cp-library-cpp

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:heavy_check_mark: test/src/transform/kronecker_power/arc132_f.test.cpp

Depends on

Code

#define PROBLEM "https://atcoder.jp/contests/arc132/tasks/arc132_f"

#include <array>
#include <iostream>

#include "library/transform/kronecker_power.hpp"

using suisen::kronecker_power_transform::kronecker_power_transform;

void trans(long long &x0, long long &x1, long long &x2, long long &x3) {
    x3 += x0 + x1 + x2;
}
 
void trans2(long long &x0, long long &x1, long long &x2, long long &x3) {
    x0 = x3 - x0;
    x1 = x3 - x1;
    x2 = x3 - x2;
    x3 = 0;
}
 
int main() {
    std::array<int, 256> mp;
    mp['P'] = 0, mp['R'] = 1, mp['S'] = 2;
 
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
 
    int k, n, m;
    std::cin >> k >> n >> m;
 
    auto count = [&](int num) {
        std::vector<long long> f(1 << (2 * k), 0);
        for (int i = 0; i < num; ++i) {
            int a = 0;
            for (int j = 0; j < k; ++j) {
                char c;
                std::cin >> c;
                a |= mp[c] << (2 * j);
            }
            ++f[a];
        }
        return f;
    };
    auto f = count(n), g = count(m);
 
    kronecker_power_transform<long long, 4, trans>(f);
    kronecker_power_transform<long long, 4, trans>(g);
    for (int i = 0; i < 1 << (2 * k); ++i) f[i] *= g[i];
    kronecker_power_transform<long long, 4, trans2>(f);
 
    int pow3 = 1;
    for (int i = 0; i < k; ++i) pow3 *= 3;
 
    for (int i = 0; i < pow3; ++i) {
        int v = 0;
        for (int t = i, j = 0; j < k; ++j, t /= 3) {
            int d = t % 3;
            v |= (d == 2 ? 0 : d + 1) << (2 * (k - j - 1));
        }
        std::cout << (long long) n * m - f[v] << '\n';
    }
    
    return 0;
}
#line 1 "test/src/transform/kronecker_power/arc132_f.test.cpp"
#define PROBLEM "https://atcoder.jp/contests/arc132/tasks/arc132_f"

#include <array>
#include <iostream>

#line 1 "library/transform/kronecker_power.hpp"



#include <cassert>
#include <utility>
#include <vector>

#line 1 "library/util/default_operator.hpp"



namespace suisen {
    namespace default_operator {
        template <typename T>
        auto zero() -> decltype(T { 0 }) { return T { 0 }; }
        template <typename T>
        auto one()  -> decltype(T { 1 }) { return T { 1 }; }
        template <typename T>
        auto add(const T &x, const T &y) -> decltype(x + y) { return x + y; }
        template <typename T>
        auto sub(const T &x, const T &y) -> decltype(x - y) { return x - y; }
        template <typename T>
        auto mul(const T &x, const T &y) -> decltype(x * y) { return x * y; }
        template <typename T>
        auto div(const T &x, const T &y) -> decltype(x / y) { return x / y; }
        template <typename T>
        auto mod(const T &x, const T &y) -> decltype(x % y) { return x % y; }
        template <typename T>
        auto neg(const T &x) -> decltype(-x) { return -x; }
        template <typename T>
        auto inv(const T &x) -> decltype(one<T>() / x)  { return one<T>() / x; }
    } // default_operator
    namespace default_operator_noref {
        template <typename T>
        auto zero() -> decltype(T { 0 }) { return T { 0 }; }
        template <typename T>
        auto one()  -> decltype(T { 1 }) { return T { 1 }; }
        template <typename T>
        auto add(T x, T y) -> decltype(x + y) { return x + y; }
        template <typename T>
        auto sub(T x, T y) -> decltype(x - y) { return x - y; }
        template <typename T>
        auto mul(T x, T y) -> decltype(x * y) { return x * y; }
        template <typename T>
        auto div(T x, T y) -> decltype(x / y) { return x / y; }
        template <typename T>
        auto mod(T x, T y) -> decltype(x % y) { return x % y; }
        template <typename T>
        auto neg(T x) -> decltype(-x) { return -x; }
        template <typename T>
        auto inv(T x) -> decltype(one<T>() / x)  { return one<T>() / x; }
    } // default_operator
} // namespace suisen


#line 9 "library/transform/kronecker_power.hpp"

namespace suisen {
    namespace kronecker_power_transform {
        namespace internal {
            template <typename UnitTransform, typename ReferenceGetter, std::size_t... Seq>
            void unit_transform(UnitTransform transform, ReferenceGetter ref_getter, std::index_sequence<Seq...>) {
                transform(ref_getter(Seq)...);
            }
        }

        template <typename T, std::size_t D, auto unit_transform>
        void kronecker_power_transform(std::vector<T> &x) {
            const std::size_t n = x.size();
            for (std::size_t block = 1; block < n; block *= D) {
                for (std::size_t l = 0; l < n; l += D * block) {
                    for (std::size_t offset = l; offset < l + block; ++offset) {
                        const auto ref_getter = [&](std::size_t i) -> T& { return x[offset + i * block]; };
                        internal::unit_transform(unit_transform, ref_getter, std::make_index_sequence<D>());
                    }
                }
            }
        }

        template <typename T, typename UnitTransform>
        void kronecker_power_transform(std::vector<T> &x, const std::size_t D, UnitTransform unit_transform) {
            const std::size_t n = x.size();
            std::vector<T> work(D);
            for (std::size_t block = 1; block < n; block *= D) {
                for (std::size_t l = 0; l < n; l += D * block) {
                    for (std::size_t offset = l; offset < l + block; ++offset) {
                        for (std::size_t i = 0; i < D; ++i) work[i] = x[offset + i * block];
                        unit_transform(work);
                        for (std::size_t i = 0; i < D; ++i) x[offset + i * block] = work[i];
                    }
                }
            }
        }

        template <typename T, auto e = default_operator::zero<T>, auto add = default_operator::add<T>, auto mul = default_operator::mul<T>>
        auto kronecker_power_transform(std::vector<T> &x, const std::vector<std::vector<T>> &A) -> decltype(e(), add(std::declval<T>(), std::declval<T>()), mul(std::declval<T>(), std::declval<T>()), void()) {
            const std::size_t D = A.size();
            assert(D == A[0].size());
            auto unit_transform = [&](std::vector<T> &x) {
                std::vector<T> y(D, e());
                for (std::size_t i = 0; i < D; ++i) for (std::size_t j = 0; j < D; ++j) {
                    y[i] = add(y[i], mul(A[i][j], x[j]));
                }
                x.swap(y);
            };
            kronecker_power_transform<T>(x, D, unit_transform);
        }
    }
} // namespace suisen



#line 7 "test/src/transform/kronecker_power/arc132_f.test.cpp"

using suisen::kronecker_power_transform::kronecker_power_transform;

void trans(long long &x0, long long &x1, long long &x2, long long &x3) {
    x3 += x0 + x1 + x2;
}
 
void trans2(long long &x0, long long &x1, long long &x2, long long &x3) {
    x0 = x3 - x0;
    x1 = x3 - x1;
    x2 = x3 - x2;
    x3 = 0;
}
 
int main() {
    std::array<int, 256> mp;
    mp['P'] = 0, mp['R'] = 1, mp['S'] = 2;
 
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
 
    int k, n, m;
    std::cin >> k >> n >> m;
 
    auto count = [&](int num) {
        std::vector<long long> f(1 << (2 * k), 0);
        for (int i = 0; i < num; ++i) {
            int a = 0;
            for (int j = 0; j < k; ++j) {
                char c;
                std::cin >> c;
                a |= mp[c] << (2 * j);
            }
            ++f[a];
        }
        return f;
    };
    auto f = count(n), g = count(m);
 
    kronecker_power_transform<long long, 4, trans>(f);
    kronecker_power_transform<long long, 4, trans>(g);
    for (int i = 0; i < 1 << (2 * k); ++i) f[i] *= g[i];
    kronecker_power_transform<long long, 4, trans2>(f);
 
    int pow3 = 1;
    for (int i = 0; i < k; ++i) pow3 *= 3;
 
    for (int i = 0; i < pow3; ++i) {
        int v = 0;
        for (int t = i, j = 0; j < k; ++j, t /= 3) {
            int d = t % 3;
            v |= (d == 2 ? 0 : d + 1) << (2 * (k - j - 1));
        }
        std::cout << (long long) n * m - f[v] << '\n';
    }
    
    return 0;
}
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