Rolling Hash
(string/rolling_hash.hpp)

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• Last update: 2023-03-05 19:05:08+09:00
• Include: #include "string/rolling_hash.hpp"

概要

• ハッシュを用いて文字列の一致判定を高速に行う。

使い方

• rolling_hash<base_num, mint>::from(s): 文字列 s のローリングハッシュを構築する。base_num 個の基数を用いて、mint でハッシュを計算する。デフォルトは、base_num = 1, mint = modint2305843009213693951。
• rlh(l, r): s[l..r] のハッシュ値を求める。
• lcp(l1, r1, l2, r2): s[l1..r1] と s[l2..r2] の LCP の長さを求める。
• rolling_hash<>::lcp(rh1, l1, r1, rh2, l2, r2): s1[l1..r1] と s2[l2..r2] の LCP の長さを求める。
• cmp(l1, r1, l2, r2): s1 = s[l1..r1] と s2 = s[l2..r2] を辞書順で比較する。返り値は、s1 < s2 ? -1 : s1 == s2 ? 0 : 1。
• rolling_hash<>::cmp(rh1, l1, r1, rh2, l2, r2): s1[l1..r1] と s2[l2..r2] を辞書順で比較する。
• rolling_hash<>::concat(h1, h2, h2_len): ハッシュ値が h1 の文字列と、ハッシュ値が h2 で長さが h2_len の文字列を連結した文字列のハッシュ値を求める。

計算量

• 構築: $\mathcal{O}(N)$
• クエリ: $\mathcal{O}(1)$
• lcp: $\mathcal{O}(\log N)$
• cmp: $\mathcal{O}(\log N)$
• concat: $\mathcal{O}(1)$

Depends on

• math/modint2305843009213693951.hpp
• math/pow_table.hpp

Verified with

• test/library-checker/enumerate_palindromes.test.cpp
• test/library-checker/suffix_array_rolling_hash.test.cpp
• test/library-checker/zalgorithm_rolling_hash.test.cpp
• test/yukicoder/2231.test.cpp

Code

#pragma once
#include <algorithm>
#include <array>
#include <cassert>
#include <random>
#include <vector>

#include "../math/modint2305843009213693951.hpp"
#include "../math/pow_table.hpp"
template <int base_num = 1, typename mint = modint2305843009213693951>
struct rolling_hash {
public:
    rolling_hash() {
    }
    rolling_hash(const std::vector<int>& a) : n(a.size()) {
        for (int base_id = 0; base_id < base_num; base_id++) {
            hashes[base_id].resize(n + 1);
            hashes[base_id][0] = 0;
            for (int i = 0; i < n; i++) {
                hashes[base_id][i + 1] =
                    hashes[base_id][i] * bases[base_id] + a[i];
            }
        }
    }
    template <typename Iterable>
    static rolling_hash from(const Iterable& s) {
        std::vector<int> a;
        for (auto&& e : s) a.push_back(int(e));
        return rolling_hash(a);
    }
    std::array<mint, base_num> operator()(int l, int r) {
        assert(0 <= l && l <= r && r <= n);
        std::array<mint, base_num> res;
        for (int base_id = 0; base_id < base_num; base_id++) {
            res[base_id] =
                hashes[base_id][r] - hashes[base_id][l] * pows[base_id][r - l];
        }
        return res;
    }
    static std::array<mint, base_num> concat(
        const std::array<mint, base_num>& h1,
        const std::array<mint, base_num>& h2, int h2_len) {
        std::array<mint, base_num> res;
        for (int base_id = 0; base_id < base_num; base_id++) {
            res[base_id] = h1[base_id] * pows[base_id][h2_len] + h2[base_id];
        }
        return res;
    }
    int lcp(int l1, int r1, int l2, int r2) {
        int len = std::min(r1 - l1, r2 - l2);
        int ok = 0, ng = len + 1;
        while (ng - ok > 1) {
            int mid = (ok + ng) / 2;
            bool f = (*this)(l1, l1 + mid) == (*this)(l2, l2 + mid);
            (f ? ok : ng) = mid;
        }
        return ok;
    }
    int cmp(int l1, int r1, int l2, int r2) {
        int x = std::min({lcp(l1, r1, l2, r2), r1 - l1, r2 - l2});
        if (l1 + x == r1 && l2 + x != r2) return -1;
        if (l1 + x == r1 && l2 + x == r2) return 0;
        if (l1 + x != r1 && l2 + x == r2) return 1;
        return (*this)(l1 + x, l1 + x + 1)[0].val() <
                       (*this)(l2 + x, l2 + x + 1)[0].val()
                   ? -1
                   : 1;
    }
    static int lcp(rolling_hash<base_num, mint>& rh1, int l1, int r1,
                   rolling_hash<base_num, mint>& rh2, int l2, int r2) {
        int len = std::min(r1 - l1, r2 - l2);
        int ok = 0, ng = len + 1;
        while (ng - ok > 1) {
            int mid = (ok + ng) / 2;
            bool f = rh1(l1, l1 + mid) == rh2(l2, l2 + mid);
            (f ? ok : ng) = mid;
        }
        return ok;
    }
    static int cmp(rolling_hash<base_num, mint>& rh1, int l1, int r1,
                   rolling_hash<base_num, mint>& rh2, int l2, int r2) {
        int x = std::min({lcp(rh1, l1, r1, rh2, l2, r2), r1 - l1, r2 - l2});
        if (l1 + x == r1 && l2 + x != r2) return -1;
        if (l1 + x == r1 && l2 + x == r2) return 0;
        if (l1 + x != r1 && l2 + x == r2) return 1;
        return rh1(l1 + x, l1 + x + 1)[0].val() <
                       rh2(l2 + x, l2 + x + 1)[0].val()
                   ? -1
                   : 1;
    }

private:
    static inline std::array<mint, base_num> gen_bases() {
        static std::mt19937_64 rng(std::random_device{}());
        std::array<mint, base_num> bases;
        for (int i = 0; i < base_num; i++) {
            while (true) {
                uint64_t k = std::uniform_int_distribution<uint64_t>(
                    1, mint::mod - 1)(rng);
                if (std::gcd(k, mint::mod - 1) != 1) continue;
                uint64_t b = mint(r).pow(k).val();
                if (b <= A) continue;
                bases[i] = b;
                break;
            }
        }
        return bases;
    }
    static inline std::array<pow_mods<mint>, base_num> init_pows(
        const std::array<mint, base_num>& bases) {
        std::array<pow_mods<mint>, base_num> pows;
        for (int i = 0; i < base_num; i++) {
            pows[i] = pow_mods<mint>(bases[i], 0);
        }
        return pows;
    }
    static inline std::array<mint, base_num> bases = gen_bases();
    static inline std::array<pow_mods<mint>, base_num> pows = init_pows(bases);
    int n;
    std::array<std::vector<mint>, base_num> hashes;
    static constexpr uint64_t r = 37;
    static constexpr uint64_t A = 2147483647;
};

#line 2 "string/rolling_hash.hpp"
#include <algorithm>
#include <array>
#include <cassert>
#include <random>
#include <vector>

#line 2 "math/modint2305843009213693951.hpp"
#include <cstdint>
struct modint2305843009213693951 {
    using mint = modint2305843009213693951;

public:
    static constexpr uint64_t mod = 2305843009213693951;
    modint2305843009213693951() : _v(0) {
    }
    modint2305843009213693951(uint64_t v) : _v(fast_mod(v)) {
    }
    static constexpr uint64_t fast_mod(uint64_t v) {
        uint64_t u = v >> 61;
        uint64_t d = v & mod;
        uint64_t x = u + d;
        if (x > mod) x -= mod;
        return x;
    }
    uint64_t val() const {
        return _v;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= mod) _v -= mod;
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= mod) _v += mod;
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        static constexpr uint64_t mask31 = (uint64_t(1) << 31) - 1;
        static constexpr uint64_t mask30 = (uint64_t(1) << 30) - 1;
        uint64_t au = _v >> 31;
        uint64_t ad = _v & mask31;
        uint64_t bu = rhs._v >> 31;
        uint64_t bd = rhs._v & mask31;
        uint64_t m = ad * bu + au * bd;
        uint64_t mu = m >> 30;
        uint64_t md = m & mask30;
        _v = fast_mod((au * bu << 1) + mu + (md << 31) + ad * bd);
        return *this;
    }
    mint operator+() const {
        return *this;
    }
    mint operator-() const {
        return mint() - *this;
    }
    mint pow(uint64_t n) const {
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

private:
    uint64_t _v;
};
#line 3 "math/pow_table.hpp"
template <typename mint>
struct pow_mods {
    pow_mods() {
    }
    pow_mods(mint base, int n) : base(base) {
        ensure(n);
    }
    const mint& operator[](int i) const {
        ensure(i);
        return pows[i];
    }
    void ensure(int n) const {
        int sz = pows.size();
        if (sz > n) return;
        pows.resize(n + 1);
        for (int i = sz; i <= n; i++) pows[i] = base * pows[i - 1];
    }

private:
    mutable std::vector<mint> pows{1};
    mint base;
    static constexpr int mod = mint::mod;
};
#line 10 "string/rolling_hash.hpp"
template <int base_num = 1, typename mint = modint2305843009213693951>
struct rolling_hash {
public:
    rolling_hash() {
    }
    rolling_hash(const std::vector<int>& a) : n(a.size()) {
        for (int base_id = 0; base_id < base_num; base_id++) {
            hashes[base_id].resize(n + 1);
            hashes[base_id][0] = 0;
            for (int i = 0; i < n; i++) {
                hashes[base_id][i + 1] =
                    hashes[base_id][i] * bases[base_id] + a[i];
            }
        }
    }
    template <typename Iterable>
    static rolling_hash from(const Iterable& s) {
        std::vector<int> a;
        for (auto&& e : s) a.push_back(int(e));
        return rolling_hash(a);
    }
    std::array<mint, base_num> operator()(int l, int r) {
        assert(0 <= l && l <= r && r <= n);
        std::array<mint, base_num> res;
        for (int base_id = 0; base_id < base_num; base_id++) {
            res[base_id] =
                hashes[base_id][r] - hashes[base_id][l] * pows[base_id][r - l];
        }
        return res;
    }
    static std::array<mint, base_num> concat(
        const std::array<mint, base_num>& h1,
        const std::array<mint, base_num>& h2, int h2_len) {
        std::array<mint, base_num> res;
        for (int base_id = 0; base_id < base_num; base_id++) {
            res[base_id] = h1[base_id] * pows[base_id][h2_len] + h2[base_id];
        }
        return res;
    }
    int lcp(int l1, int r1, int l2, int r2) {
        int len = std::min(r1 - l1, r2 - l2);
        int ok = 0, ng = len + 1;
        while (ng - ok > 1) {
            int mid = (ok + ng) / 2;
            bool f = (*this)(l1, l1 + mid) == (*this)(l2, l2 + mid);
            (f ? ok : ng) = mid;
        }
        return ok;
    }
    int cmp(int l1, int r1, int l2, int r2) {
        int x = std::min({lcp(l1, r1, l2, r2), r1 - l1, r2 - l2});
        if (l1 + x == r1 && l2 + x != r2) return -1;
        if (l1 + x == r1 && l2 + x == r2) return 0;
        if (l1 + x != r1 && l2 + x == r2) return 1;
        return (*this)(l1 + x, l1 + x + 1)[0].val() <
                       (*this)(l2 + x, l2 + x + 1)[0].val()
                   ? -1
                   : 1;
    }
    static int lcp(rolling_hash<base_num, mint>& rh1, int l1, int r1,
                   rolling_hash<base_num, mint>& rh2, int l2, int r2) {
        int len = std::min(r1 - l1, r2 - l2);
        int ok = 0, ng = len + 1;
        while (ng - ok > 1) {
            int mid = (ok + ng) / 2;
            bool f = rh1(l1, l1 + mid) == rh2(l2, l2 + mid);
            (f ? ok : ng) = mid;
        }
        return ok;
    }
    static int cmp(rolling_hash<base_num, mint>& rh1, int l1, int r1,
                   rolling_hash<base_num, mint>& rh2, int l2, int r2) {
        int x = std::min({lcp(rh1, l1, r1, rh2, l2, r2), r1 - l1, r2 - l2});
        if (l1 + x == r1 && l2 + x != r2) return -1;
        if (l1 + x == r1 && l2 + x == r2) return 0;
        if (l1 + x != r1 && l2 + x == r2) return 1;
        return rh1(l1 + x, l1 + x + 1)[0].val() <
                       rh2(l2 + x, l2 + x + 1)[0].val()
                   ? -1
                   : 1;
    }

private:
    static inline std::array<mint, base_num> gen_bases() {
        static std::mt19937_64 rng(std::random_device{}());
        std::array<mint, base_num> bases;
        for (int i = 0; i < base_num; i++) {
            while (true) {
                uint64_t k = std::uniform_int_distribution<uint64_t>(
                    1, mint::mod - 1)(rng);
                if (std::gcd(k, mint::mod - 1) != 1) continue;
                uint64_t b = mint(r).pow(k).val();
                if (b <= A) continue;
                bases[i] = b;
                break;
            }
        }
        return bases;
    }
    static inline std::array<pow_mods<mint>, base_num> init_pows(
        const std::array<mint, base_num>& bases) {
        std::array<pow_mods<mint>, base_num> pows;
        for (int i = 0; i < base_num; i++) {
            pows[i] = pow_mods<mint>(bases[i], 0);
        }
        return pows;
    }
    static inline std::array<mint, base_num> bases = gen_bases();
    static inline std::array<pow_mods<mint>, base_num> pows = init_pows(bases);
    int n;
    std::array<std::vector<mint>, base_num> hashes;
    static constexpr uint64_t r = 37;
    static constexpr uint64_t A = 2147483647;
};

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