runs.hpp¶
#include "noya/runs.hpp"
#ifndef NOYA_RUNS_HPP
#define NOYA_RUNS_HPP 1
#include "noya/rolling_hash.hpp"
#include <ranges>
#include <string>
#include <tuple>
#include <vector>
namespace noya {
/// @brief Compute all runs (maximal periodicities) in a sequence.
/// @return Vector of (period, left, right) where the run covers [left, right).
template <class T>
std::vector<std::tuple<int, int, int>> runs(const std::vector<T> &s) {
int n = int(s.size());
noya::double_hash_array<mint1, mint2, T> H;
H.build(s);
std::vector<std::tuple<int, int, int>> runs;
for (bool inv : {false, true}) {
std::vector<int> lyn(n, n), stack;
for (int i = 0; i < n; i += 1) {
while (!stack.empty()) {
int j = stack.back(), k = lcp(H, i, H, j);
if (i + k < n && ((s[i + k] > s[j + k]) ^ inv))
break;
lyn[j] = i;
stack.pop_back();
}
stack.push_back(i);
}
for (int i = 0; i < n; i += 1) {
int j = lyn[i], t = j - i, l = i - lcs(H, i - 1, H, j - 1),
r = j + lcp(H, i, H, j);
if (r - l >= 2 * t)
runs.emplace_back(t, l, r);
}
}
std::ranges::sort(runs);
runs.erase(std::ranges::unique(runs).begin(), runs.end());
return runs;
}
std::vector<std::tuple<int, int, int>> runs(const std::string &s) {
std::vector<char> a(s.begin(), s.end());
return runs(a);
}
} // namespace noya
#endif // NOYA_RUNS_HPP
#include <algorithm>
#include <cassert>
#include <ctime>
#include <intrin.h>
#include <numeric>
#include <random>
#include <ranges>
#include <string>
#include <tuple>
#include <type_traits>
#include <utility>
#include <vector>
#ifdef _MSC_VER
#endif
#ifdef _MSC_VER
#endif
namespace atcoder {
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
unsigned int _m;
unsigned long long im;
// @param m `1 <= m`
explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const {
// [1] m = 1
// a = b = im = 0, so okay
// [2] m >= 2
// im = ceil(2^64 / m)
// -> im * m = 2^64 + r (0 <= r < m)
// let z = a*b = c*m + d (0 <= c, d < m)
// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
// ((ab * im) >> 64) == c or c + 1
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned long long y = x * _m;
return (unsigned int)(z - y + (z < y ? _m : 0));
}
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if (m0 < 0) m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
unsigned long long floor_sum_unsigned(unsigned long long n,
unsigned long long m,
unsigned long long a,
unsigned long long b) {
unsigned long long ans = 0;
while (true) {
if (a >= m) {
ans += n * (n - 1) / 2 * (a / m);
a %= m;
}
if (b >= m) {
ans += n * (b / m);
b %= m;
}
unsigned long long y_max = a * n + b;
if (y_max < m) break;
// y_max < m * (n + 1)
// floor(y_max / m) <= n
n = (unsigned long long)(y_max / m);
b = (unsigned long long)(y_max % m);
std::swap(m, a);
}
return ans;
}
} // namespace internal
} // namespace atcoder
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
namespace atcoder {
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
dynamic_modint(T v) {
long long x = (long long)(v % (long long)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt(998244353);
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
} // namespace atcoder
namespace noya {
using ull = unsigned long long;
namespace internal {
inline std::mt19937_64 &gen_values() {
static std::mt19937_64 gen(time(0));
return gen;
}
} // namespace internal
inline std::vector<int> random_permutation(int N) {
std::vector<int> p(N);
std::iota(p.begin(), p.end(), 0);
std::shuffle(p.begin(), p.end(), internal::gen_values());
return p;
}
inline std::vector<ull> random_hash_values(int N) {
std::vector<ull> X(N);
std::generate(X.begin(), X.end(), internal::gen_values());
return X;
}
inline std::vector<std::vector<int>> random_tree(int N) {
std::vector<std::vector<int>> g(N);
for (int i = 1; i < N; i++) {
int p = internal::gen_values()() % i;
g[p].push_back(i);
}
return g;
}
} // namespace noya
namespace noya {
inline int64_t rolling_hash_base() {
static int64_t base = internal::gen_values()();
return base;
}
template <class T, class S> struct hash_array {
int n;
std::vector<T> H;
std::vector<T> pw;
const T base = T(rolling_hash_base());
hash_array(const std::vector<S> &a) { build(a); }
hash_array(const std::string &a) {
std::vector<S> a0(a.begin(), a.end());
build(a0);
}
hash_array() {}
void build(const std::vector<S> &a) {
n = int(a.size());
H.resize(n + 1);
for (int i = 0; i < n; i++) {
H[i + 1] = H[i] * base + T(a[i]);
}
pw.resize(n + 1);
pw[0] = 1;
for (int i = 0; i < n; i++) {
pw[i + 1] = pw[i] * base;
}
}
void build(const std::string &a) {
std::vector<S> a0(a.begin(), a.end());
build(a0);
}
/// @brief Hash of [l, r).
T prod(int l, int r) const {
assert(0 <= l && l <= r && r <= n);
T X = H[r] - H[l] * pw[r - l];
return X;
}
};
template <class A, class B, class S> struct double_hash_array {
int n;
hash_array<A, S> A_hash_array;
hash_array<B, S> B_hash_array;
double_hash_array(const std::vector<S> &a) { build(a); }
double_hash_array() {}
double_hash_array(const std::string &a) {
std::vector<S> a0(a.begin(), a.end());
build(a0);
}
void build(const std::vector<S> &a) {
n = int(a.size());
A_hash_array.build(a);
B_hash_array.build(a);
}
void build(const std::string &a) {
std::vector<S> a0(a.begin(), a.end());
build(a0);
}
/// @brief Hash of [l, r).
std::pair<A, B> prod(int l, int r) const {
return std::make_pair(A_hash_array.prod(l, r), B_hash_array.prod(l, r));
}
};
using mint1 = atcoder::modint1000000007;
using mint2 = atcoder::modint998244353;
using mint3 = uint64_t;
template <class T> int lcp(const T &A, int i, const T &B, int j) {
int n = A.n;
int m = B.n;
int l = 0;
int r = std::min(n - i, m - j) + 1;
while (r - l > 1) {
int mid = (l + r) / 2;
if (A.prod(i, i + mid) == B.prod(j, j + mid))
l = mid;
else
r = mid;
}
return l;
}
template <class T> int lcs(const T &A, int i, const T &B, int j) {
int l = 0;
int r = std::min(i + 1, j + 1) + 1;
while (r - l > 1) {
int mid = (l + r) / 2;
if (A.prod(i + 1 - mid, i + 1) == B.prod(j + 1 - mid, j + 1))
l = mid;
else
r = mid;
}
return l;
}
template <class T>
/// @brief Check if A[l1, r1) == B[l2, r2).
bool same(const T &A, int l1, int r1, const T &B, int l2, int r2) {
int n1 = r1 - l1;
int n2 = r2 - l2;
assert(0 <= l1 && l1 <= r1 && r1 <= A.n);
assert(0 <= l2 && l2 <= r2 && r2 <= B.n);
if (n1 != n2)
return false;
int lc = lcp(A, l1, B, l2);
return lc == n1;
}
} // namespace noya
namespace noya {
/// @brief Compute all runs (maximal periodicities) in a sequence.
/// @return Vector of (period, left, right) where the run covers [left, right).
template <class T>
std::vector<std::tuple<int, int, int>> runs(const std::vector<T> &s) {
int n = int(s.size());
noya::double_hash_array<mint1, mint2, T> H;
H.build(s);
std::vector<std::tuple<int, int, int>> runs;
for (bool inv : {false, true}) {
std::vector<int> lyn(n, n), stack;
for (int i = 0; i < n; i += 1) {
while (!stack.empty()) {
int j = stack.back(), k = lcp(H, i, H, j);
if (i + k < n && ((s[i + k] > s[j + k]) ^ inv))
break;
lyn[j] = i;
stack.pop_back();
}
stack.push_back(i);
}
for (int i = 0; i < n; i += 1) {
int j = lyn[i], t = j - i, l = i - lcs(H, i - 1, H, j - 1),
r = j + lcp(H, i, H, j);
if (r - l >= 2 * t)
runs.emplace_back(t, l, r);
}
}
std::ranges::sort(runs);
runs.erase(std::ranges::unique(runs).begin(), runs.end());
return runs;
}
std::vector<std::tuple<int, int, int>> runs(const std::string &s) {
std::vector<char> a(s.begin(), s.end());
return runs(a);
}
} // namespace noya