CP-Algorithms Library

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:heavy_check_mark: Wildcard Pattern Matching (verify/poly/wildcard.test.cpp)

Depends on

Code

// @brief Wildcard Pattern Matching
#define PROBLEM "https://judge.yosupo.jp/problem/wildcard_pattern_matching"
#pragma GCC optimize("Ofast,unroll-loops")
#define CP_ALGO_CHECKPOINT
#include "cp-algo/math/cvector.hpp"
#include "cp-algo/random/rng.hpp"
#include <bits/stdc++.h>

using namespace std;
using namespace cp_algo::math;

using fft::ftype;
using fft::point;
using fft::cvector;

void semicorr(auto &a, auto &b) {
    a.fft();
    b.fft();
    a.dot(b);
    a.ifft();
}

auto is_integer = [](point a) {
    static const double eps = 1e-8;
    return abs(imag(a)) < eps
        && abs(real(a) - round(real(a))) < eps;
};

string matches(string const& A, string const& B, char wild = '*') {
    static const int sigma = 26;
    static point project[2][sigma];
    static bool init = false;
    if(!init) {
        init = true;
        for(int i = 0; i < sigma; i++) {
            project[0][i] = cp_algo::polar(1., (ftype)cp_algo::random::rng());
            project[1][i] = conj(project[0][i]);
        }
    }
    vector<cvector> P;
    P.emplace_back(size(A));
    P.emplace_back(size(A));
    for(auto [i, c]: A | views::enumerate) {
        P[0].set(i, (c != wild) * project[0][c - 'a']);
    }
    for(auto [i, c]: B | views::reverse | views::enumerate) {
        P[1].set(i, (c != wild) * project[1][c - 'a']);
    }
    cp_algo::checkpoint("cvector fill");
    semicorr(P[0], P[1]);
    string ans(size(A) - size(B) + 1, '0');
    for(size_t j = 0; j < size(ans); j++) {
        ans[j] = '0' + is_integer(P[0].get(size(B) - 1 + j));
    }
    cp_algo::checkpoint("fill answer");
    return ans;
}

void solve() {
    string a, b;
    cin >> a >> b;
    cp_algo::checkpoint("input");
    cout << matches(a, b) << "\n";
    cp_algo::checkpoint("output");
    cp_algo::checkpoint<true>("done");
}

signed main() {
    //freopen("input.txt", "r", stdin);
    ios::sync_with_stdio(0);
    cin.tie(0);
    int t = 1;
    //cin >> t;
    while(t--) {
        solve();
    }
}

#line 1 "verify/poly/wildcard.test.cpp"
// @brief Wildcard Pattern Matching
#define PROBLEM "https://judge.yosupo.jp/problem/wildcard_pattern_matching"
#pragma GCC optimize("Ofast,unroll-loops")
#define CP_ALGO_CHECKPOINT
#line 1 "cp-algo/math/cvector.hpp"


#line 1 "cp-algo/util/complex.hpp"


#include <iostream>
#include <cmath>
namespace cp_algo {
    // Custom implementation, since std::complex is UB on non-floating types
    template<typename T>
    struct complex {
        using value_type = T;
        T x, y;
        constexpr complex() {}
        constexpr complex(T x): x(x), y() {}
        constexpr complex(T x, T y): x(x), y(y) {}
        complex& operator *= (T t) {x *= t; y *= t; return *this;}
        complex& operator /= (T t) {x /= t; y /= t; return *this;}
        complex operator * (T t) const {return complex(*this) *= t;}
        complex operator / (T t) const {return complex(*this) /= t;}
        complex& operator += (complex t) {x += t.x; y += t.y; return *this;}
        complex& operator -= (complex t) {x -= t.x; y -= t.y; return *this;}
        complex operator * (complex t) const {return {x * t.x - y * t.y, x * t.y + y * t.x};}
        complex operator / (complex t) const {return *this * t.conj() / t.norm();}
        complex operator + (complex t) const {return complex(*this) += t;}
        complex operator - (complex t) const {return complex(*this) -= t;}
        complex& operator *= (complex t) {return *this = *this * t;}
        complex& operator /= (complex t) {return *this = *this / t;}
        complex operator - () const {return {-x, -y};}
        complex conj() const {return {x, -y};}
        T norm() const {return x * x + y * y;}
        T abs() const {return std::sqrt(norm());}
        T real() const {return x;}
        T imag() const {return y;}
        T& real() {return x;}
        T& imag() {return y;}
        static constexpr complex polar(T r, T theta) {return {r * cos(theta), r * sin(theta)};}
        auto operator <=> (complex const& t) const = default;
    };
    template<typename T>
    complex<T> operator * (auto x, complex<T> y) {return y *= x;}
    template<typename T> complex<T> conj(complex<T> x) {return x.conj();}
    template<typename T> T norm(complex<T> x) {return x.norm();}
    template<typename T> T abs(complex<T> x) {return x.abs();}
    template<typename T> T& real(complex<T> &x) {return x.real();}
    template<typename T> T& imag(complex<T> &x) {return x.imag();}
    template<typename T> T real(complex<T> const& x) {return x.real();}
    template<typename T> T imag(complex<T> const& x) {return x.imag();}
    template<typename T>
    constexpr complex<T> polar(T r, T theta) {
        return complex<T>::polar(r, theta);
    }
    template<typename T>
    std::ostream& operator << (std::ostream &out, complex<T> x) {
        return out << x.real() << ' ' << x.imag();
    }
}

#line 1 "cp-algo/util/checkpoint.hpp"


#line 4 "cp-algo/util/checkpoint.hpp"
#include <chrono>
#include <string>
namespace cp_algo {
    template<bool final = false>
    void checkpoint([[maybe_unused]] std::string const& msg = "") {
#ifdef CP_ALGO_CHECKPOINT
        static double last = 0;
        double now = (double)clock() / CLOCKS_PER_SEC;
        double delta = now - last;
        last = now;
        if(msg.size()) {
            std::cerr << msg << ": " << (final ? now : delta) * 1000 << " ms\n";
        }
#endif
    }
}

#line 1 "cp-algo/util/new_big.hpp"


#include <sys/mman.h>
namespace cp_algo {
    template<typename T>
    auto new_big(size_t len) {
        auto raw = mmap(nullptr, len * sizeof(T),
            PROT_READ | PROT_WRITE,
            MAP_PRIVATE | MAP_ANONYMOUS,
            -1, 0);
        madvise(raw, len * sizeof(T), MADV_HUGEPAGE);
        madvise(raw, len * sizeof(T), MADV_POPULATE_WRITE);
        return static_cast<T*>(raw);
    }
    template<typename T>
    void delete_big(T* ptr, size_t len) {
        munmap(ptr, len * sizeof(T));
    }
}

#line 6 "cp-algo/math/cvector.hpp"
#include <experimental/simd>
#include <ranges>

namespace stdx = std::experimental;
namespace cp_algo::math::fft {
    using ftype = double;
    static constexpr size_t bytes = 32;
    static constexpr size_t flen = bytes / sizeof(ftype);
    using point = complex<ftype>;
    using vftype [[gnu::vector_size(bytes)]] = ftype;
    using vpoint = complex<vftype>;
    static constexpr vftype vz = {};
    static constexpr vpoint vi = {vz, vz + 1};

    struct cvector {
        vpoint *r;
        size_t sz;
        cvector(size_t n) {
            sz = std::max(flen, std::bit_ceil(n));
            r = new_big<vpoint>(sz / flen);
            checkpoint("cvector create");
        }
        cvector(cvector const& t) {
            sz = t.sz;
            r = new_big<vpoint>(sz / flen);
            memcpy(r, t.r, (sz / flen) * sizeof(vpoint));
            checkpoint("cvector copy");
        }
        cvector(cvector&& t) noexcept {
            sz = t.sz;
            r = std::exchange(t.r, nullptr);
        }
        ~cvector() noexcept {
            if(r) {
                delete_big(r, sz / flen);
            }
        }

        vpoint& at(size_t k) {return r[k / flen];}
        vpoint at(size_t k) const {return r[k / flen];}
        template<class pt = point>
        void set(size_t k, pt t) {
            if constexpr(std::is_same_v<pt, point>) {
                real(r[k / flen])[k % flen] = real(t);
                imag(r[k / flen])[k % flen] = imag(t);
            } else {
                at(k) = t;
            }
        }
        template<class pt = point>
        pt get(size_t k) const {
            if constexpr(std::is_same_v<pt, point>) {
                return {real(r[k / flen])[k % flen], imag(r[k / flen])[k % flen]};
            } else {
                return at(k);
            }
        }

        size_t size() const {
            return sz;
        }
        static size_t eval_arg(size_t n) {
            if(n < pre_roots) {
                return eval_args[n];
            } else {
                return eval_arg(n / 2) | (n & 1) << (std::bit_width(n) - 1);
            }
        }
        static auto root(size_t n, size_t k) {
            if(n < pre_roots) {
                return roots[n + k];
            } else {
                return polar(1., std::numbers::pi / (ftype)n * (ftype)k);
            }
        }
        static point eval_point(size_t n) {
            if(n < pre_roots) {
                return evalp[n];
            } else {
                return root(2 * std::bit_floor(n), eval_arg(n));
            }
        }
        static void exec_on_roots(size_t n, size_t m, auto &&callback) {
            point cur;
            point arg = root(n, 1);
            for(size_t i = 0; i < m; i++) {
                if(i % 32 == 0 || n < pre_roots) {
                    cur = root(n, i);
                } else {
                    cur *= arg;
                }
                callback(i, cur);
            }
        }
        template<int step = 1>
        static void exec_on_evals(size_t n, auto &&callback) {
            for(size_t i = 0; i < n; i++) {
                callback(i, eval_point(step * i));
            }
        }
        static auto dot_block(size_t k, cvector const& A, cvector const& B) {
            auto rt = eval_point(k / flen / 2);
            if(k / flen % 2) {
                rt = -rt;
            }
            auto [Ax, Ay] = A.at(k);
            auto Bv = B.at(k);
            vpoint res = vz;
            for (size_t i = 0; i < flen; i++) {
                res += vpoint(vz + Ax[i], vz + Ay[i]) * Bv;
                real(Bv) = __builtin_shufflevector(real(Bv), real(Bv), 3, 0, 1, 2);
                imag(Bv) = __builtin_shufflevector(imag(Bv), imag(Bv), 3, 0, 1, 2);
                auto x = real(Bv)[0], y = imag(Bv)[0];
                real(Bv)[0] = x * real(rt) - y * imag(rt);
                imag(Bv)[0] = x * imag(rt) + y * real(rt);
            }
            return res;
        }

        void dot(cvector const& t) {
            size_t n = this->size();
            for(size_t k = 0; k < n; k += flen) {
                set(k, dot_block(k, *this, t));
            }
            checkpoint("dot");
        }

        void ifft() {
            size_t n = size();
            for(size_t i = flen; i <= n / 2; i *= 2) {
                if (4 * i <= n) { // radix-4
                    exec_on_evals<2>(n / (4 * i), [&](size_t k, point rt) {
                        k *= 4 * i;
                        vpoint v1 = {vz + real(rt), vz - imag(rt)};
                        vpoint v2 = v1 * v1;
                        vpoint v3 = v1 * v2;
                        for(size_t j = k; j < k + i; j += flen) {
                            auto A = at(j);
                            auto B = at(j + i);
                            auto C = at(j + 2 * i);
                            auto D = at(j + 3 * i);
                            at(j) = (A + B + C + D);
                            at(j + 2 * i) = (A + B - C - D) * v2;
                            at(j +     i) = (A - B - vi * (C - D)) * v1;
                            at(j + 3 * i) = (A - B + vi * (C - D)) * v3;
                        }
                    });
                    i *= 2;
                } else { // radix-2 fallback
                    exec_on_evals(n / (2 * i), [&](size_t k, point rt) {
                        k *= 2 * i;
                        vpoint cvrt = {vz + real(rt), vz - imag(rt)};
                        for(size_t j = k; j < k + i; j += flen) {
                            auto B = at(j) - at(j + i);
                            at(j) += at(j + i);
                            at(j + i) = B * cvrt;
                        }
                    });
                }
            }
            checkpoint("ifft");
            for(size_t k = 0; k < n; k += flen) {
                set(k, get<vpoint>(k) /= vz + (ftype)(n / flen));
            }
        }
        void fft() {
            size_t n = size();
            for(size_t i = n / 2; i >= flen; i /= 2) {
                if (i / 2 >= flen) { // radix-4
                    i /= 2;
                    exec_on_evals<2>(n / (4 * i), [&](size_t k, point rt) {
                        k *= 4 * i;
                        vpoint v1 = {vz + real(rt), vz + imag(rt)};
                        vpoint v2 = v1 * v1;
                        vpoint v3 = v1 * v2;
                        for(size_t j = k; j < k + i; j += flen) {
                            auto A = at(j);
                            auto B = at(j + i) * v1;
                            auto C = at(j + 2 * i) * v2;
                            auto D = at(j + 3 * i) * v3;
                            at(j)         = (A + C) + (B + D);
                            at(j + i)     = (A + C) - (B + D);
                            at(j + 2 * i) = (A - C) + vi * (B - D);
                            at(j + 3 * i) = (A - C) - vi * (B - D);
                        }
                    });
                } else { // radix-2 fallback
                    exec_on_evals(n / (2 * i), [&](size_t k, point rt) {
                        k *= 2 * i;
                        vpoint vrt = {vz + real(rt), vz + imag(rt)};
                        for(size_t j = k; j < k + i; j += flen) {
                            auto t = at(j + i) * vrt;
                            at(j + i) = at(j) - t;
                            at(j) += t;
                        }
                    });
                }
            }
            checkpoint("fft");
        }
        static constexpr size_t pre_roots = 1 << 16;
        static constexpr std::array<point, pre_roots> roots = []() {
            std::array<point, pre_roots> res = {};
            for(size_t n = 1; n < res.size(); n *= 2) {
                for(size_t k = 0; k < n; k++) {
                    res[n + k] = polar(1., std::numbers::pi / ftype(n) * ftype(k));
                }
            }
            return res;
        }();
        static constexpr std::array<size_t, pre_roots> eval_args = []() {
            std::array<size_t, pre_roots> res = {};
            for(size_t i = 1; i < pre_roots; i++) {
                res[i] = res[i >> 1] | (i & 1) << (std::bit_width(i) - 1);
            }
            return res;
        }();
        static constexpr std::array<point, pre_roots> evalp = []() {
            std::array<point, pre_roots> res = {};
            res[0] = 1;
            for(size_t n = 1; n < pre_roots; n++) {
                res[n] = polar(1., std::numbers::pi * ftype(eval_args[n]) / ftype(2 * std::bit_floor(n)));
            }
            return res;
        }();
    };
}

#line 1 "cp-algo/random/rng.hpp"


#line 4 "cp-algo/random/rng.hpp"
#include <random>
namespace cp_algo::random {
    uint64_t rng() {
        static std::mt19937_64 rng(
            std::chrono::steady_clock::now().time_since_epoch().count()
        );
        return rng();
    }
}

#line 7 "verify/poly/wildcard.test.cpp"
#include <bits/stdc++.h>

using namespace std;
using namespace cp_algo::math;

using fft::ftype;
using fft::point;
using fft::cvector;

void semicorr(auto &a, auto &b) {
    a.fft();
    b.fft();
    a.dot(b);
    a.ifft();
}

auto is_integer = [](point a) {
    static const double eps = 1e-8;
    return abs(imag(a)) < eps
        && abs(real(a) - round(real(a))) < eps;
};

string matches(string const& A, string const& B, char wild = '*') {
    static const int sigma = 26;
    static point project[2][sigma];
    static bool init = false;
    if(!init) {
        init = true;
        for(int i = 0; i < sigma; i++) {
            project[0][i] = cp_algo::polar(1., (ftype)cp_algo::random::rng());
            project[1][i] = conj(project[0][i]);
        }
    }
    vector<cvector> P;
    P.emplace_back(size(A));
    P.emplace_back(size(A));
    for(auto [i, c]: A | views::enumerate) {
        P[0].set(i, (c != wild) * project[0][c - 'a']);
    }
    for(auto [i, c]: B | views::reverse | views::enumerate) {
        P[1].set(i, (c != wild) * project[1][c - 'a']);
    }
    cp_algo::checkpoint("cvector fill");
    semicorr(P[0], P[1]);
    string ans(size(A) - size(B) + 1, '0');
    for(size_t j = 0; j < size(ans); j++) {
        ans[j] = '0' + is_integer(P[0].get(size(B) - 1 + j));
    }
    cp_algo::checkpoint("fill answer");
    return ans;
}

void solve() {
    string a, b;
    cin >> a >> b;
    cp_algo::checkpoint("input");
    cout << matches(a, b) << "\n";
    cp_algo::checkpoint("output");
    cp_algo::checkpoint<true>("done");
}

signed main() {
    //freopen("input.txt", "r", stdin);
    ios::sync_with_stdio(0);
    cin.tie(0);
    int t = 1;
    //cin >> t;
    while(t--) {
        solve();
    }
}

Test cases

Env Name Status Elapsed Memory
g++ alternating_00 :heavy_check_mark: AC 17 ms 23 MB
g++ alternating_01 :heavy_check_mark: AC 18 ms 23 MB
g++ alternating_02 :heavy_check_mark: AC 7 ms 6 MB
g++ alternating_03 :heavy_check_mark: AC 16 ms 23 MB
g++ alternating_04 :heavy_check_mark: AC 15 ms 22 MB
g++ example_00 :heavy_check_mark: AC 5 ms 4 MB
g++ hack_998244353_00 :heavy_check_mark: AC 17 ms 23 MB
g++ hack_998244353_01 :heavy_check_mark: AC 17 ms 23 MB
g++ hack_998244353_02 :heavy_check_mark: AC 17 ms 23 MB
g++ random_00 :heavy_check_mark: AC 16 ms 23 MB
g++ random_01 :heavy_check_mark: AC 16 ms 23 MB
g++ random_02 :heavy_check_mark: AC 7 ms 6 MB
g++ random_03 :heavy_check_mark: AC 16 ms 23 MB
g++ random_04 :heavy_check_mark: AC 15 ms 22 MB
g++ random_ab_00 :heavy_check_mark: AC 16 ms 22 MB
g++ random_ab_01 :heavy_check_mark: AC 17 ms 23 MB
g++ random_ab_02 :heavy_check_mark: AC 7 ms 6 MB
g++ random_ab_03 :heavy_check_mark: AC 18 ms 22 MB
g++ random_ab_04 :heavy_check_mark: AC 16 ms 22 MB
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