根付き木のハッシュ
(tree/tree-hash.hpp)
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#pragma once
#include <array>
#include <chrono>
#include <random>
#include <vector>
using namespace std;
#include "../internal/internal-hash.hpp"
template <typename G>
struct TreeHash {
using Hash = internal::Hash<3>;
const G& g;
int n;
vector<Hash> hash;
vector<int> depth;
static vector<Hash>& xs() {
static vector<Hash> _xs;
return _xs;
}
TreeHash(const G& _g, int root = 0) : g(_g), n(g.size()) {
hash.resize(n);
depth.resize(n, 0);
while ((int)xs().size() <= n) xs().push_back(Hash::get_basis());
dfs(root, -1);
}
private:
int dfs(int c, int p) {
int dep = 0;
for (auto& d : g[c]) {
if (d != p) dep = max(dep, dfs(d, c) + 1);
}
Hash x = xs()[dep], h = Hash::set(1);
for (auto& d : g[c]) {
if (d != p) h = h * (x + hash[d]);
}
hash[c] = h;
return depth[c] = dep;
}
};
/**
* @brief 根付き木のハッシュ
*/
#line 2 "tree/tree-hash.hpp"
#include <array>
#include <chrono>
#include <random>
#include <vector>
using namespace std;
#line 2 "internal/internal-hash.hpp"
namespace internal {
using i64 = long long;
using u64 = unsigned long long;
using u128 = __uint128_t;
template <int BASE_NUM = 2>
struct Hash : array<u64, BASE_NUM> {
using array<u64, BASE_NUM>::operator[];
static constexpr int n = BASE_NUM;
Hash() : array<u64, BASE_NUM>() {}
static constexpr u64 md = (1ull << 61) - 1;
constexpr static Hash set(const i64 &a) {
Hash res;
fill(begin(res), end(res), cast(a));
return res;
}
Hash &operator+=(const Hash &r) {
for (int i = 0; i < n; i++)
if (((*this)[i] += r[i]) >= md) (*this)[i] -= md;
return *this;
}
Hash &operator+=(const i64 &r) {
u64 s = cast(r);
for (int i = 0; i < n; i++)
if (((*this)[i] += s) >= md) (*this)[i] -= md;
return *this;
}
Hash &operator-=(const Hash &r) {
for (int i = 0; i < n; i++)
if (((*this)[i] += md - r[i]) >= md) (*this)[i] -= md;
return *this;
}
Hash &operator-=(const i64 &r) {
u64 s = cast(r);
for (int i = 0; i < n; i++)
if (((*this)[i] += md - s) >= md) (*this)[i] -= md;
return *this;
}
Hash &operator*=(const Hash &r) {
for (int i = 0; i < n; i++) (*this)[i] = modmul((*this)[i], r[i]);
return *this;
}
Hash &operator*=(const i64 &r) {
u64 s = cast(r);
for (int i = 0; i < n; i++) (*this)[i] = modmul((*this)[i], s);
return *this;
}
Hash operator+(const Hash &r) { return Hash(*this) += r; }
Hash operator+(const i64 &r) { return Hash(*this) += r; }
Hash operator-(const Hash &r) { return Hash(*this) -= r; }
Hash operator-(const i64 &r) { return Hash(*this) -= r; }
Hash operator*(const Hash &r) { return Hash(*this) *= r; }
Hash operator*(const i64 &r) { return Hash(*this) *= r; }
Hash operator-() const {
Hash res;
for (int i = 0; i < n; i++) res[i] = (*this)[i] == 0 ? 0 : md - (*this)[i];
return res;
}
friend Hash pfma(const Hash &a, const Hash &b, const Hash &c) {
Hash res;
for (int i = 0; i < n; i++) res[i] = modfma(a[i], b[i], c[i]);
return res;
}
friend Hash pfma(const Hash &a, const Hash &b, const i64 &c) {
Hash res;
u64 s = cast(c);
for (int i = 0; i < n; i++) res[i] = modfma(a[i], b[i], s);
return res;
}
Hash pow(long long e) {
Hash a{*this}, res{Hash::set(1)};
for (; e; a *= a, e >>= 1) {
if (e & 1) res *= a;
}
return res;
}
static Hash get_basis() {
static auto rand_time =
chrono::duration_cast<chrono::nanoseconds>(
chrono::high_resolution_clock::now().time_since_epoch())
.count();
static mt19937_64 rng(rand_time);
Hash h;
for (int i = 0; i < n; i++) {
while (isPrimitive(h[i] = rng() % (md - 1) + 1) == false)
;
}
return h;
}
private:
static u64 modpow(u64 a, u64 b) {
u64 r = 1;
for (a %= md; b; a = modmul(a, a), b >>= 1) r = modmul(r, a);
return r;
}
static bool isPrimitive(u64 x) {
for (auto &d : vector<u64>{2, 3, 5, 7, 11, 13, 31, 41, 61, 151, 331, 1321})
if (modpow(x, (md - 1) / d) <= 1) return false;
return true;
}
static inline constexpr u64 cast(const long long &a) {
return a < 0 ? a + md : a;
}
static inline constexpr u64 modmul(const u64 &a, const u64 &b) {
u128 d = u128(a) * b;
u64 ret = (u64(d) & md) + u64(d >> 61);
return ret >= md ? ret - md : ret;
}
static inline constexpr u64 modfma(const u64 &a, const u64 &b, const u64 &c) {
u128 d = u128(a) * b + c;
u64 ret = (d >> 61) + (u64(d) & md);
return ret >= md ? ret - md : ret;
}
};
} // namespace internal
/**
* @brief ハッシュ構造体
* @docs docs/internal/internal-hash.md
*/
#line 10 "tree/tree-hash.hpp"
template <typename G>
struct TreeHash {
using Hash = internal::Hash<3>;
const G& g;
int n;
vector<Hash> hash;
vector<int> depth;
static vector<Hash>& xs() {
static vector<Hash> _xs;
return _xs;
}
TreeHash(const G& _g, int root = 0) : g(_g), n(g.size()) {
hash.resize(n);
depth.resize(n, 0);
while ((int)xs().size() <= n) xs().push_back(Hash::get_basis());
dfs(root, -1);
}
private:
int dfs(int c, int p) {
int dep = 0;
for (auto& d : g[c]) {
if (d != p) dep = max(dep, dfs(d, c) + 1);
}
Hash x = xs()[dep], h = Hash::set(1);
for (auto& d : g[c]) {
if (d != p) h = h * (x + hash[d]);
}
hash[c] = h;
return depth[c] = dep;
}
};
/**
* @brief 根付き木のハッシュ
*/
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