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#include "string/rolling-hash.hpp"
文字列の一致判定を mod $2^{61}-1$ のハッシュを用いて効率的に行う.
RollingHash(base)
: 基数 base
のローリングハッシュを構築する.generate_base()
: $2^{61} - 1$ 以下の乱数を返す。これを base
とすると Hack されにくい.build(s)
: 文字列 s
のハッシュテーブルを返す.query(s, l, r)
: s
の区間 $[l, r)$ のハッシュ値を返す.combine(h1, h2, h2len)
: ハッシュ値 h1
と長さ h2len
のハッシュ値 h2
を結合する. power[h2len]
での配列外参照に注意(TODO 実装).lcp(a, l1, r1, b, l2, r2)
: ハッシュテーブル a
の区間 $[l1, r1)$ と, ハッシュテーブル b
の区間 $[l2, r2)$ の文字列の最長共通接頭辞の長さを返す.build()
: $O(n)$lcp()
: $O(\log n)$/**
* @brief Rolling-Hash(ローリングハッシュ)
* @see https://qiita.com/keymoon/items/11fac5627672a6d6a9f6
*
*/
struct RollingHash {
static const uint64_t mod = (1ull << 61ull) - 1;
using uint128_t = __uint128_t;
vector< uint64_t > power;
const uint64_t base;
static inline uint64_t add(uint64_t a, uint64_t b) {
if((a += b) >= mod) a -= mod;
return a;
}
static inline uint64_t mul(uint64_t a, uint64_t b) {
uint128_t c = (uint128_t) a * b;
return add(c >> 61, c & mod);
}
static inline uint64_t generate_base() {
mt19937_64 mt(chrono::steady_clock::now().time_since_epoch().count());
uniform_int_distribution< uint64_t > rand(1, RollingHash::mod - 1);
return rand(mt);
}
inline void expand(size_t sz) {
if(power.size() < sz + 1) {
int pre_sz = (int) power.size();
power.resize(sz + 1);
for(int i = pre_sz - 1; i < sz; i++) {
power[i + 1] = mul(power[i], base);
}
}
}
explicit RollingHash(uint64_t base = generate_base()) : base(base), power{1} {}
vector< uint64_t > build(const string &s) const {
int sz = s.size();
vector< uint64_t > hashed(sz + 1);
for(int i = 0; i < sz; i++) {
hashed[i + 1] = add(mul(hashed[i], base), s[i]);
}
return hashed;
}
template< typename T >
vector< uint64_t > build(const vector< T > &s) const {
int sz = s.size();
vector< uint64_t > hashed(sz + 1);
for(int i = 0; i < sz; i++) {
hashed[i + 1] = add(mul(hashed[i], base), s[i]);
}
return hashed;
}
uint64_t query(const vector< uint64_t > &s, int l, int r) {
expand(r - l);
return add(s[r], mod - mul(s[l], power[r - l]));
}
uint64_t combine(uint64_t h1, uint64_t h2, size_t h2len) {
expand(h2len);
return add(mul(h1, power[h2len]), h2);
}
int lcp(const vector< uint64_t > &a, int l1, int r1, const vector< uint64_t > &b, int l2, int r2) {
int len = min(r1 - l1, r2 - l2);
int low = 0, high = len + 1;
while(high - low > 1) {
int mid = (low + high) / 2;
if(query(a, l1, l1 + mid) == query(b, l2, l2 + mid)) low = mid;
else high = mid;
}
return low;
}
};
#line 1 "string/rolling-hash.hpp"
/**
* @brief Rolling-Hash(ローリングハッシュ)
* @see https://qiita.com/keymoon/items/11fac5627672a6d6a9f6
*
*/
struct RollingHash {
static const uint64_t mod = (1ull << 61ull) - 1;
using uint128_t = __uint128_t;
vector< uint64_t > power;
const uint64_t base;
static inline uint64_t add(uint64_t a, uint64_t b) {
if((a += b) >= mod) a -= mod;
return a;
}
static inline uint64_t mul(uint64_t a, uint64_t b) {
uint128_t c = (uint128_t) a * b;
return add(c >> 61, c & mod);
}
static inline uint64_t generate_base() {
mt19937_64 mt(chrono::steady_clock::now().time_since_epoch().count());
uniform_int_distribution< uint64_t > rand(1, RollingHash::mod - 1);
return rand(mt);
}
inline void expand(size_t sz) {
if(power.size() < sz + 1) {
int pre_sz = (int) power.size();
power.resize(sz + 1);
for(int i = pre_sz - 1; i < sz; i++) {
power[i + 1] = mul(power[i], base);
}
}
}
explicit RollingHash(uint64_t base = generate_base()) : base(base), power{1} {}
vector< uint64_t > build(const string &s) const {
int sz = s.size();
vector< uint64_t > hashed(sz + 1);
for(int i = 0; i < sz; i++) {
hashed[i + 1] = add(mul(hashed[i], base), s[i]);
}
return hashed;
}
template< typename T >
vector< uint64_t > build(const vector< T > &s) const {
int sz = s.size();
vector< uint64_t > hashed(sz + 1);
for(int i = 0; i < sz; i++) {
hashed[i + 1] = add(mul(hashed[i], base), s[i]);
}
return hashed;
}
uint64_t query(const vector< uint64_t > &s, int l, int r) {
expand(r - l);
return add(s[r], mod - mul(s[l], power[r - l]));
}
uint64_t combine(uint64_t h1, uint64_t h2, size_t h2len) {
expand(h2len);
return add(mul(h1, power[h2len]), h2);
}
int lcp(const vector< uint64_t > &a, int l1, int r1, const vector< uint64_t > &b, int l2, int r2) {
int len = min(r1 - l1, r2 - l2);
int low = 0, high = len + 1;
while(high - low > 1) {
int mid = (low + high) / 2;
if(query(a, l1, l1 + mid) == query(b, l2, l2 + mid)) low = mid;
else high = mid;
}
return low;
}
};