cplib-cpp

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:heavy_check_mark: string/test/run_enumerate_lyndon_hash.test.cpp

Depends on

Code

#include "../../modint.hpp"
#include "../lyndon.hpp"
#include "../rolling_hash_1d.hpp"
#include <iostream>
#include <string>
#define PROBLEM "https://judge.yosupo.jp/problem/runenumerate"
using namespace std;

int main() {
    cin.tie(nullptr), ios::sync_with_stdio(false);
    string S;
    cin >> S;
    auto ret = run_enumerate<rolling_hash<PairHash<ModInt998244353, ModInt998244353>>>(S);
    cout << ret.size() << '\n';
    for (auto p : ret) cout << get<0>(p) << ' ' << get<1>(p) << ' ' << get<2>(p) << '\n';
}
#line 2 "modint.hpp"
#include <cassert>
#include <iostream>
#include <set>
#include <vector>

template <int md> struct ModInt {
    using lint = long long;
    constexpr static int mod() { return md; }
    static int get_primitive_root() {
        static int primitive_root = 0;
        if (!primitive_root) {
            primitive_root = [&]() {
                std::set<int> fac;
                int v = md - 1;
                for (lint i = 2; i * i <= v; i++)
                    while (v % i == 0) fac.insert(i), v /= i;
                if (v > 1) fac.insert(v);
                for (int g = 1; g < md; g++) {
                    bool ok = true;
                    for (auto i : fac)
                        if (ModInt(g).pow((md - 1) / i) == 1) {
                            ok = false;
                            break;
                        }
                    if (ok) return g;
                }
                return -1;
            }();
        }
        return primitive_root;
    }
    int val_;
    int val() const noexcept { return val_; }
    constexpr ModInt() : val_(0) {}
    constexpr ModInt &_setval(lint v) { return val_ = (v >= md ? v - md : v), *this; }
    constexpr ModInt(lint v) { _setval(v % md + md); }
    constexpr explicit operator bool() const { return val_ != 0; }
    constexpr ModInt operator+(const ModInt &x) const {
        return ModInt()._setval((lint)val_ + x.val_);
    }
    constexpr ModInt operator-(const ModInt &x) const {
        return ModInt()._setval((lint)val_ - x.val_ + md);
    }
    constexpr ModInt operator*(const ModInt &x) const {
        return ModInt()._setval((lint)val_ * x.val_ % md);
    }
    constexpr ModInt operator/(const ModInt &x) const {
        return ModInt()._setval((lint)val_ * x.inv().val() % md);
    }
    constexpr ModInt operator-() const { return ModInt()._setval(md - val_); }
    constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
    constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
    constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
    constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
    friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt(a) + x; }
    friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt(a) - x; }
    friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt(a) * x; }
    friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt(a) / x; }
    constexpr bool operator==(const ModInt &x) const { return val_ == x.val_; }
    constexpr bool operator!=(const ModInt &x) const { return val_ != x.val_; }
    constexpr bool operator<(const ModInt &x) const {
        return val_ < x.val_;
    } // To use std::map<ModInt, T>
    friend std::istream &operator>>(std::istream &is, ModInt &x) {
        lint t;
        return is >> t, x = ModInt(t), is;
    }
    constexpr friend std::ostream &operator<<(std::ostream &os, const ModInt &x) {
        return os << x.val_;
    }

    constexpr ModInt pow(lint n) const {
        ModInt ans = 1, tmp = *this;
        while (n) {
            if (n & 1) ans *= tmp;
            tmp *= tmp, n >>= 1;
        }
        return ans;
    }

    static constexpr int cache_limit = std::min(md, 1 << 21);
    static std::vector<ModInt> facs, facinvs, invs;

    constexpr static void _precalculation(int N) {
        const int l0 = facs.size();
        if (N > md) N = md;
        if (N <= l0) return;
        facs.resize(N), facinvs.resize(N), invs.resize(N);
        for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i;
        facinvs[N - 1] = facs.back().pow(md - 2);
        for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1);
        for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1];
    }

    constexpr ModInt inv() const {
        if (this->val_ < cache_limit) {
            if (facs.empty()) facs = {1}, facinvs = {1}, invs = {0};
            while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);
            return invs[this->val_];
        } else {
            return this->pow(md - 2);
        }
    }
    constexpr ModInt fac() const {
        while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);
        return facs[this->val_];
    }
    constexpr ModInt facinv() const {
        while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);
        return facinvs[this->val_];
    }
    constexpr ModInt doublefac() const {
        lint k = (this->val_ + 1) / 2;
        return (this->val_ & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac())
                                : ModInt(k).fac() * ModInt(2).pow(k);
    }

    constexpr ModInt nCr(int r) const {
        if (r < 0 or this->val_ < r) return ModInt(0);
        return this->fac() * (*this - r).facinv() * ModInt(r).facinv();
    }

    constexpr ModInt nPr(int r) const {
        if (r < 0 or this->val_ < r) return ModInt(0);
        return this->fac() * (*this - r).facinv();
    }

    static ModInt binom(int n, int r) {
        static long long bruteforce_times = 0;

        if (r < 0 or n < r) return ModInt(0);
        if (n <= bruteforce_times or n < (int)facs.size()) return ModInt(n).nCr(r);

        r = std::min(r, n - r);

        ModInt ret = ModInt(r).facinv();
        for (int i = 0; i < r; ++i) ret *= n - i;
        bruteforce_times += r;

        return ret;
    }

    // Multinomial coefficient, (k_1 + k_2 + ... + k_m)! / (k_1! k_2! ... k_m!)
    // Complexity: O(sum(ks))
    template <class Vec> static ModInt multinomial(const Vec &ks) {
        ModInt ret{1};
        int sum = 0;
        for (int k : ks) {
            assert(k >= 0);
            ret *= ModInt(k).facinv(), sum += k;
        }
        return ret * ModInt(sum).fac();
    }

    // Catalan number, C_n = binom(2n, n) / (n + 1)
    // C_0 = 1, C_1 = 1, C_2 = 2, C_3 = 5, C_4 = 14, ...
    // https://oeis.org/A000108
    // Complexity: O(n)
    static ModInt catalan(int n) {
        if (n < 0) return ModInt(0);
        return ModInt(n * 2).fac() * ModInt(n + 1).facinv() * ModInt(n).facinv();
    }

    ModInt sqrt() const {
        if (val_ == 0) return 0;
        if (md == 2) return val_;
        if (pow((md - 1) / 2) != 1) return 0;
        ModInt b = 1;
        while (b.pow((md - 1) / 2) == 1) b += 1;
        int e = 0, m = md - 1;
        while (m % 2 == 0) m >>= 1, e++;
        ModInt x = pow((m - 1) / 2), y = (*this) * x * x;
        x *= (*this);
        ModInt z = b.pow(m);
        while (y != 1) {
            int j = 0;
            ModInt t = y;
            while (t != 1) j++, t *= t;
            z = z.pow(1LL << (e - j - 1));
            x *= z, z *= z, y *= z;
            e = j;
        }
        return ModInt(std::min(x.val_, md - x.val_));
    }
};
template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0};

using ModInt998244353 = ModInt<998244353>;
// using mint = ModInt<998244353>;
// using mint = ModInt<1000000007>;
#line 2 "string/lyndon.hpp"
#include <algorithm>
#line 4 "string/lyndon.hpp"
#include <functional>
#include <string>
#include <tuple>
#include <utility>
#line 9 "string/lyndon.hpp"

// CUT begin
// Lyndon factorization based on Duval's algorithm
// **NOT VERIFIED YET**
// Reference:
// [1] K. T. Chen, R. H. Fox, R. C. Lyndon,
//     "Free Differential Calculus, IV. The Quotient Groups of the Lower Central Series,"
//     Annals of Mathematics, 68(1), 81-95, 1958.
// [2] J. P. Duval, "Factorizing words over an ordered alphabet,"
//     Journal of Algorithms, 4(4), 363-381, 1983.
// - https://cp-algorithms.com/string/lyndon_factorization.html
// - https://qiita.com/nakashi18/items/66882bd6e0127174267a
template <typename T>
std::vector<std::pair<int, int>> lyndon_factorization(const std::vector<T> &S) {
    const int N = S.size();
    std::vector<std::pair<int, int>> ret;
    for (int l = 0; l < N;) {
        int i = l, j = i + 1;
        while (j < N and S[i] <= S[j]) i = (S[i] == S[j] ? i + 1 : l), j++;
        int n = (j - l) / (j - i);
        for (int t = 0; t < n; t++) ret.emplace_back(l, j - i), l += j - i;
    }
    return ret;
}

std::vector<std::pair<int, int>> lyndon_factorization(const std::string &s) {
    const int N = int(s.size());
    std::vector<int> v(N);
    for (int i = 0; i < N; i++) v[i] = s[i];
    return lyndon_factorization<int>(v);
}

// Compute the longest Lyndon prefix for each suffix s[i:N]
// (Our implementation is $O(N \cdot (complexity of lcplen()))$)
// Example:
// - `teletelepathy` -> [1,4,1,2,1,4,1,2,1,4,1,2,1]
// Reference:
// [1] H. Bannai et al., "The "Runs" Theorem,"
//     SIAM Journal on Computing, 46(5), 1501-1514, 2017.
template <typename String, typename LCPLENCallable>
std::vector<int> longest_lyndon_prefixes(const String &s, const LCPLENCallable &lcp) {
    const int N = s.size();
    std::vector<std::pair<int, int>> st{{N, N}};
    std::vector<int> ret(N);
    for (int i = N - 1, j = i; i >= 0; i--, j = i) {
        while (st.size() > 1) {
            int iv = st.back().first, jv = st.back().second;
            int l = lcp.lcplen(i, iv);
            if (!(iv + l < N and s[i + l] < s[iv + l])) break;
            j = jv;
            st.pop_back();
        }
        st.emplace_back(i, j);
        ret[i] = j - i + 1;
    }
    return ret;
}

// Compute all runs in given string
// Complexity: $O(N \cdot (complexity of lcplen()))$ in this implementation
// (Theoretically $O(N)$ achievable)
// N = 2e5 -> ~120 ms
// Reference:
// [1] H. Bannai et al., "The "Runs" Theorem,"
//     SIAM Journal on Computing, 46(5), 1501-1514, 2017.
template <typename LCPLENCallable, typename String>
std::vector<std::tuple<int, int, int>> run_enumerate(String s) {
    if (s.empty()) return {};
    LCPLENCallable lcp(s);
    std::reverse(s.begin(), s.end());
    LCPLENCallable revlcp(s);
    std::reverse(s.begin(), s.end());
    auto t = s;
    auto lo = *std::min_element(s.begin(), s.end()), hi = *std::max_element(s.begin(), s.end());
    for (auto &c : t) c = hi - (c - lo);
    auto l1 = longest_lyndon_prefixes(s, lcp), l2 = longest_lyndon_prefixes(t, lcp);
    int N = s.size();
    std::vector<std::tuple<int, int, int>> ret;
    for (int i = 0; i < N; i++) {
        int j = i + l1[i], L = i - revlcp.lcplen(N - i, N - j), R = j + lcp.lcplen(i, j);
        if (R - L >= (j - i) * 2) ret.emplace_back(j - i, L, R);

        if (l1[i] != l2[i]) {
            j = i + l2[i], L = i - revlcp.lcplen(N - i, N - j), R = j + lcp.lcplen(i, j);
            if (R - L >= (j - i) * 2) ret.emplace_back(j - i, L, R);
        }
    }
    std::sort(ret.begin(), ret.end());
    ret.erase(std::unique(ret.begin(), ret.end()), ret.end());
    return ret;
}

// Enumerate Lyndon words up to length n in lexical order
// https://github.com/bqi343/USACO/blob/master/Implementations/content/combinatorial%20(11.2)/DeBruijnSeq.h
// Example: k=2, n=4 => [[0,],[0,0,0,1,],[0,0,1,],[0,0,1,1,],[0,1,],[0,1,1,],[0,1,1,1,],[1,],]
// Verified: https://codeforces.com/gym/102001/problem/C / https://codeforces.com/gym/100162/problem/G
std::vector<std::vector<int>> enumerate_lyndon_words(int k, int n) {
    assert(k > 0);
    assert(n > 0);
    std::vector<std::vector<int>> ret;
    std::vector<int> aux(n + 1);

    std::function<void(int, int)> gen = [&](int t, int p) {
        // t: current length
        // p: current min cycle length
        if (t == n) {
            std::vector<int> tmp(aux.begin() + 1, aux.begin() + p + 1);
            ret.push_back(std::move(tmp));
        } else {
            ++t;
            aux[t] = aux[t - p];
            gen(t, p);
            while (++aux[t] < k) gen(t, t);
        }
    };
    gen(0, 1);
    return ret;
}
#line 3 "string/rolling_hash_1d.hpp"
#include <chrono>
#include <random>
#line 8 "string/rolling_hash_1d.hpp"

template <class T1, class T2> struct PairHash : public std::pair<T1, T2> {
    using PH = PairHash<T1, T2>;
    explicit PairHash(T1 x, T2 y) : std::pair<T1, T2>(x, y) {}
    explicit PairHash(int x) : std::pair<T1, T2>(x, x) {}
    PairHash() : PairHash(0) {}
    PH operator+(const PH &x) const { return PH(this->first + x.first, this->second + x.second); }
    PH operator-(const PH &x) const { return PH(this->first - x.first, this->second - x.second); }
    PH operator*(const PH &x) const { return PH(this->first * x.first, this->second * x.second); }
    PH operator+(int x) const { return PH(this->first + x, this->second + x); }
    static PH randgen(bool force_update = false) {
        static PH b(0);
        if (b == PH(0) or force_update) {
            std::mt19937 mt(std::chrono::steady_clock::now().time_since_epoch().count());
            std::uniform_int_distribution<int> d(1 << 30);
            b = PH(T1(d(mt)), T2(d(mt)));
        }
        return b;
    }

    template <class OStream> friend OStream &operator<<(OStream &os, const PH &x) {
        return os << "(" << x.first << ", " << x.second << ")";
    }
};

template <class T1, class T2, class T3> struct TupleHash3 : public std::tuple<T1, T2, T3> {
    using TH = TupleHash3<T1, T2, T3>;
    explicit TupleHash3(T1 x, T2 y, T3 z) : std::tuple<T1, T2, T3>(x, y, z) {}
    explicit TupleHash3(int x) : std::tuple<T1, T2, T3>(x, x, x) {}
    TupleHash3() : TupleHash3(0) {}

    inline const T1 &v1() const noexcept { return std::get<0>(*this); }
    inline const T2 &v2() const noexcept { return std::get<1>(*this); }
    inline const T3 &v3() const noexcept { return std::get<2>(*this); }

    TH operator+(const TH &x) const { return TH(v1() + x.v1(), v2() + x.v2(), v3() + x.v3()); }
    TH operator-(const TH &x) const { return TH(v1() - x.v1(), v2() - x.v2(), v3() - x.v3()); }
    TH operator*(const TH &x) const { return TH(v1() * x.v1(), v2() * x.v2(), v3() * x.v3()); }
    TH operator+(int x) const { return TH(v1() + x, v2() + x, v3() + x); }
    static TH randgen(bool force_update = false) {
        static TH b(0);
        if (b == TH(0) or force_update) {
            std::mt19937 mt(std::chrono::steady_clock::now().time_since_epoch().count());
            std::uniform_int_distribution<int> d(1 << 30);
            b = TH(T1(d(mt)), T2(d(mt)), T3(d(mt)));
        }
        return b;
    }

    template <class OStream> friend OStream &operator<<(OStream &os, const TH &x) {
        return os << "(" << x.v1() << ", " << x.v2() << ", " << x.v3() << ")";
    }
};

// Rolling Hash (Rabin-Karp), 1dim
template <typename V> struct rolling_hash {
    int N;
    const V B;
    std::vector<V> hash;         // hash[i] = s[0] * B^(i - 1) + ... + s[i - 1]
    static std::vector<V> power; // power[i] = B^i
    void _extend_powvec() {
        if (power.size() > 1 and power.at(1) != B) power = {V(1)};
        while (static_cast<int>(power.size()) <= N) {
            auto tmp = power.back() * B;
            power.push_back(tmp);
        }
    }
    template <typename Int>
    rolling_hash(const std::vector<Int> &s, V b = V::randgen()) : N(s.size()), B(b), hash(N + 1) {
        for (int i = 0; i < N; i++) hash[i + 1] = hash[i] * B + s[i];
        _extend_powvec();
    }
    rolling_hash(const std::string &s = "", V b = V::randgen()) : N(s.size()), B(b), hash(N + 1) {
        for (int i = 0; i < N; i++) hash[i + 1] = hash[i] * B + s[i];
        _extend_powvec();
    }
    void addchar(const char &c) {
        V hnew = hash[N] * B + c;
        N++, hash.emplace_back(hnew);
        _extend_powvec();
    }

    struct Hash {
        int length;
        V val;
        Hash() : length(0), val(V()) {}
        Hash(int len, const V &v) : length(len), val(v) {}

        bool operator==(const Hash &r) const noexcept {
            return length == r.length and val == r.val;
        }

        bool operator<(const Hash &x) const { // To use std::map
            if (length != x.length) return length < x.length;
            return val < x.val;
        }

        Hash operator*(const Hash &r) const {
            return Hash(length + r.length, val * power.at(r.length) + r.val);
        }

        template <class OStream> friend OStream &operator<<(OStream &os, const Hash &x) {
            return os << "(length=" << x.length << ", val=" << x.val << ")";
        }
    };

    Hash get(int l, int r) const { // s[l] * B^(r - l - 1) + ... + s[r - 1]
        if (l >= r) return Hash();
        return Hash(r - l, hash[r] - hash[l] * power[r - l]);
    }

    int lcplen(int l1, int l2) const { return longest_common_prefix(*this, l1, *this, l2); }
};
template <typename V> std::vector<V> rolling_hash<V>::power{V(1)};

// Longest common prerfix between s1[l1, N1) and s2[l2, N2)
template <typename T>
int longest_common_prefix(const rolling_hash<T> &rh1, int l1, const rolling_hash<T> &rh2, int l2) {
    int lo = 0, hi = std::min(rh1.N + 1 - l1, rh2.N + 1 - l2);
    while (hi - lo > 1) {
        const int c = (lo + hi) / 2;
        auto h1 = rh1.get(l1, l1 + c), h2 = rh2.get(l2, l2 + c);
        (h1 == h2 ? lo : hi) = c;
    }
    return lo;
}
// Longest common suffix between s1[0, r1) and s2[0, r2)
template <typename T>
int longest_common_suffix(const rolling_hash<T> &rh1, int r1, const rolling_hash<T> &rh2, int r2) {
    int lo = 0, hi = std::min(r1, r2) + 1;
    while (hi - lo > 1) {
        const int c = (lo + hi) / 2;
        auto h1 = rh1.get(r1 - c, r1), h2 = rh2.get(r2 - c, r2);
        (h1 == h2 ? lo : hi) = c;
    }
    return lo;
}
#line 6 "string/test/run_enumerate_lyndon_hash.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/runenumerate"
using namespace std;

int main() {
    cin.tie(nullptr), ios::sync_with_stdio(false);
    string S;
    cin >> S;
    auto ret = run_enumerate<rolling_hash<PairHash<ModInt998244353, ModInt998244353>>>(S);
    cout << ret.size() << '\n';
    for (auto p : ret) cout << get<0>(p) << ' ' << get<1>(p) << ' ' << get<2>(p) << '\n';
}
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