RollingHash
(src/string/rolling_hash.hpp)

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• Last update: 2024-11-09 01:34:39+09:00
• Include: #include "src/string/rolling_hash.hpp"

RollingHash

長さ $n$ の文字列 s に対して，

• 部分文字列のハッシュ値の取得

を 前計算 $O(n)$ クエリ $O(1)$ で行えるアルゴリズムです．

コンストラクタ

RollingHash rh(string s, ull BASE = 0)

• 長さ $n$ の文字列 s に対するローリングハッシュ，rh を構築します．

• 法は $2^{61} - 1$ です．BASE を指定しないときや $0$ を指定したとき，基数は乱数となります．

計算量

• $O(n)$

get

ull rh.get(int lower, int upper)

部分文字列 s[lower, upper) のハッシュ値を返します．

制約

• $0 \leq \mathrm{lower} \leq \mathrm{upper} \leq n$

計算量

• $O(1)$

get_hash

ull rh.get_hash(string t)

長さ $m$ の文字列 t のハッシュ値を返します．

計算量

• $O(m)$

find

int rh.find(string t, int lower = 0)

s の $\mathrm{lower}$ 文字目以降で初めて文字列 t が現れるインデックスを返します．
(存在しない場合は $-1$ を返します．)

計算量

• $O(n)$

lcp

int rh.lcp(RollingHash a, RollingHash b, int al, int bl)

文字列 a[al, a.size()) と文字列 b[bl, b.size()) のLongest Common Prefix (先頭から何文字一致するか) を返します．
$\mathrm{min} (a.\mathrm{size}() - al, b.\mathrm{size}() - bl) \geq 0$ のときは $0$ を返します．

計算量

• $O(\log (a.\mathrm{size}() + b.\mathrm{size}()))$

Depends on

• Modint_2_61m1 (src/template/modint_2_61m1.hpp)
• template (src/template/template.hpp)

Verified with

• verify/aizu_online_judge/alds1/string_search.test.cpp
• verify/library_checker/string/number_of_substrings.test.cpp

Code

#pragma once
#include "../template/template.hpp"
#include "../template/modint_2_61m1.hpp"
struct RollingHash {
    using mint = Modint_2_61m1;
    RollingHash(const string& s, unsigned long long BASE = 0)
        : len((int)s.size()), pow(len + 1), hash(len + 1) {
        if(BASE == 0) {
            mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
            uniform_int_distribution<unsigned long long> dist(1ull << 10, 1ull << 60);
            BASE = dist(mt);
        }
        base = BASE;
        pow[0] = 1;
        for(int i = 0; i < len; ++i) {
            pow[i + 1] = pow[i] * base;
        }
        for(int i = 0; i < len; ++i) {
            hash[i + 1] = hash[i] * base + s[i];
        }
    }
    unsigned long long get(const int lower, const int upper) const {
        assert(0 <= lower and lower <= upper and upper <= len);
        return (hash[upper] - hash[lower] * pow[upper - lower]).val();
    }
    unsigned long long get_hash(const string& t) const {
        mint res = 0;
        for(int i = 0; i < (int)t.size(); ++i) {
            res = res * base + t[i];
        }
        return res.val();
    }
    int find(const string& t, const int lower = 0) const {
        if((int)t.size() > len) return -1;
        const unsigned long long ha = get_hash(t);
        for(int i = lower; i < len - (int)t.size() + 1; ++i) {
            if(ha == get(i, i + (int)t.size())) return i;
        }
        return -1;
    }
    int lcp(const RollingHash& a, const RollingHash& b, const int al, const int bl) const {
        int ok = 0, ng = min(a.len - al, b.len - bl) + 1;
        while(ok + 1 < ng) {
            const int med = (ok + ng) / 2;
            if(a.get(al, med + al) == b.get(bl, med + bl)) {
                ok = med;
            } else {
                ng = med;
            }
        }
        return ok;
    }

   private:
    int len;
    mint base;
    vector<mint> pow;
    vector<mint> hash;
};

#line 2 "src/template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<long long, long long>;
#define rep(i, a, b) for(long long i = (a); i < (b); ++i)
#define rrep(i, a, b) for(long long i = (a); i >= (b); --i)
constexpr long long inf = 4e18;
struct SetupIO {
    SetupIO() {
        ios::sync_with_stdio(0);
        cin.tie(0);
        cout << fixed << setprecision(30);
    }
} setup_io;
#line 3 "src/template/modint_2_61m1.hpp"
struct Modint_2_61m1 {
    using mint = Modint_2_61m1;
    using u64 = uint64_t;
    using u128 = __uint128_t;
    static constexpr u64 mod() {
        return m;
    }
    static constexpr mint raw(const u64 v) {
        mint a;
        a._v = v;
        return a;
    }
    constexpr Modint_2_61m1()
        : _v(0) {}
    template <class T>
    constexpr Modint_2_61m1(const T& v) {
        static_assert(is_integral_v<T>);
        if constexpr(is_signed_v<T>) {
            int64_t x = int64_t(v % int64_t(m));
            if(x < 0) x += m;
            _v = u64(x);
        } else _v = u64(v % m);
    }
    constexpr u64 val() const {
        return _v;
    }
    constexpr mint& operator++() {
        return *this += 1;
    }
    constexpr mint& operator--() {
        return *this -= 1;
    }
    constexpr mint operator++(int) {
        mint res = *this;
        ++*this;
        return res;
    }
    constexpr mint operator--(int) {
        mint res = *this;
        --*this;
        return res;
    }
    constexpr mint& operator+=(mint rhs) {
        if(_v >= m - rhs._v) _v -= m;
        _v += rhs._v;
        return *this;
    }
    constexpr mint& operator-=(mint rhs) {
        if(_v < rhs._v) _v += m;
        _v -= rhs._v;
        return *this;
    }
    constexpr mint& operator*=(mint rhs) {
        return *this = *this * rhs;
    }
    constexpr mint& operator/=(mint rhs) {
        return *this *= rhs.inv();
    }
    constexpr mint operator+() const {
        return *this;
    }
    constexpr mint operator-() const {
        return mint{} - *this;
    }
    constexpr mint pow(u64 n) const {
        if(n == 0) return 1;
        mint x = *this, r = 1;
        while(1) {
            if(n & 1) r *= x;
            n >>= 1;
            if(n == 0) return r;
            x *= x;
        }
    }
    constexpr mint inv() const {
        assert(_v);
        return pow(m - 2);
    }
    friend constexpr mint operator+(mint lhs, mint rhs) {
        return lhs += rhs;
    }
    friend constexpr mint operator-(mint lhs, mint rhs) {
        return lhs -= rhs;
    }
    friend constexpr mint operator*(mint lhs, mint rhs) {
        return raw(modulo(u128(lhs._v) * rhs._v));
    }
    friend constexpr mint operator/(mint lhs, mint rhs) {
        return lhs /= rhs;
    }
    friend constexpr bool operator==(mint lhs, mint rhs) {
        return lhs._v == rhs._v;
    }
    friend constexpr bool operator!=(mint lhs, mint rhs) {
        return lhs._v != rhs._v;
    }
    friend istream& operator>>(istream& in, mint& x) {
        long long a;
        in >> a;
        x = a;
        return in;
    }
    friend ostream& operator<<(ostream& out, const mint& x) {
        return out << x.val();
    }

   private:
    static constexpr u64 m = (1ull << 61) - 1;
    u64 _v = 0;
    inline static constexpr u64 modulo(const u128& x) {
        const u64 val = (x >> 61) + (x & m);
        return val >= m ? val - m : val;
    }
};
#line 4 "src/string/rolling_hash.hpp"
struct RollingHash {
    using mint = Modint_2_61m1;
    RollingHash(const string& s, unsigned long long BASE = 0)
        : len((int)s.size()), pow(len + 1), hash(len + 1) {
        if(BASE == 0) {
            mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
            uniform_int_distribution<unsigned long long> dist(1ull << 10, 1ull << 60);
            BASE = dist(mt);
        }
        base = BASE;
        pow[0] = 1;
        for(int i = 0; i < len; ++i) {
            pow[i + 1] = pow[i] * base;
        }
        for(int i = 0; i < len; ++i) {
            hash[i + 1] = hash[i] * base + s[i];
        }
    }
    unsigned long long get(const int lower, const int upper) const {
        assert(0 <= lower and lower <= upper and upper <= len);
        return (hash[upper] - hash[lower] * pow[upper - lower]).val();
    }
    unsigned long long get_hash(const string& t) const {
        mint res = 0;
        for(int i = 0; i < (int)t.size(); ++i) {
            res = res * base + t[i];
        }
        return res.val();
    }
    int find(const string& t, const int lower = 0) const {
        if((int)t.size() > len) return -1;
        const unsigned long long ha = get_hash(t);
        for(int i = lower; i < len - (int)t.size() + 1; ++i) {
            if(ha == get(i, i + (int)t.size())) return i;
        }
        return -1;
    }
    int lcp(const RollingHash& a, const RollingHash& b, const int al, const int bl) const {
        int ok = 0, ng = min(a.len - al, b.len - bl) + 1;
        while(ok + 1 < ng) {
            const int med = (ok + ng) / 2;
            if(a.get(al, med + al) == b.get(bl, med + bl)) {
                ok = med;
            } else {
                ng = med;
            }
        }
        return ok;
    }

   private:
    int len;
    mint base;
    vector<mint> pow;
    vector<mint> hash;
};

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