library2
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string/2d-hash.hpp
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- Last update: 2025-08-23 23:14:39+02:00
- Include:
#include "string/2d-hash.hpp"
Depends on
math/mint.hppCode
#include <bits/stdc++.h>
#include "./math/mint.hpp"
using namespace std;
/*
sum[i][j] = sum[i - 1][j - 1] - sum[i - 1][j] - sum[i][j - 1] + s[i][j] * base1^i * base2^j
*/
typedef unsigned long long ULL;
ULL Seed_Pool[] = {911, 146527, 19260817, 91815541};
constexpr int md = 998244353;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;
struct Hash {
ULL Seed1, Seed2;
vector<string> s;
vector<Mint> base1, base2;
vector<vector<Mint>> sum;
vector<int> perm;
int char_size, margin;
Hash() {}
Hash(ULL Seed1, ULL Seed2, const vector<string>& s, int char_size, int margin) : Seed1(Seed1), Seed2(Seed2), s(s), char_size(char_size), margin(margin) {
int n = s.size(), m = s[0].size();
base1.resize(n + 1);
base2.resize(m + 1);
sum.resize(n + 1, vector<Mint>(m + 1));
perm.resize(char_size);
iota(perm.begin(), perm.end(), 0);
// std::random_device rd;
// std::mt19937 g(rd());
// shuffle(perm.begin(), perm.end(), g);
indexInit();
}
void indexInit() {
base1[0] = 1;
base2[0] = 1;
int n = s.size();
for (int i = 1; i <= n; i++) {
base1[i] = base1[i - 1] * Seed1;
}
int m = s[0].size();
for (int i = 1; i <= m; i++) {
base2[i] = base2[i - 1] * Seed2;
}
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= m; j++) {
sum[i][j] = sum[i][j - 1] + sum[i - 1][j] - sum[i - 1][j - 1] + Mint(perm[s[i - 1][j - 1] - margin]) * base1[i - 1] * base2[j - 1];
}
}
}
Mint getHash(int x1, int y1, int x2, int y2) {
int n = s.size();
int m = s[0].size();
x1++, y1++, x2++, y2++;
Mint res = sum[x2][y2] - sum[x1 - 1][y2] - sum[x2][y1 - 1] + sum[x1 - 1][y1 - 1];
return res * base1[n - x1] * base2[m - y1];
}
};#line 1 "string/2d-hash.hpp"
#include <bits/stdc++.h>
#line 2 "math/mint.hpp"
using namespace std;
template <typename T>
T inverse(T a, T m) {
T u = 0, v = 1;
while (a != 0) {
T t = m / a;
m -= t * a;
swap(a, m);
u -= t * v;
swap(u, v);
}
assert(m == 1);
return u;
}
template <typename T>
class Modular {
public:
using Type = typename decay<decltype(T::value)>::type;
constexpr Modular() : value() {}
template <typename U>
Modular(const U& x) {
value = normalize(x);
}
template <typename U>
static Type normalize(const U& x) {
Type v;
if (-mod() <= x && x < mod())
v = static_cast<Type>(x);
else
v = static_cast<Type>(x % mod());
if (v < 0) v += mod();
return v;
}
const Type& operator()() const { return value; }
template <typename U>
explicit operator U() const { return static_cast<U>(value); }
constexpr static Type mod() { return T::value; }
Modular& operator+=(const Modular& other) {
if ((value += other.value) >= mod()) value -= mod();
return *this;
}
Modular& operator-=(const Modular& other) {
if ((value -= other.value) < 0) value += mod();
return *this;
}
template <typename U>
Modular& operator+=(const U& other) { return *this += Modular(other); }
template <typename U>
Modular& operator-=(const U& other) { return *this -= Modular(other); }
Modular& operator++() { return *this += 1; }
Modular& operator--() { return *this -= 1; }
Modular operator++(int) {
Modular result(*this);
*this += 1;
return result;
}
Modular operator--(int) {
Modular result(*this);
*this -= 1;
return result;
}
Modular operator-() const { return Modular(-value); }
template <typename U = T>
typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
#ifdef _WIN32
uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
asm(
"divl %4; \n\t"
: "=a"(d), "=d"(m)
: "d"(xh), "a"(xl), "r"(mod()));
value = m;
#else
value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
#endif
return *this;
}
template <typename U = T>
typename enable_if<is_same<typename Modular<U>::Type, long long>::value, Modular>::type& operator*=(const Modular& rhs) {
long long q = static_cast<long long>(static_cast<long double>(value) * rhs.value / mod());
value = normalize(value * rhs.value - q * mod());
return *this;
}
template <typename U = T>
typename enable_if<!is_integral<typename Modular<U>::Type>::value, Modular>::type& operator*=(const Modular& rhs) {
value = normalize(value * rhs.value);
return *this;
}
Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }
friend const Type& abs(const Modular& x) { return x.value; }
template <typename U>
friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);
template <typename U>
friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);
template <typename V, typename U>
friend V& operator>>(V& stream, Modular<U>& number);
private:
Type value;
};
template <typename T>
bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value == rhs.value; }
template <typename T, typename U>
bool operator==(const Modular<T>& lhs, U rhs) { return lhs == Modular<T>(rhs); }
template <typename T, typename U>
bool operator==(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) == rhs; }
template <typename T>
bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T, typename U>
bool operator!=(const Modular<T>& lhs, U rhs) { return !(lhs == rhs); }
template <typename T, typename U>
bool operator!=(U lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T>
bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value < rhs.value; }
template <typename T>
Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U>
Modular<T> operator+(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U>
Modular<T> operator+(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T>
Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U>
Modular<T> operator-(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U>
Modular<T> operator-(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T>
Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U>
Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U>
Modular<T> operator*(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T>
Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U>
Modular<T> operator/(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U>
Modular<T> operator/(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
assert(b >= 0);
Modular<T> x = a, res = 1;
U p = b;
while (p > 0) {
if (p & 1) res *= x;
x *= x;
p >>= 1;
}
return res;
}
template <typename T>
bool IsZero(const Modular<T>& number) {
return number() == 0;
}
template <typename T>
string to_string(const Modular<T>& number) {
return to_string(number());
}
// U == std::ostream? but done this way because of fastoutput
template <typename U, typename T>
U& operator<<(U& stream, const Modular<T>& number) {
return stream << number();
}
// U == std::istream? but done this way because of fastinput
template <typename U, typename T>
U& operator>>(U& stream, Modular<T>& number) {
typename common_type<typename Modular<T>::Type, long long>::type x;
stream >> x;
number.value = Modular<T>::normalize(x);
return stream;
}
/*
using ModType = int;
struct VarMod { static ModType value; };
ModType VarMod::value;
ModType& md = VarMod::value;
using Mint = Modular<VarMod>;
*/
/*
constexpr int md = 998244353;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;
vector<Mint> fact(1, 1);
vector<Mint> inv_fact(1, 1);
Mint C(int n, int k) {
if (k < 0 || k > n) {
return 0;
}
while ((int)fact.size() < n + 1) {
fact.push_back(fact.back() * (int)fact.size());
inv_fact.push_back(1 / fact.back());
}
return fact[n] * inv_fact[k] * inv_fact[n - k];
}
Mint A(int n, int k) {
if (k < 0 || k > n) {
return 0;
}
while ((int)fact.size() < n + 1) {
fact.push_back(fact.back() * (int)fact.size());
inv_fact.push_back(1 / fact.back());
}
return fact[n] * inv_fact[n - k];
}
*/
#line 4 "string/2d-hash.hpp"
using namespace std;
/*
sum[i][j] = sum[i - 1][j - 1] - sum[i - 1][j] - sum[i][j - 1] + s[i][j] * base1^i * base2^j
*/
typedef unsigned long long ULL;
ULL Seed_Pool[] = {911, 146527, 19260817, 91815541};
constexpr int md = 998244353;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;
struct Hash {
ULL Seed1, Seed2;
vector<string> s;
vector<Mint> base1, base2;
vector<vector<Mint>> sum;
vector<int> perm;
int char_size, margin;
Hash() {}
Hash(ULL Seed1, ULL Seed2, const vector<string>& s, int char_size, int margin) : Seed1(Seed1), Seed2(Seed2), s(s), char_size(char_size), margin(margin) {
int n = s.size(), m = s[0].size();
base1.resize(n + 1);
base2.resize(m + 1);
sum.resize(n + 1, vector<Mint>(m + 1));
perm.resize(char_size);
iota(perm.begin(), perm.end(), 0);
// std::random_device rd;
// std::mt19937 g(rd());
// shuffle(perm.begin(), perm.end(), g);
indexInit();
}
void indexInit() {
base1[0] = 1;
base2[0] = 1;
int n = s.size();
for (int i = 1; i <= n; i++) {
base1[i] = base1[i - 1] * Seed1;
}
int m = s[0].size();
for (int i = 1; i <= m; i++) {
base2[i] = base2[i - 1] * Seed2;
}
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= m; j++) {
sum[i][j] = sum[i][j - 1] + sum[i - 1][j] - sum[i - 1][j - 1] + Mint(perm[s[i - 1][j - 1] - margin]) * base1[i - 1] * base2[j - 1];
}
}
}
Mint getHash(int x1, int y1, int x2, int y2) {
int n = s.size();
int m = s[0].size();
x1++, y1++, x2++, y2++;
Mint res = sum[x2][y2] - sum[x1 - 1][y2] - sum[x2][y1 - 1] + sum[x1 - 1][y1 - 1];
return res * base1[n - x1] * base2[m - y1];
}
};