DynamicRollingHash
(src/string/dynamic_rolling_hash.hpp)

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Last update: 2024-11-09 01:50:04+09:00
Include: #include "src/string/dynamic_rolling_hash.hpp"

DynamicRollingHash

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
1文字更新

を，前計算 $O(n \log n)$ クエリ $O(\log n)$ で行えるアルゴリズムです．

コンストラクタ

DynamicRollingHash drh(string s, ull BASE = 0)

長さ $n$ の文字列 s に対する動的ローリングハッシュ，drh 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

$O(n \log n)$

get

ull drh.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

$O(\log n)$

get_hash

ull drh.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

$O(m)$

set

void drh.set(int idx, char c)

s[idx] を c に更新します．

制約

$0 \leq \mathrm{idx} < n$

計算量

$O(\log n)$

Depends on

Verified with

verify/unit_test/string/dynamic_rolling_hash.test.cpp

Code

#pragma once
#include "../template/template.hpp"
#include "../template/modint_2_61m1.hpp"
#include "../data_structure/fenwick_tree.hpp"
struct DynamicRollingHash {
    using mint = Modint_2_61m1;
    DynamicRollingHash(const string& s, unsigned long long BASE = 0)
        : len((int)s.size()), pow(len + 1), inv_pow(len + 1), hash(len) {
        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;
        }
        inv = base.inv();
        inv_pow[0] = 1;
        for(int i = 0; i < len; ++i) {
            inv_pow[i + 1] = inv_pow[i] * inv;
        }
        for(int i = 0; i < len; ++i) {
            hash.add(i, pow[i] * s[i]);
        }
    }
    unsigned long long get(const int lower, const int upper) const {
        assert(0 <= lower and lower <= upper and upper <= len);
        return (hash.sum(lower, upper) * inv_pow[lower]).val();
    }
    unsigned long long get_hash(const string& t) const {
        mint res = 0;
        for(int i = 0; i < (int)t.size(); ++i) {
            res += pow[i] * t[i];
        }
        return res.val();
    }
    void set(const int idx, const char c) {
        assert(0 <= idx and idx < len);
        hash.add(idx, pow[idx] * c - hash.get(idx));
    }

   private:
    int len;
    mint base, inv;
    vector<mint> pow, inv_pow;
    FenwickTree<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 3 "src/data_structure/fenwick_tree.hpp"
template <typename T>
struct FenwickTree {
    FenwickTree(const int N)
        : n(N), data(N) {}
    void add(int p, const T& x) {
        assert(0 <= p and p < n);
        ++p;
        while(p <= n) {
            data[p - 1] += x;
            p += p & -p;
        }
    }
    T sum(const int l, const int r) const {
        assert(0 <= l and l <= r and r <= n);
        return sum(r) - sum(l);
    }
    T get(const int x) const {
        assert(0 <= x and x < n);
        return sum(x + 1) - sum(x);
    }

   private:
    int n;
    vector<T> data;
    inline T sum(int r) const {
        T s = 0;
        while(r > 0) {
            s += data[r - 1];
            r -= r & -r;
        }
        return s;
    }
};
#line 5 "src/string/dynamic_rolling_hash.hpp"
struct DynamicRollingHash {
    using mint = Modint_2_61m1;
    DynamicRollingHash(const string& s, unsigned long long BASE = 0)
        : len((int)s.size()), pow(len + 1), inv_pow(len + 1), hash(len) {
        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;
        }
        inv = base.inv();
        inv_pow[0] = 1;
        for(int i = 0; i < len; ++i) {
            inv_pow[i + 1] = inv_pow[i] * inv;
        }
        for(int i = 0; i < len; ++i) {
            hash.add(i, pow[i] * s[i]);
        }
    }
    unsigned long long get(const int lower, const int upper) const {
        assert(0 <= lower and lower <= upper and upper <= len);
        return (hash.sum(lower, upper) * inv_pow[lower]).val();
    }
    unsigned long long get_hash(const string& t) const {
        mint res = 0;
        for(int i = 0; i < (int)t.size(); ++i) {
            res += pow[i] * t[i];
        }
        return res.val();
    }
    void set(const int idx, const char c) {
        assert(0 <= idx and idx < len);
        hash.add(idx, pow[idx] * c - hash.get(idx));
    }

   private:
    int len;
    mint base, inv;
    vector<mint> pow, inv_pow;
    FenwickTree<mint> hash;
};

DynamicRollingHash (src/string/dynamic_rolling_hash.hpp)

DynamicRollingHash

コンストラクタ

get

get_hash

set

Depends on

Verified with

Code

DynamicRollingHash
(src/string/dynamic_rolling_hash.hpp)