convolution/test/subset_convolution_exp_log.test.cpp

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• Last update: 2023-05-04 19:50:45+09:00
• Problem: https://onlinejudge.u-aizu.ac.jp/courses/lesson/2/ITP1/1/ITP1_1_A

Depends on

• convolution/subset_convolution.hpp
• convolution/subset_convolution_exp.hpp
• convolution/subset_convolution_internal.hpp
• convolution/subset_convolution_log.hpp
• number_theory/mod_int.hpp
• number_theory/utils.hpp
• other/xorshift.hpp
• template/template.hpp

Code

#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/lesson/2/ITP1/1/ITP1_1_A"

#define FAST_IO

#include "../../template/template.hpp"
#include "../../convolution/subset_convolution_exp.hpp"
#include "../../convolution/subset_convolution_log.hpp"
#include "../../number_theory/mod_int.hpp"
#include "../../other/xorshift.hpp"

constexpr u32 MOD = 998244353;
using Mint = ModInt<MOD>;

void test1(const Vec<Mint> &a) {
    Vec<Mint> exp_a = subset_convolution_exp(a);
    Vec<Mint> log_exp_a = subset_convolution_log(exp_a);
    assert(a == log_exp_a);
}

void test2(const Vec<Mint> &a) {
    Vec<Mint> log_a = subset_convolution_log(a);
    Vec<Mint> exp_log_a = subset_convolution_exp(log_a);
    assert(a == exp_log_a);
}

int main() {
    constexpr u64 SEED = 1309420975327ull;
    XorShift64 rd(SEED);
    
    REP(iter, 5) {
        i32 n = rd.uniform(1, 16);
        Vec<Mint> a(1 << n);
        REP(i, 1, 1 << n) {
            a[i] = rd.uniform(0u, MOD - 1u);
        }
        test1(a);
    }
    REP(iter, 5) {
        i32 n = rd.uniform(1, 16);
        Vec<Mint> a(1 << n);
        a[0] = Mint(1);
        REP(i, 1, 1 << n) {
            a[i] = rd.uniform(0u, MOD - 1u);
        }
        test2(a);
    }
    
    cout << "Hello World\n";
}

#line 1 "convolution/test/subset_convolution_exp_log.test.cpp"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/lesson/2/ITP1/1/ITP1_1_A"

#define FAST_IO

#line 1 "template/template.hpp"
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32) (n); ++i)
#define REP3(i, m, n) for (i32 i = (i32) (m); i < (i32) (n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER(i, n) for (i32 i = (i32) (n) - 1; i >= 0; --i)
#define ALL(x) begin(x), end(x)

using namespace std;

using u32 = unsigned int;
using u64 = unsigned long long;
using u128 = __uint128_t;
using i32 = signed int;
using i64 = signed long long;
using i128 = __int128_t;
using f64 = double;
using f80 = long double;

template <typename T>
using Vec = vector<T>;

template <typename T>
bool chmin(T &x, const T &y) {
    if (x > y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
    if (x < y) {
        x = y;
        return true;
    }
    return false;
}

istream &operator>>(istream &is, i128 &x) {
    i64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, i128 x) {
    os << (i64) x;
    return os;
}
istream &operator>>(istream &is, u128 &x) {
    u64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, u128 x) {
    os << (u64) x;
    return os;
}

[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
    SetUpIO() {
#ifdef FAST_IO
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
#endif
        cout << fixed << setprecision(15);
    }
} set_up_io;
#line 2 "convolution/subset_convolution_exp.hpp"

#line 2 "convolution/subset_convolution.hpp"

#line 2 "convolution/subset_convolution_internal.hpp"

#line 5 "convolution/subset_convolution_internal.hpp"

namespace subset_convolution_internal {

template <typename T>
void add(std::vector<T> &a, const std::vector<T> &b, int to) {
    for (int i = 0; i <= to; ++i) {
        a[i] += b[i];
    }
}

template <typename T>
void sub(std::vector<T> &a, const std::vector<T> &b, int from) {
    for (int i = from; i < (int) a.size(); ++i) {
        a[i] -= b[i];
    }
}

template <typename T>
std::vector<std::vector<T>> setps(int n, const std::vector<T> &a) {
    std::vector<std::vector<T>> sps(1 << n, std::vector<T>(n + 1, T(0)));
    for (int i = 0; i < (1 << n); ++i) {
        sps[i][__builtin_popcount(i)] = a[i];
    }
    return sps;
}

template <typename T>
std::vector<T> rev_setps(int n, const std::vector<std::vector<T>> &sps) {
    std::vector<T> a(1 << n);
    for (int i = 0; i < (1 << n); ++i) {
        a[i] = sps[i][__builtin_popcount(i)];
    }
    return a;
}

} // namespace subset_convolution_internal
#line 4 "convolution/subset_convolution.hpp"

#line 6 "convolution/subset_convolution.hpp"

template <typename T>
std::vector<T> _subset_conv_mul(const std::vector<T> &a, const std::vector<T> &b, int to) {
    std::vector<T> c(a.size(), T(0));
    for (int i = 0; i <= to; ++i) {
        for (int j = 0; j <= std::min((int) a.size() - i - 1, to); ++j) {
            c[i + j] += a[i] * b[j];
        }
    }
    return c;
}

template <typename T>
std::vector<T> subset_convolution(const std::vector<T> &a, const std::vector<T> &b) {
    int n = 0;
    while ((1 << n) < (int) a.size()) {
        ++n;
    }
    assert((int) a.size() == (1 << n));
    assert((int) b.size() == (1 << n));
    
    std::vector<std::vector<T>> a_ = subset_convolution_internal::setps(n, a);
    std::vector<std::vector<T>> b_ = subset_convolution_internal::setps(n, b);
    for (int d = 0; d < n; ++ d) {
        for (int i = 0; i < (1 << n); ++i) {
            if (i & (1 << d)) {
                subset_convolution_internal::add(a_[i], a_[i ^ (1 << d)], __builtin_popcount(i) - 1);
                subset_convolution_internal::add(b_[i], b_[i ^ (1 << d)], __builtin_popcount(i) - 1);
            }
        }
    }
    for (int i = 0; i < (1 << n); ++i) {
        a_[i] = _subset_conv_mul(a_[i], b_[i], __builtin_popcount(i));
    }
    for (int d = 0; d < n; ++ d) {
        for (int i = 0; i < (1 << n); ++i) {
            if (i & (1 << d)) {
                subset_convolution_internal::sub(a_[i], a_[i ^ (1 << d)], __builtin_popcount(i));
            }
        }
    }
    return subset_convolution_internal::rev_setps(n, a_);
}
#line 4 "convolution/subset_convolution_exp.hpp"

template <typename T>
std::vector<T> subset_convolution_exp(const std::vector<T> &a) {
    int n = 0;
    while ((1 << n) < (int)a.size()) {
        ++n;
    }
    assert((int)a.size() == (1 << n));
    assert(a[0] == T(0));
    
    std::vector<T> b;
    b.reserve(1 << n);
    b.push_back(T(1));
    for (int i = 0; i < n; ++i) {
        std::vector<T> c(a.begin() + (1 << i), a.begin() + (2 << i));
        std::vector<T> sc = subset_convolution(b, c);
        for (int j = 0; j < (1 << i); ++j) {
            b.push_back(sc[j]);
        }
    }
    return b;
}
#line 2 "convolution/subset_convolution_log.hpp"

#line 4 "convolution/subset_convolution_log.hpp"

#line 6 "convolution/subset_convolution_log.hpp"

template <typename T>
std::vector<T> _subset_conv_log(const std::vector<T> &a, int to) {
    std::vector<T> b(a.size());
    for (int i = 1; i < (int) a.size(); ++i) {
        b[i] = a[i] * T(i);
        for (int j = 1; j <= std::min(to, i); ++j) {
            b[i] -= a[j] * b[i - j];
        }
    }
    for (int i = 1; i < (int) a.size(); ++i) {
        b[i] /= T(i);
    }
    return b;
}

template <typename T>
std::vector<T> subset_convolution_log(const std::vector<T> &a) {
    int n = 0;
    while ((1 << n) < (int) a.size()) {
        ++n;
    }
    assert((int) a.size() == (1 << n));
    assert(a[0] == T(1));
    
    std::vector<std::vector<T>> a_ = subset_convolution_internal::setps(n, a);
    for (int d = 0; d < n; ++ d) {
        for (int i = 0; i < (1 << n); ++i) {
            if (i & (1 << d)) {
                subset_convolution_internal::add(a_[i], a_[i ^ (1 << d)], __builtin_popcount(i) - 1);
            }
        }
    }
    for (int i = 0; i < (1 << n); ++i) {
        a_[i] = _subset_conv_log(a_[i], __builtin_popcount(i));
    }
    for (int d = 0; d < n; ++ d) {
        for (int i = 0; i < (1 << n); ++i) {
            if (i & (1 << d)) {
                subset_convolution_internal::sub(a_[i], a_[i ^ (1 << d)], __builtin_popcount(i));
            }
        }
    }
    return subset_convolution_internal::rev_setps(n, a_);
}
#line 2 "number_theory/mod_int.hpp"

#line 5 "number_theory/mod_int.hpp"
#include <type_traits>

#line 2 "number_theory/utils.hpp"

constexpr bool is_prime(unsigned n) {
    if (n == 0 || n == 1) {
        return false;
    }
    for (unsigned i = 2; i * i <= n; ++i) {
        if (n % i == 0) {
            return false;
        }
    }
    return true;
}

constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) {
    unsigned ret = 1, self = x;
    while (y != 0) {
        if (y & 1) {
            ret = (unsigned) ((unsigned long long) ret * self % mod);
        }
        self = (unsigned) ((unsigned long long) self * self % mod);
        y /= 2;
    }
    return ret;
}

template <unsigned mod>
constexpr unsigned primitive_root() {
    static_assert(is_prime(mod), "`mod` must be a prime number.");
    if (mod == 2) {
        return 1;
    }

    unsigned primes[32] = {};
    int it = 0;
    {
        unsigned m = mod - 1;
        for (unsigned i = 2; i * i <= m; ++i) {
            if (m % i == 0) {
                primes[it++] = i;
                while (m % i == 0) {
                    m /= i;
                }
            }
        }
        if (m != 1) {
            primes[it++] = m;
        }
    }
    for (unsigned i = 2; i < mod; ++i) {
        bool ok = true;
        for (int j = 0; j < it; ++j) {
            if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) {
                ok = false;
                break;
            }
        }
        if (ok)
            return i;
    }
    return 0;
}

// y >= 1
template <typename T>
constexpr T safe_mod(T x, T y) {
    x %= y;
    if (x < 0) {
        x += y;
    }
    return x;
}

// y != 0
template <typename T>
constexpr T floor_div(T x, T y) {
    if (y < 0) {
        x *= -1;
        y *= -1;
    }
    if (x >= 0) {
        return x / y;
    } else {
        return -((-x + y - 1) / y);
    }
}

// y != 0
template <typename T>
constexpr T ceil_div(T x, T y) {
    if (y < 0) {
        x *= -1;
        y *= -1;
    }
    if (x >= 0) {
        return (x + y - 1) / y;
    } else {
        return -(-x / y);
    }
}
#line 8 "number_theory/mod_int.hpp"

template <unsigned mod>
class ModInt {
    static_assert(mod != 0, "`mod` must not be equal to 0.");
    static_assert(
        mod < (1u << 31),
        "`mod` must be less than (1u << 31) = 2147483648.");

    unsigned val;

public:
    static constexpr unsigned get_mod() {
        return mod;
    }
    
    constexpr ModInt() : val(0) {}
    template <typename T, std::enable_if_t<std::is_signed_v<T>> * = nullptr>
    constexpr ModInt(T x) : val((unsigned) ((long long) x % (long long) mod + (x < 0 ? mod : 0))) {}
    template <typename T, std::enable_if_t<std::is_unsigned_v<T>> * = nullptr>
    constexpr ModInt(T x) : val((unsigned) (x % mod)) {}

    static constexpr ModInt raw(unsigned x) {
        ModInt<mod> ret;
        ret.val = x;
        return ret;
    }

    constexpr unsigned get_val() const {
        return val;
    }

    constexpr ModInt operator+() const {
        return *this;
    }
    constexpr ModInt operator-() const {
        return ModInt<mod>(0u) - *this;
    }

    constexpr ModInt &operator+=(const ModInt &rhs) {
        val += rhs.val;
        if (val >= mod)
            val -= mod;
        return *this;
    }
    constexpr ModInt &operator-=(const ModInt &rhs) {
        if (val < rhs.val)
            val += mod;
        val -= rhs.val;
        return *this;
    }
    constexpr ModInt &operator*=(const ModInt &rhs) {
        val = (unsigned long long)val * rhs.val % mod;
        return *this;
    }
    constexpr ModInt &operator/=(const ModInt &rhs) {
        val = (unsigned long long)val * rhs.inv().val % mod;
        return *this;
    }

    friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) += rhs;
    }
    friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) -= rhs;
    }
    friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) *= rhs;
    }
    friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) /= rhs;
    }

    constexpr ModInt pow(unsigned long long x) const {
        ModInt<mod> ret = ModInt<mod>::raw(1);
        ModInt<mod> self = *this;
        while (x != 0) {
            if (x & 1)
                ret *= self;
            self *= self;
            x >>= 1;
        }
        return ret;
    }
    constexpr ModInt inv() const {
        static_assert(is_prime(mod), "`mod` must be a prime number.");
        assert(val != 0);
        return this->pow(mod - 2);
    }

    friend std::istream &operator>>(std::istream &is, ModInt<mod> &x) {
        long long val;
        is >> val;
        x.val = val % mod + (val < 0 ? mod : 0);
        return is;
    }

    friend std::ostream &operator<<(std::ostream &os, const ModInt<mod> &x) {
        os << x.val;
        return os;
    }

    friend bool operator==(const ModInt &lhs, const ModInt &rhs) {
        return lhs.val == rhs.val;
    }
    
    friend bool operator!=(const ModInt &lhs, const ModInt &rhs) {
        return lhs.val != rhs.val;
    }
};

[[maybe_unused]] constexpr unsigned mod998244353 = 998244353;
[[maybe_unused]] constexpr unsigned mod1000000007 = 1000000007;

#line 2 "other/xorshift.hpp"

class XorShift64 {
    unsigned long long x;
    
public:
    XorShift64(unsigned long long seed) : x((seed + 14213124131ull) ^ 103920984124ull) {}
    
    unsigned long long operator()() {
        x = x ^ (x << 13);
        x = x ^ (x >> 7);
        x = x ^ (x << 17);
        return x;
    }
    
    template <typename T>
    T uniform(T mn, T mx) {
        return mn + (T) ((*this)() % (mx - mn + 1));
    }
    
    double as_f64() {
        return (double) (*this)() / ~0ull;
    }
};
#line 10 "convolution/test/subset_convolution_exp_log.test.cpp"

constexpr u32 MOD = 998244353;
using Mint = ModInt<MOD>;

void test1(const Vec<Mint> &a) {
    Vec<Mint> exp_a = subset_convolution_exp(a);
    Vec<Mint> log_exp_a = subset_convolution_log(exp_a);
    assert(a == log_exp_a);
}

void test2(const Vec<Mint> &a) {
    Vec<Mint> log_a = subset_convolution_log(a);
    Vec<Mint> exp_log_a = subset_convolution_exp(log_a);
    assert(a == exp_log_a);
}

int main() {
    constexpr u64 SEED = 1309420975327ull;
    XorShift64 rd(SEED);
    
    REP(iter, 5) {
        i32 n = rd.uniform(1, 16);
        Vec<Mint> a(1 << n);
        REP(i, 1, 1 << n) {
            a[i] = rd.uniform(0u, MOD - 1u);
        }
        test1(a);
    }
    REP(iter, 5) {
        i32 n = rd.uniform(1, 16);
        Vec<Mint> a(1 << n);
        a[0] = Mint(1);
        REP(i, 1, 1 << n) {
            a[i] = rd.uniform(0u, MOD - 1u);
        }
        test2(a);
    }
    
    cout << "Hello World\n";
}

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