                    return DiceFace::bottom;
                case DiceFace::bottom:
                    return DiceFace::east;
                case DiceFace::east:
                    return DiceFace::top;
                default:
                    return direction;
            }
    }
    return direction;
}

constexpr DiceFace rotate_direction_clockwise(DiceFace direction) noexcept {
    switch (direction) {
        case DiceFace::north:
            return DiceFace::east;
        case DiceFace::east:
            return DiceFace::south;
        case DiceFace::south:
            return DiceFace::west;
        case DiceFace::west:
            return DiceFace::north;
        default:
            return direction;
    }
}

constexpr DiceFace rotate_direction_counterclockwise(DiceFace direction) noexcept {
    switch (direction) {
        case DiceFace::north:
            return DiceFace::west;
        case DiceFace::west:
            return DiceFace::south;
        case DiceFace::south:
            return DiceFace::east;
        case DiceFace::east:
            return DiceFace::north;
        default:
            return direction;
    }
}

template <typename T>
class Dice {
private:
    static constexpr std::size_t face_count = 6;
    std::array<T, face_count> faces_;

    static constexpr std::size_t index(DiceFace face) noexcept {
        return static_cast<std::size_t>(face);
    }

public:
    constexpr Dice(
        T top,
        T bottom,
        T north,
        T south,
        T east,
        T west
    )
        : faces_{
              std::move(top),
              std::move(bottom),
              std::move(north),
              std::move(south),
              std::move(east),
              std::move(west)
          } {}

    explicit constexpr Dice(std::array<T, face_count> faces)
        : faces_(std::move(faces)) {}

    [[nodiscard]] constexpr const T& operator[](DiceFace face) const noexcept {
        return faces_[index(face)];
    }

    [[nodiscard]] constexpr T& operator[](DiceFace face) noexcept {
        return faces_[index(face)];
    }

    [[nodiscard]] constexpr const T& top() const noexcept {
        return (*this)[DiceFace::top];
    }

    [[nodiscard]] constexpr const T& bottom() const noexcept {
        return (*this)[DiceFace::bottom];
    }

    [[nodiscard]] constexpr const T& north() const noexcept {
        return (*this)[DiceFace::north];
    }

    [[nodiscard]] constexpr const T& south() const noexcept {
        return (*this)[DiceFace::south];
    }

    [[nodiscard]] constexpr const T& east() const noexcept {
        return (*this)[DiceFace::east];
    }

    [[nodiscard]] constexpr const T& west() const noexcept {
        return (*this)[DiceFace::west];
    }

    [[nodiscard]] constexpr const std::array<T, face_count>& faces() const noexcept {
        return faces_;
    }

    constexpr Dice& roll_north() {
        T old_top = std::move((*this)[DiceFace::top]);
        (*this)[DiceFace::top] = std::move((*this)[DiceFace::south]);
        (*this)[DiceFace::south] = std::move((*this)[DiceFace::bottom]);
        (*this)[DiceFace::bottom] = std::move((*this)[DiceFace::north]);
        (*this)[DiceFace::north] = std::move(old_top);
        return *this;
    }

    constexpr Dice& roll_south() {
        T old_top = std::move((*this)[DiceFace::top]);
        (*this)[DiceFace::top] = std::move((*this)[DiceFace::north]);
        (*this)[DiceFace::north] = std::move((*this)[DiceFace::bottom]);
        (*this)[DiceFace::bottom] = std::move((*this)[DiceFace::south]);
        (*this)[DiceFace::south] = std::move(old_top);
        return *this;
    }

    constexpr Dice& roll_east() {
        T old_top = std::move((*this)[DiceFace::top]);
        (*this)[DiceFace::top] = std::move((*this)[DiceFace::west]);
        (*this)[DiceFace::west] = std::move((*this)[DiceFace::bottom]);
        (*this)[DiceFace::bottom] = std::move((*this)[DiceFace::east]);
        (*this)[DiceFace::east] = std::move(old_top);
        return *this;
    }

    constexpr Dice& roll_west() {
        T old_top = std::move((*this)[DiceFace::top]);
        (*this)[DiceFace::top] = std::move((*this)[DiceFace::east]);
        (*this)[DiceFace::east] = std::move((*this)[DiceFace::bottom]);
        (*this)[DiceFace::bottom] = std::move((*this)[DiceFace::west]);
        (*this)[DiceFace::west] = std::move(old_top);
        return *this;
    }

    constexpr Dice& roll(DiceDirection direction) {
        switch (direction) {
            case DiceDirection::north:
                return roll_north();
            case DiceDirection::south:
                return roll_south();
            case DiceDirection::east:
                return roll_east();
            case DiceDirection::west:
                return roll_west();
        }
        return *this;
    }

    constexpr Dice& rotate_clockwise() {
        T old_north = std::move((*this)[DiceFace::north]);
        (*this)[DiceFace::north] = std::move((*this)[DiceFace::west]);
        (*this)[DiceFace::west] = std::move((*this)[DiceFace::south]);
        (*this)[DiceFace::south] = std::move((*this)[DiceFace::east]);
        (*this)[DiceFace::east] = std::move(old_north);
        return *this;
    }

    constexpr Dice& rotate_counterclockwise() {
        T old_north = std::move((*this)[DiceFace::north]);
        (*this)[DiceFace::north] = std::move((*this)[DiceFace::east]);
        (*this)[DiceFace::east] = std::move((*this)[DiceFace::south]);
        (*this)[DiceFace::south] = std::move((*this)[DiceFace::west]);
        (*this)[DiceFace::west] = std::move(old_north);
        return *this;
    }

    [[nodiscard]] constexpr std::array<Dice, 24> orientations() const {
        Dice top_top = *this;
        Dice north_top = *this;
        north_top.roll_south();
        Dice south_top = *this;
        south_top.roll_north();
        Dice east_top = *this;
        east_top.roll_west();
        Dice west_top = *this;
        west_top.roll_east();
        Dice bottom_top = *this;
        bottom_top.roll_north().roll_north();

        std::array<Dice, 6> top_orientations{
            std::move(top_top),
            std::move(north_top),
            std::move(south_top),
            std::move(east_top),
            std::move(west_top),
            std::move(bottom_top)
        };

        std::array<Dice, 24> result{
            *this, *this, *this, *this, *this, *this,
            *this, *this, *this, *this, *this, *this,
            *this, *this, *this, *this, *this, *this,
            *this, *this, *this, *this, *this, *this
        };
        std::size_t result_index = 0;
        for (Dice oriented : top_orientations) {
            for (int rotation = 0; rotation < 4; ++rotation) {
                result[result_index++] = oriented;
                oriented.rotate_clockwise();
            }
        }
        return result;
    }

    [[nodiscard]] constexpr std::optional<Dice> orientation(
        const T& top_value,
        const T& south_value
    ) const {
        for (const Dice& oriented : orientations()) {
            if (oriented.top() == top_value && oriented.south() == south_value) {
                return oriented;
            }
        }
        return std::nullopt;
    }

    [[nodiscard]] constexpr bool equivalent(const Dice& other) const {
        for (const Dice& oriented : orientations()) {
            if (oriented == other) {
                return true;
            }
        }
        return false;
    }

    friend constexpr bool operator==(const Dice&, const Dice&) = default;
};

class ArrowDice {
private:
    struct Vector {
        int x;
        int y;
        int z;

        friend constexpr bool operator==(const Vector&, const Vector&) = default;
    };

    struct Frame {
        Vector normal;
        Vector up;
        Vector right;

        friend constexpr bool operator==(const Frame&, const Frame&) = default;
    };

    Dice<DiceFace> arrows_;

    static constexpr Vector negate(Vector vector) noexcept {
        return Vector{-vector.x, -vector.y, -vector.z};
    }

    static constexpr DiceFace vector_to_face(Vector vector) {
        if (vector == Vector{0, 0, 1}) return DiceFace::top;
        if (vector == Vector{0, 0, -1}) return DiceFace::bottom;
        if (vector == Vector{0, 1, 0}) return DiceFace::north;
        if (vector == Vector{0, -1, 0}) return DiceFace::south;
        if (vector == Vector{1, 0, 0}) return DiceFace::east;
        if (vector == Vector{-1, 0, 0}) return DiceFace::west;
        throw std::invalid_argument("vector is not a cube direction");
    }

    static constexpr Frame adjacent_frame(
        const Frame& frame,
        DiceDirection direction
    ) noexcept {
        switch (direction) {
            case DiceDirection::north:
                return Frame{frame.up, negate(frame.normal), frame.right};
            case DiceDirection::south:
                return Frame{negate(frame.up), frame.normal, frame.right};
            case DiceDirection::east:
                return Frame{frame.right, frame.up, negate(frame.normal)};
            case DiceDirection::west:
                return Frame{negate(frame.right), frame.up, frame.normal};
        }
        return frame;
    }

    static constexpr DiceFace arrow_from_character(
        char arrow,
        const Frame& frame
    ) {
        if (arrow == '^') return vector_to_face(frame.up);
        if (arrow == 'v') return vector_to_face(negate(frame.up));
        if (arrow == '>') return vector_to_face(frame.right);
        if (arrow == '<') return vector_to_face(negate(frame.right));
        throw std::invalid_argument("arrow dice net contains an invalid character");
    }

    constexpr void rotate_arrows(DiceDirection direction) noexcept {
        for (DiceFace face : all_faces()) {
            arrows_[face] = rotate_direction(arrows_[face], direction);
        }
    }

    static constexpr std::array<DiceFace, 6> all_faces() noexcept {
        return std::array<DiceFace, 6>{
            DiceFace::top,
            DiceFace::bottom,
            DiceFace::north,
            DiceFace::south,
            DiceFace::east,
            DiceFace::west
        };
    }

public:
    constexpr ArrowDice(
        DiceFace top,
        DiceFace bottom,
        DiceFace north,
        DiceFace south,
        DiceFace east,
        DiceFace west
    )
        : arrows_(top, bottom, north, south, east, west) {}

    explicit constexpr ArrowDice(Dice<DiceFace> arrows)
        : arrows_(std::move(arrows)) {}

    [[nodiscard]] constexpr DiceFace arrow(DiceFace face) const noexcept {
        return arrows_[face];
    }

    [[nodiscard]] constexpr const Dice<DiceFace>& arrows() const noexcept {
        return arrows_;
    }

    constexpr ArrowDice& roll(DiceDirection direction) {
        arrows_.roll(direction);
        rotate_arrows(direction);
        return *this;
    }

    constexpr ArrowDice& roll_north() {
        return roll(DiceDirection::north);
    }

    constexpr ArrowDice& roll_south() {
        return roll(DiceDirection::south);
    }

    constexpr ArrowDice& roll_east() {
        return roll(DiceDirection::east);
    }

    constexpr ArrowDice& roll_west() {
        return roll(DiceDirection::west);
    }

    constexpr ArrowDice& rotate_clockwise() {
        arrows_.rotate_clockwise();
        for (DiceFace face : all_faces()) {
            arrows_[face] = rotate_direction_clockwise(arrows_[face]);
        }
        return *this;
    }

    constexpr ArrowDice& rotate_counterclockwise() {
        arrows_.rotate_counterclockwise();
        for (DiceFace face : all_faces()) {
            arrows_[face] = rotate_direction_counterclockwise(arrows_[face]);
        }
        return *this;
    }

    [[nodiscard]] constexpr std::array<ArrowDice, 24> orientations() const {
        ArrowDice top_top = *this;
        ArrowDice north_top = *this;
        north_top.roll_south();
        ArrowDice south_top = *this;
        south_top.roll_north();
        ArrowDice east_top = *this;
        east_top.roll_west();
        ArrowDice west_top = *this;
        west_top.roll_east();
        ArrowDice bottom_top = *this;
        bottom_top.roll_north().roll_north();

        std::array<ArrowDice, 6> top_orientations{
            top_top,
            north_top,
            south_top,
            east_top,
            west_top,
            bottom_top
        };
        std::array<ArrowDice, 24> result{
            *this, *this, *this, *this, *this, *this,
            *this, *this, *this, *this, *this, *this,
            *this, *this, *this, *this, *this, *this,
            *this, *this, *this, *this, *this, *this
        };

        std::size_t result_index = 0;
        for (ArrowDice oriented : top_orientations) {
            for (int rotation = 0; rotation < 4; ++rotation) {
                result[result_index++] = oriented;
                oriented.rotate_clockwise();
            }
        }
        return result;
    }

    [[nodiscard]] constexpr int difference(const ArrowDice& other) const noexcept {
        int result = 0;
        for (DiceFace face : all_faces()) {
            result += arrow(face) != other.arrow(face);
        }
        return result;
    }

    [[nodiscard]] constexpr int distance(const ArrowDice& other) const {
        int result = 6;
        for (const ArrowDice& oriented : orientations()) {
            int current = oriented.difference(other);
            if (current < result) result = current;
        }
        return result;
    }

    [[nodiscard]] static ArrowDice from_net(
        const std::vector<std::string>& net,
        char empty = '.'
    ) {
        if (net.empty()) {
            throw std::invalid_argument("arrow dice net is empty");
        }
        std::size_t width = net.front().size();
        if (width == 0) {
            throw std::invalid_argument("arrow dice net is empty");
        }
        for (const std::string& row : net) {
            if (row.size() != width) {
                throw std::invalid_argument("arrow dice net must be rectangular");
            }
        }

        int height = static_cast<int>(net.size());
        int integer_width = static_cast<int>(width);
        std::vector<std::vector<std::optional<Frame>>> frames(
            net.size(),
            std::vector<std::optional<Frame>>(width)
        );
        auto character_at = [&](int row, int column) -> char {
            return net[static_cast<std::size_t>(row)]
                      [static_cast<std::size_t>(column)];
        };
        auto frame_at = [&](int row, int column) -> std::optional<Frame>& {
            return frames[static_cast<std::size_t>(row)]
                         [static_cast<std::size_t>(column)];
        };
        std::vector<std::pair<int, int>> queue;
        int face_count = 0;
        for (int row = 0; row < height; ++row) {
            for (int column = 0; column < integer_width; ++column) {
                if (character_at(row, column) != empty) {
                    ++face_count;
                    if (queue.empty()) queue.emplace_back(row, column);
                }
            }
        }
        if (face_count != 6) {
            throw std::invalid_argument("arrow dice net must contain six faces");
        }

        Frame initial{
            Vector{0, 0, 1},
            Vector{0, 1, 0},
            Vector{1, 0, 0}
        };
        frame_at(queue.front().first, queue.front().second) = initial;

        constexpr std::array<int, 4> row_delta{-1, 1, 0, 0};
        constexpr std::array<int, 4> column_delta{0, 0, 1, -1};
        constexpr std::array<DiceDirection, 4> directions{
            DiceDirection::north,
            DiceDirection::south,
            DiceDirection::east,
            DiceDirection::west
        };
        for (std::size_t head = 0; head < queue.size(); ++head) {
            int row = queue[head].first;
            int column = queue[head].second;
            Frame frame = *frame_at(row, column);
            for (std::size_t edge = 0; edge < directions.size(); ++edge) {
                int next_row = row + row_delta[edge];
                int next_column = column + column_delta[edge];
                if (
                    next_row < 0 || next_row >= height ||
                    next_column < 0 || next_column >= integer_width ||
                    character_at(next_row, next_column) == empty
                ) {
                    continue;
                }

                Frame next_frame = adjacent_frame(frame, directions[edge]);
                std::optional<Frame>& known = frame_at(next_row, next_column);
                if (!known.has_value()) {
                    known = next_frame;
                    queue.emplace_back(next_row, next_column);
                } else if (*known != next_frame) {
                    throw std::invalid_argument("arrow dice net folds inconsistently");
                }
            }
        }
        if (queue.size() != 6) {
            throw std::invalid_argument("arrow dice net is disconnected");
        }

        std::array<std::optional<DiceFace>, 6> arrows;
        for (const std::pair<int, int>& cell : queue) {
            int row = cell.first;
            int column = cell.second;
            Frame frame = *frame_at(row, column);
            DiceFace face = vector_to_face(frame.normal);
            std::optional<DiceFace>& slot =
                arrows[static_cast<std::size_t>(face)];
            if (slot.has_value()) {
                throw std::invalid_argument("arrow dice net overlaps when folded");
            }
            slot = arrow_from_character(character_at(row, column), frame);
        }
        for (const std::optional<DiceFace>& arrow : arrows) {
            if (!arrow.has_value()) {
                throw std::invalid_argument("arrow dice net does not form a cube");
            }
        }

        return ArrowDice(
            *arrows[static_cast<std::size_t>(DiceFace::top)],
            *arrows[static_cast<std::size_t>(DiceFace::bottom)],
            *arrows[static_cast<std::size_t>(DiceFace::north)],
            *arrows[static_cast<std::size_t>(DiceFace::south)],
            *arrows[static_cast<std::size_t>(DiceFace::east)],
            *arrows[static_cast<std::size_t>(DiceFace::west)]
        );
    }

    friend constexpr bool operator==(const ArrowDice&, const ArrowDice&) = default;
};

}  // namespace utilities
}  // namespace m1une


#line 4 "verify/utilities/dice.test.cpp"

#line 6 "verify/utilities/dice.test.cpp"
#include <cassert>
#line 1 "utilities/fast_io.hpp"



#include <algorithm>
#line 6 "utilities/fast_io.hpp"
#include <cerrno>
#include <charconv>
#line 9 "utilities/fast_io.hpp"
#include <cstdio>
#include <cstdlib>
#include <cstdint>
#include <cstring>
#include <iterator>
#line 15 "utilities/fast_io.hpp"
#include <sys/stat.h>
#include <type_traits>
#line 18 "utilities/fast_io.hpp"
#include <unistd.h>
#line 20 "utilities/fast_io.hpp"

namespace m1une {
namespace utilities {

struct FastOutput;

namespace internal {

// Shared with the convenience helpers in template.hpp.
inline FastOutput* standard_output_instance = nullptr;

// Detect std::begin(x), std::end(x).
template <class T, class = void>
struct is_range : std::false_type {};

template <class T>
struct is_range<T, std::void_t<
    decltype(std::begin(std::declval<T&>())),
    decltype(std::end(std::declval<T&>()))
>> : std::true_type {};

template <class T>
inline constexpr bool is_range_v = is_range<T>::value;

template <class T>
using range_reference_t = decltype(*std::begin(std::declval<T&>()));

template <class T>
using range_value_t = std::remove_cv_t<std::remove_reference_t<range_reference_t<T>>>;

template <class T, class = void>
struct range_stored_value {
    using type = range_value_t<T>;
};

template <class T>
struct range_stored_value<T, std::void_t<typename std::remove_cv_t<std::remove_reference_t<T>>::value_type>> {
    using type = typename std::remove_cv_t<std::remove_reference_t<T>>::value_type;
};

template <class T>
using range_stored_value_t = typename range_stored_value<T>::type;

// Treat strings and C strings as scalar output objects, not as ranges.
template <class T>
struct is_char_array : std::false_type {};

template <class T, std::size_t N>
struct is_char_array<T[N]>
    : std::bool_constant<std::is_same_v<std::remove_cv_t<T>, char>> {};

template <class T>
struct is_string_like
    : std::bool_constant<
          std::is_same_v<std::decay_t<T>, std::string>
          || std::is_same_v<std::decay_t<T>, const char*>
          || std::is_same_v<std::decay_t<T>, char*>
          || is_char_array<std::remove_reference_t<T>>::value
      > {};

template <class T>
inline constexpr bool is_string_like_v = is_string_like<T>::value;

// ModInt-like type: x.val() is printable, and x can be assigned from long long.
template <class T, class = void>
struct has_val_method : std::false_type {};

template <class T>
struct has_val_method<T, std::void_t<decltype(std::declval<const T&>().val())>>
    : std::true_type {};

template <class T>
inline constexpr bool has_val_method_v = has_val_method<T>::value;

template <class T, class = void>
struct has_static_mod_raw : std::false_type {};

template <class T>
struct has_static_mod_raw<
    T, std::void_t<decltype(T::mod()), decltype(T::raw(std::declval<uint32_t>()))>>
    : std::true_type {};

template <class T>
inline constexpr bool has_static_mod_raw_v = has_static_mod_raw<T>::value;

// libstdc++ before GCC 16 does not classify __int128 as an integral type in
// strict ISO modes such as -std=c++23. Keep the fast-I/O interface independent
// of that implementation detail.
template <class T>
inline constexpr bool is_integral_v =
    std::is_integral_v<T>
    || std::is_same_v<std::remove_cv_t<T>, __int128_t>
    || std::is_same_v<std::remove_cv_t<T>, __uint128_t>;

template <class T>
inline constexpr bool is_signed_v =
    std::is_signed_v<T>
    || std::is_same_v<std::remove_cv_t<T>, __int128_t>;

template <class T>
struct make_unsigned {
    using type = std::make_unsigned_t<T>;
};

template <>
struct make_unsigned<__int128_t> {
    using type = __uint128_t;
};

template <>
struct make_unsigned<__uint128_t> {
    using type = __uint128_t;
};

template <class T>
using make_unsigned_t = typename make_unsigned<std::remove_cv_t<T>>::type;

}  // namespace internal

struct FastInput {
    static constexpr int buffer_size = 1 << 20;

   private:
    std::FILE* _stream;
    char _buffer[buffer_size];
    int _position;
    int _length;
    int _file_descriptor;
    bool _streaming;

    bool refill() {
        _position = 0;
        if (_streaming) {
            ssize_t length;
            do {
                length = ::read(_file_descriptor, _buffer, buffer_size);
            } while (length < 0 && errno == EINTR);
            if (length <= 0) {
                _length = 0;
                return false;
            }
            _length = int(length);
        } else {
            _length = int(std::fread(_buffer, 1, buffer_size, _stream));
        }
        return _length != 0;
    }

    template <class T>
    bool read_integer_from_stream(T& value) {
        if (!skip_spaces()) return false;
        int c = read_char_raw();

        bool negative = false;
        if (c == '-') {
            negative = true;
            c = read_char_raw();
        }

        if constexpr (internal::is_signed_v<T>) {
            T result = 0;
            while ('0' <= c && c <= '9') {
                result = negative ? result * 10 - (c - '0')
                                  : result * 10 + (c - '0');
                c = read_char_raw();
            }
            value = result;
        } else {
            T result = 0;
            while ('0' <= c && c <= '9') {
                result = result * 10 + T(c - '0');
                c = read_char_raw();
            }
            value = negative ? T(0) - result : result;
        }
        return true;
    }

    bool prepare_number() {
        if (_length - _position >= 64) return true;
        const int remaining = _length - _position;
        if (remaining > 0) std::memmove(_buffer, _buffer + _position, remaining);
        const int added = int(std::fread(_buffer + remaining, 1, buffer_size - remaining, _stream));
        _position = 0;
        _length = remaining + added;
        if (_length < buffer_size) _buffer[_length] = '\0';
        return _length != 0;
    }

   public:
    explicit FastInput(std::FILE* stream = stdin)
        : _stream(stream),
          _position(0),
          _length(0),
          _file_descriptor(::fileno(stream)),
          _streaming([&] {
              struct stat status;
              return _file_descriptor >= 0
                     && ::fstat(_file_descriptor, &status) == 0
                     && !S_ISREG(status.st_mode);
          }()) {}

    FastInput(const FastInput&) = delete;
    FastInput& operator=(const FastInput&) = delete;

    int read_char_raw() {
        if (_position == _length && !refill()) return EOF;
        return _buffer[_position++];
    }

    bool skip_spaces() {
        int c = read_char_raw();
        while (c != EOF && c <= ' ') c = read_char_raw();
        if (c == EOF) return false;
        --_position;
        return true;
    }

    bool read(char& value) {
        if (!skip_spaces()) return false;
        value = char(read_char_raw());
        return true;
    }

    bool read(std::string& value) {
        if (!skip_spaces()) return false;
        value.clear();
        while (true) {
            const int begin = _position;
            while (_position < _length &&
                   static_cast<unsigned char>(_buffer[_position]) > ' ') {
                ++_position;
            }
            value.append(_buffer + begin, _position - begin);
            if (_position < _length) {
                ++_position;
                return true;
            }
            if (!refill()) return true;
        }
    }

    bool read(bool& value) {
        int x;
        if (!read(x)) return false;
        value = x != 0;
        return true;
    }

    template <class T>
    std::enable_if_t<
        internal::is_integral_v<T>
            && !std::is_same_v<std::remove_cv_t<T>, bool>
            && !std::is_same_v<std::remove_cv_t<T>, char>,
        bool
    >
    read(T& value) {
        if (_streaming) return read_integer_from_stream(value);
        if (!prepare_number()) return false;
        int c = static_cast<unsigned char>(_buffer[_position++]);
        while (c <= ' ') c = static_cast<unsigned char>(_buffer[_position++]);

        bool negative = false;
        if (c == '-') {
            negative = true;
            c = static_cast<unsigned char>(_buffer[_position++]);
        }

        if constexpr (internal::is_signed_v<T>) {
            T result = 0;
            while ('0' <= c && c <= '9') {
                const int first = c - '0';
                const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
                if (0 <= second && second <= 9) {
                    result = negative ? result * 100 - (first * 10 + second)
                                      : result * 100 + (first * 10 + second);
                    ++_position;
                } else {
                    result = negative ? result * 10 - first : result * 10 + first;
                }
                c = static_cast<unsigned char>(_buffer[_position++]);
            }
            value = result;
        } else {
            T result = 0;
            while ('0' <= c && c <= '9') {
                const unsigned first = unsigned(c - '0');
                const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
                if (0 <= second && second <= 9) {
                    result = result * 100 + T(first * 10 + unsigned(second));
                    ++_position;
                } else {
                    result = result * 10 + T(first);
                }
                c = static_cast<unsigned char>(_buffer[_position++]);
            }
            value = negative ? T(0) - result : result;
        }
        if (_position > _length) _position = _length;
        return true;
    }

    template <class T>
    std::enable_if_t<std::is_floating_point_v<T>, bool>
    read(T& value) {
        if (!skip_spaces()) return false;
        int c = read_char_raw();
        bool negative = false;
        if (c == '-' || c == '+') {
            negative = c == '-';
            c = read_char_raw();
        }

        long double result = 0;
        while ('0' <= c && c <= '9') {
            result = result * 10 + (c - '0');
            c = read_char_raw();
        }
        if (c == '.') {
            long double place = 0.1L;
            c = read_char_raw();
            while ('0' <= c && c <= '9') {
                result += (c - '0') * place;
                place *= 0.1L;
                c = read_char_raw();
            }
        }
        if (c == 'e' || c == 'E') {
            c = read_char_raw();
            bool exponent_negative = false;
            if (c == '-' || c == '+') {
                exponent_negative = c == '-';
                c = read_char_raw();
            }
            int exponent = 0;
            while ('0' <= c && c <= '9') {
                exponent = exponent * 10 + (c - '0');
                c = read_char_raw();
            }
            long double scale = 1;
            long double power = 10;
            while (exponent > 0) {
                if (exponent & 1) scale *= power;
                power *= power;
                exponent >>= 1;
            }
            result = exponent_negative ? result / scale : result * scale;
        }
        value = static_cast<T>(negative ? -result : result);
        return true;
    }

    template <class T>
    std::enable_if_t<
        internal::has_val_method_v<T>
            && !internal::is_integral_v<T>
            && !internal::is_range_v<T>,
        bool
    >
    read(T& value) {
        long long x;
        if (!read(x)) return false;
        if constexpr (internal::has_static_mod_raw_v<T>) {
            if (x >= 0 && uint64_t(x) < uint64_t(T::mod())) {
                value = T::raw(uint32_t(x));
            } else {
                value = T(x);
            }
        } else {
            value = T(x);
        }
        return true;
    }

    template <class First, class Second>
    bool read(std::pair<First, Second>& value) {
        if (!read(value.first)) return false;
        return read(value.second);
    }

    template <class Range>
    std::enable_if_t<
        internal::is_range_v<Range>
            && !internal::is_string_like_v<Range>,
        bool
    >
    read(Range& range) {
        using StoredValue = internal::range_stored_value_t<Range>;
        constexpr bool nested = internal::is_range_v<StoredValue>
                                && !internal::is_string_like_v<StoredValue>;

        for (auto&& value : range) {
            if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
                bool x;
                if (!read(x)) return false;
                value = x;
            } else {
                if (!read(value)) return false;
            }
        }
        return true;
    }

    template <class First, class Second, class... Rest>
    bool read(First& first, Second& second, Rest&... rest) {
        if (!read(first)) return false;
        return read(second, rest...);
    }

    template <class T>
    FastInput& operator>>(T& value) {
        if (!read(value)) std::abort();
        return *this;
    }
};

struct FastOutput {
    static constexpr int buffer_size = 1 << 20;

   private:
    inline static const auto digit_quads = [] {
        std::array<char, 40000> result{};
        for (int i = 0; i < 10000; i++) {
            int value = i;
            for (int j = 3; j >= 0; j--) {
                result[4 * i + j] = char('0' + value % 10);
                value /= 10;
            }
        }
        return result;
    }();

    std::FILE* _stream;
    char _buffer[buffer_size];
    int _position;
    int _precision;
    std::chars_format _float_format;
    char _range_separator;
    std::string* _capture = nullptr;

    template <class T>
    std::string format_cell(const T& value) {
        std::string result;
        struct CaptureGuard {
            std::string*& target;
            std::string* previous;
            ~CaptureGuard() { target = previous; }
        } guard{_capture, _capture};
        _capture = &result;
        write(value);
        return result;
    }

    template <class Matrix>
    void write_aligned_matrix(const Matrix& matrix) {
        std::vector<std::vector<std::string>> rows;
        std::vector<std::size_t> widths;
        for (const auto& row : matrix) {
            auto& cells = rows.emplace_back();
            std::size_t column = 0;
            for (const auto& value : row) {
                cells.push_back(format_cell(value));
                if (column == widths.size()) widths.push_back(0);
                widths[column] = std::max(widths[column], cells.back().size());
                ++column;
            }
        }
        bool first = true;
        for (const auto& row : rows) {
            if (!first) write_char('\n');
            first = false;
            for (std::size_t column = 0; column < row.size(); ++column) {
                if (column != 0) write_char(_range_separator);
                for (std::size_t padding = row[column].size();
                     padding < widths[column]; ++padding) {
                    write_char(' ');
                }
                write(row[column]);
            }
        }
    }

   public:
    explicit FastOutput(std::FILE* stream = stdout)
        : _stream(stream),
          _position(0),
          _precision(6),
          _float_format(std::chars_format::general),
          _range_separator(' ') {
        if (_stream == stdout
            && internal::standard_output_instance == nullptr) {
            internal::standard_output_instance = this;
        }
    }

    FastOutput(const FastOutput&) = delete;
    FastOutput& operator=(const FastOutput&) = delete;

    ~FastOutput() {
        flush();
        if (internal::standard_output_instance == this) {
            internal::standard_output_instance = nullptr;
        }
    }

    void flush() {
        if (_position != 0) {
            std::fwrite(_buffer, 1, _position, _stream);
            _position = 0;
        }
        std::fflush(_stream);
    }

    void write_char(char c) {
        if (_capture != nullptr) {
            _capture->push_back(c);
            return;
        }
        if (_position == buffer_size) flush();
        _buffer[_position++] = c;
    }

    void write(const char* s) {
        while (*s != '\0') write_char(*s++);
    }

    void write(const std::string& s) {
        if (_capture != nullptr) {
            _capture->append(s);
            return;
        }
        std::size_t position = 0;
        while (position < s.size()) {
            if (_position == buffer_size) flush();
            const std::size_t copied =
                std::min<std::size_t>(buffer_size - _position, s.size() - position);
            std::memcpy(_buffer + _position, s.data() + position, copied);
            _position += int(copied);
            position += copied;
        }
    }

    void write(char c) {
        write_char(c);
    }

    void write(bool value) {
        write_char(value ? '1' : '0');
    }

    template <class T>
    std::enable_if_t<std::is_floating_point_v<T>>
    write(T value) {
        char digits[128];
        auto [end, error] = std::to_chars(
            digits,
            digits + sizeof(digits),
            value,
            _float_format,
            _precision
        );
        if (error != std::errc()) std::abort();
        for (const char* pointer = digits; pointer != end; pointer++) {
            write_char(*pointer);
        }
    }

    template <class T>
    std::enable_if_t<
        internal::is_integral_v<T>
            && !std::is_same_v<std::remove_cv_t<T>, bool>
            && !std::is_same_v<std::remove_cv_t<T>, char>
    >
    write(T value) {
        using Raw = std::remove_cv_t<T>;
        using Unsigned = internal::make_unsigned_t<Raw>;

        Unsigned magnitude;
        if constexpr (internal::is_signed_v<Raw>) {
            if (value < 0) {
                write_char('-');
                magnitude = Unsigned(0) - Unsigned(value);
            } else {
                magnitude = Unsigned(value);
            }
        } else {
            magnitude = value;
        }

        if (magnitude == 0) {
            write_char('0');
            return;
        }

        unsigned chunks[16];
        int count = 0;
        while (magnitude >= 10000) {
            const Unsigned quotient = magnitude / 10000;
            chunks[count++] = unsigned(magnitude - quotient * 10000);
            magnitude = quotient;
        }
        if (_capture == nullptr && _position > buffer_size - 64) flush();
        char captured[64];
        char* const begin = _capture != nullptr ? captured : _buffer + _position;
        char* destination = begin;
        const unsigned leading = unsigned(magnitude);
        const char* first = digit_quads.data() + 4 * leading;
        int skip = leading < 10 ? 3 : leading < 100 ? 2 : leading < 1000 ? 1 : 0;
        for (; skip < 4; skip++) *destination++ = first[skip];
        while (count--) {
            const char* digits = digit_quads.data() + 4 * chunks[count];
            std::memcpy(destination, digits, 4);
            destination += 4;
        }
        if (_capture != nullptr) {
            _capture->append(begin, destination - begin);
        } else {
            _position += int(destination - begin);
        }
    }

    template <class T>
    std::enable_if_t<
        internal::has_val_method_v<T>
            && !internal::is_integral_v<T>
            && !internal::is_range_v<T>
    >
    write(const T& value) {
        write(value.val());
    }

    template <class First, class Second>
    void write(const std::pair<First, Second>& value) {
        write(value.first);
        write_char(' ');
        write(value.second);
    }

    template <class Range>
    std::enable_if_t<
        internal::is_range_v<Range>
            && !internal::is_string_like_v<Range>
    >
    write(const Range& range) {
        using StoredValue = internal::range_stored_value_t<const Range>;
        constexpr bool nested = internal::is_range_v<StoredValue>
                                && !internal::is_string_like_v<StoredValue>;

        bool first = true;
        for (const auto& value : range) {
            if (!first) write_char(nested ? '\n' : _range_separator);
            first = false;
            if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
                write(static_cast<bool>(value));
            } else {
                write(value);
            }
        }
    }

    template <class First, class... Rest>
    void print(const First& first, const Rest&... rest) {
        write(first);
        ((write_char(' '), write(rest)), ...);
    }

    void println() {
        write_char('\n');
    }

    void set_precision(int precision) {
        _precision = precision;
    }

    void set_fixed(int precision = 6) {
        _float_format = std::chars_format::fixed;
        _precision = precision;
    }

    void set_general(int precision = 6) {
        _float_format = std::chars_format::general;
        _precision = precision;
    }

    void set_range_separator(char separator) {
        _range_separator = separator;
    }

    template <class Matrix>
    void write_aligned(const Matrix& matrix) {
        using Row = internal::range_stored_value_t<const Matrix>;
        using Cell = internal::range_stored_value_t<const Row>;
        static_assert(internal::is_range_v<Row> && !internal::is_string_like_v<Row>,
                      "write_aligned requires a two-dimensional range");
        static_assert(!internal::is_range_v<Cell> || internal::is_string_like_v<Cell>,
                      "write_aligned requires scalar cells");
        write_aligned_matrix(matrix);
    }

    template <class Matrix>
    void println_aligned(const Matrix& matrix) {
        write_aligned(matrix);
        write_char('\n');
    }

    template <class... Args>
    void println(const Args&... args) {
        print(args...);
        write_char('\n');
    }

    template <class T>
    FastOutput& operator<<(const T& value) {
        write(value);
        return *this;
    }
};

}  // namespace utilities
}  // namespace m1une


#line 8 "verify/utilities/dice.test.cpp"
#include <set>
#line 10 "verify/utilities/dice.test.cpp"

namespace {

using m1une::utilities::Dice;
using m1une::utilities::DiceDirection;
using m1une::utilities::DiceFace;

void test_rolls() {
    Dice<int> original(1, 6, 5, 2, 3, 4);

    Dice<int> north = original;
    north.roll_north();
    std::array<int, 6> expected_north{2, 5, 1, 6, 3, 4};
    assert(north.faces() == expected_north);
    north.roll_south();
    assert(north == original);

    Dice<int> east = original;
    east.roll_east();
    std::array<int, 6> expected_east{4, 3, 5, 2, 1, 6};
    assert(east.faces() == expected_east);
    east.roll_west();
    assert(east == original);

    Dice<int> cycle = original;
    for (int step = 0; step < 4; ++step) cycle.roll(DiceDirection::north);
    assert(cycle == original);
    for (int step = 0; step < 4; ++step) cycle.rotate_clockwise();
    assert(cycle == original);
    cycle.rotate_clockwise().rotate_counterclockwise();
    assert(cycle == original);
}

void test_orientations() {
    Dice<int> die(0, 1, 2, 3, 4, 5);
    std::array<Dice<int>, 24> orientations = die.orientations();
    std::set<std::array<int, 6>> distinct;
    std::array<int, 6> top_count{};

    for (const Dice<int>& oriented : orientations) {
        distinct.insert(oriented.faces());
        ++top_count[static_cast<std::size_t>(oriented.top())];
        assert(oriented[DiceFace::bottom] == oriented.bottom());
    }
    assert(distinct.size() == 24);
    for (int count : top_count) assert(count == 4);

    for (int top = 0; top < 6; ++top) {
        for (int south = 0; south < 6; ++south) {
            bool are_opposite =
                (top == 0 && south == 1) ||
                (top == 1 && south == 0) ||
                (top == 2 && south == 3) ||
                (top == 3 && south == 2) ||
                (top == 4 && south == 5) ||
                (top == 5 && south == 4);
            auto oriented = die.orientation(top, south);
            assert(oriented.has_value() == (top != south && !are_opposite));
            if (oriented.has_value()) {
                assert(oriented->top() == top);
                assert(oriented->south() == south);
            }
        }
    }
}

void test_equivalence() {
    Dice<std::string> first("T", "B", "N", "S", "E", "W");
    Dice<std::string> rotated = first;
    rotated.roll_north().roll_east().rotate_clockwise();
    assert(first != rotated);
    assert(first.equivalent(rotated));

    Dice<std::string> reflected("T", "B", "N", "S", "W", "E");
    assert(!first.equivalent(reflected));

    Dice<int> repeated(1, 1, 2, 2, 3, 3);
    assert(repeated.orientations().size() == 24);
    assert(repeated.equivalent(repeated));
}

void test_opposites() {
    using m1une::utilities::opposite;
    for (DiceFace face : {
             DiceFace::top,
             DiceFace::bottom,
             DiceFace::north,
             DiceFace::south,
             DiceFace::east,
             DiceFace::west
         }) {
        assert(opposite(opposite(face)) == face);
    }
}

}  // namespace

int main() {
    m1une::utilities::FastInput fast_input;
    m1une::utilities::FastOutput fast_output;

    test_rolls();
    test_orientations();
    test_equivalence();
    test_opposites();

    std::array<int, 6> input;
    for (int& value : input) fast_input >> value;

    Dice<int> die(
        input[0],
        input[5],
        input[4],
        input[1],
        input[2],
        input[3]
    );

    std::string commands;
    fast_input >> commands;
    for (char command : commands) {
        if (command == 'N') die.roll_north();
        if (command == 'S') die.roll_south();
        if (command == 'E') die.roll_east();
        if (command == 'W') die.roll_west();
    }
    fast_output << die.top() << '\n';
}

m1une's library

This documentation is automatically generated by online-judge-tools/verification-helper

verify/utilities/dice.test.cpp

Depends on

Code