#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#include "template/template.hpp"
#include "string/rolling-hash.hpp"
#include "string/rolling-hash-segment-tree.hpp"
#include "util/xorshift.hpp"
void check_static(const vector<int>& a) {
RollingHash hash(a);
RollingHashSegmentTree<int> seg(a);
assert(hash.size() == (int)a.size());
for (int l = 0; l <= (int)a.size(); l++) {
for (int r = l; r <= (int)a.size(); r++) {
RollingHash direct(vector<int>(a.begin() + l, a.begin() + r));
assert(hash.slice(l, r) == direct.slice(0, r - l));
assert(seg.prod(l, r) == hash.slice(l, r));
}
}
for (int l = 0; l <= (int)a.size(); l++) {
for (int m = l; m <= (int)a.size(); m++) {
for (int r = m; r <= (int)a.size(); r++) {
assert(hash.slice(l, m) + hash.slice(m, r) == hash.slice(l, r));
}
}
}
}
void test_value() {
static_assert(sizeof(RollingHashValue) == 2 * sizeof(uint64_t));
static_assert(sizeof(RollingHashValueReversible) == 3 * sizeof(uint64_t));
RollingHashBase::base = 911382323;
assert(RollingHashValue() == RollingHashValue(0, 1));
assert(RollingHashValue::single(-1).hash == RollingHashBase::MOD - 1);
assert(RollingHashValue::single(0).hash == 0);
assert(RollingHashValue::single(1).hash == 1);
RollingHash zero(vector<int>{0});
RollingHash zeros(vector<int>{0, 0});
assert(zero.slice(0, 1).hash == zeros.slice(0, 2).hash);
assert(zero.slice(0, 1) != zeros.slice(0, 2));
for (long long v :
{numeric_limits<long long>::min(), -(long long)RollingHashBase::MOD - 1, -1ll, 0ll, 1ll,
(long long)RollingHashBase::MOD, numeric_limits<long long>::max()}) {
RollingHashBase::i128 expected = RollingHashBase::i128(v) % RollingHashBase::MOD;
if (expected < 0) expected += RollingHashBase::MOD;
assert(RollingHashBase::normalize(v) == RollingHashBase::u64(expected));
}
assert(RollingHashBase::restore<int>(RollingHashBase::normalize(numeric_limits<int>::min())) ==
numeric_limits<int>::min());
assert(RollingHashBase::restore<int>(RollingHashBase::normalize(numeric_limits<int>::max())) ==
numeric_limits<int>::max());
auto x = RollingHashValueReversible::single(-1);
assert(x.hash == RollingHashBase::MOD - 1);
assert(x.hash == x.reverse_hash);
assert(x.reversed() == x);
}
void test_static() {
check_static({});
check_static({0});
check_static({-3, 0, 1, -1, 1000000000, -1000000000});
string s = "abracadabra";
RollingHash hash(s);
RollingHashSegmentTree seg(s);
for (int l = 0; l <= (int)s.size(); l++)
for (int r = l; r <= (int)s.size(); r++) assert(seg.prod(l, r) == hash.slice(l, r));
}
void test_segment_tree() {
int n = 30;
vector<int> a(n);
for (int i = 0; i < n; i++) a[i] = int(XORShift::xor32() % 2001) - 1000;
RollingHashSegmentTree<int> seg(a);
for (int t = 0; t < 1000; t++) {
if (XORShift::xor32() & 1) {
int p = XORShift::xor32() % n;
a[p] = int(XORShift::xor32() % 2000000001) - 1000000000;
seg.set(p, a[p]);
assert(seg.get(p) == a[p]);
} else {
int l = XORShift::xor32() % (n + 1);
int r = XORShift::xor32() % (n + 1);
if (l > r) swap(l, r);
RollingHash hash(a);
assert(seg.prod(l, r) == hash.slice(l, r));
}
}
}
void test_reversible() {
vector<int> a = {-3, 0, 1, -1, 4, 0};
RollingHashSegmentTreeReversible<int> seg(a);
RollingHash hash(a);
for (int l = 0; l <= (int)a.size(); l++) {
for (int r = l; r <= (int)a.size(); r++) {
auto value = seg.prod(l, r);
vector<int> b(a.begin() + l, a.begin() + r);
reverse(b.begin(), b.end());
RollingHash reversed(b);
assert(value.hash == hash.slice(l, r).hash);
assert(value.reverse_hash == reversed.slice(0, b.size()).hash);
assert(value.power == hash.slice(l, r).power);
assert(value.reversed().hash == value.reverse_hash);
assert(value.reversed().reverse_hash == value.hash);
for (int m = l; m <= r; m++) {
auto left = seg.prod(l, m), right = seg.prod(m, r);
assert(left + right == value);
assert(value.reversed() == right.reversed() + left.reversed());
}
}
}
seg.set(2, -100);
a[2] = -100;
assert(seg.get(2) == a[2]);
RollingHash updated(a);
assert(seg.prod(0, a.size()).hash == updated.slice(0, a.size()).hash);
}
int main() {
test_value();
test_static();
test_segment_tree();
test_reversible();
int a, b;
in(a, b);
out(a + b);
}
#line 1 "verify/string/UNIT_rolling_hash.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#line 2 "template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
#line 2 "template/macro.hpp"
#define rep(i, a, b) for (int i = (a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b) - 1; i >= (a); i--)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())
#define YN(b) cout << ((b) ? "YES" : "NO") << "\n";
#define Yn(b) cout << ((b) ? "Yes" : "No") << "\n";
#define yn(b) cout << ((b) ? "yes" : "no") << "\n";
#line 6 "template/template.hpp"
#line 2 "template/util.hpp"
using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <class T>
using priority_queue_asc = priority_queue<T, vector<T>, greater<T>>;
template <class T, class S = T>
S SUM(const vector<T>& a) {
return accumulate(ALL(a), S(0));
}
template <class T1, class T2>
inline bool chmin(T1& a, T2 b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template <class T1, class T2>
inline bool chmax(T1& a, T2 b) {
if (a < b) {
a = b;
return true;
}
return false;
}
template <class T1, class T2>
inline bool chmin_opt(optional<T1>& a, T2 b) {
if (!a || a > b) {
a = b;
return true;
}
return false;
}
template <class T1, class T2>
inline bool chmax_opt(optional<T1>& a, T2 b) {
if (!a || a < b) {
a = b;
return true;
}
return false;
}
template <class T>
int popcnt(T x) {
return __builtin_popcountll(x);
}
template <class T>
int topbit(T x) {
return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <class T>
int lowbit(T x) {
return (x == 0 ? -1 : __builtin_ctzll(x));
}
#line 8 "template/template.hpp"
#line 2 "template/inout.hpp"
struct Fast {
Fast() {
cin.tie(nullptr);
ios_base::sync_with_stdio(false);
cout << fixed << setprecision(15);
}
} fast;
ostream& operator<<(ostream& os, __uint128_t x) {
char buf[40];
size_t k = 0;
while (x > 0) buf[k++] = (char)(x % 10 + '0'), x /= 10;
if (k == 0) buf[k++] = '0';
while (k) os << buf[--k];
return os;
}
ostream& operator<<(ostream& os, __int128_t x) {
return x < 0 ? (os << '-' << (__uint128_t)(-x)) : (os << (__uint128_t)x);
}
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a);
template <class T1, class T2>
istream& operator>>(istream& is, pair<T1, T2>& p) {
return is >> p.first >> p.second;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
return os << p.first << " " << p.second;
}
template <class T>
istream& operator>>(istream& is, vector<T>& a) {
for (auto& v : a) is >> v;
return is;
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& a) {
for (auto it = a.begin(); it != a.end();) {
os << *it;
if (++it != a.end()) os << " ";
}
return os;
}
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a) {
for (auto it = a.begin(); it != a.end();) {
os << *it;
if (++it != a.end()) os << " ";
}
return os;
}
template <class T>
ostream& operator<<(ostream& os, const set<T>& st) {
os << "{";
for (auto it = st.begin(); it != st.end();) {
os << *it;
if (++it != st.end()) os << ",";
}
os << "}";
return os;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const map<T1, T2>& mp) {
os << "{";
for (auto it = mp.begin(); it != mp.end();) {
os << it->first << ":" << it->second;
if (++it != mp.end()) os << ",";
}
os << "}";
return os;
}
void in() {}
template <typename T, class... U>
void in(T& t, U&... u) {
cin >> t;
in(u...);
}
template <class... T>
void in_zip(int n, T&... t) {
assert(n >= 0 && ((size(t) >= static_cast<size_t>(n)) && ...));
for (int i = 0; i < n; i++) in(t[i]...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T& t, const U&... u) {
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
template <class T, class U>
void out_opt(const optional<T>& opt, const U& fallback, ostream& os = cout) {
if (opt.has_value())
os << opt.value();
else
os << fallback;
os << "\n";
}
template <class T, class U>
void out_opt(const vector<optional<T>>& vec, const U& fallback, ostream& os = cout) {
for (auto it = vec.begin(); it != vec.end();) {
if ((*it).has_value())
os << (*it).value();
else
os << fallback;
if (++it != vec.end()) os << " ";
}
os << "\n";
}
namespace IO {
template <class T, class... U>
T read(U&&... u) {
T t = T(forward<U>(u)...);
in(t);
return t;
}
namespace Graph {
vector<vector<int>> unweighted(int n, int m, bool directed = false, int offset = 1) {
vector<vector<int>> g(n);
for (int i = 0; i < m; i++) {
int u, v;
cin >> u >> v;
u -= offset, v -= offset;
g[u].push_back(v);
if (!directed) g[v].push_back(u);
}
return g;
}
template <class T>
vector<vector<pair<int, T>>> weighted(int n, int m, bool directed = false, int offset = 1) {
vector<vector<pair<int, T>>> g(n);
for (int i = 0; i < m; i++) {
int u, v;
T w;
cin >> u >> v >> w;
u -= offset, v -= offset;
g[u].push_back({v, w});
if (!directed) g[v].push_back({u, w});
}
return g;
}
} // namespace Graph
namespace Tree {
vector<vector<int>> unweighted(int n, bool directed = false, int offset = 1) {
return Graph::unweighted(n, n - 1, directed, offset);
}
template <class T>
vector<vector<pair<int, T>>> weighted(int n, bool directed = false, int offset = 1) {
return Graph::weighted<T>(n, n - 1, directed, offset);
}
vector<vector<int>> rooted(int n, bool to_root = true, bool to_leaf = true, int offset = 1) {
vector<vector<int>> g(n);
for (int i = 1; i < n; i++) {
int p;
cin >> p;
p -= offset;
if (to_root) g[i].push_back(p);
if (to_leaf) g[p].push_back(i);
}
return g;
}
} // namespace Tree
} // namespace IO
#line 10 "template/template.hpp"
#line 2 "template/debug.hpp"
#ifdef LOCAL
#define debug 1
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define debug 0
#define show(...) true
#endif
template <class T>
void _show(int, T) {
cerr << '\n';
}
template <class T1, class T2, class... T3>
void _show(int i, const T1& a, const T2& b, const T3&... c) {
for (; a[i] != ',' && a[i] != '\0'; i++) cerr << a[i];
cerr << ":" << b << " ";
_show(i + 1, a, c...);
}
#line 2 "string/rolling-hash.hpp"
#line 2 "string/rolling-hash-value.hpp"
#line 2 "string/rolling-hash-base.hpp"
struct RollingHashBase {
using u128 = __uint128_t;
using i128 = __int128_t;
using u64 = uint64_t;
static constexpr u64 MOD = (1ull << 61) - 1;
static u64 base;
static u64 add(u64 x, u64 y) {
if ((x += y) >= MOD) x -= MOD;
return x;
}
static u64 sub(u64 x, u64 y) {
if ((x -= y) >= MOD) x += MOD;
return x;
}
static u64 mul(u64 x, u64 y) {
u128 z = (u128)x * y;
u64 v = (u64(z) & MOD) + u64(z >> 61);
return v >= MOD ? v - MOD : v;
}
static u64 normalize(u64 v) {
u64 x = (v & MOD) + (v >> 61);
return x >= MOD ? x - MOD : x;
}
template <class T>
static u64 normalize(T v) {
static_assert(is_integral_v<T> && sizeof(T) <= sizeof(u64));
if constexpr (is_signed_v<T>) {
if (v < 0) {
u64 x = normalize(u64(-i128(v)));
return x == 0 ? 0 : MOD - x;
}
}
return normalize(u64(v));
}
template <class T>
static T restore(u64 v) {
static_assert(is_integral_v<T> && sizeof(T) <= sizeof(u64));
assert(v < MOD);
if constexpr (is_signed_v<T>) {
if (v <= u64(numeric_limits<T>::max())) return T(v);
u64 x = MOD - v;
assert(i128(x) <= -i128(numeric_limits<T>::min()));
return T(-i128(x));
} else {
assert(v <= u64(numeric_limits<T>::max()));
return T(v);
}
}
};
inline RollingHashBase::u64 RollingHashBase::base = []() {
random_device seed_gen;
mt19937_64 rnd(seed_gen());
return uniform_int_distribution<u64>(256, MOD - 2)(rnd);
}();
#line 4 "string/rolling-hash-value.hpp"
struct RollingHashValue : RollingHashBase {
u64 hash, power;
RollingHashValue() : hash(0), power(1) {}
RollingHashValue(u64 h, u64 p) : hash(h), power(p) {}
template <class T>
static RollingHashValue single(T v) {
return RollingHashValue(normalize(v), base);
}
RollingHashValue& operator+=(RollingHashValue rhs) {
hash = add(mul(hash, rhs.power), rhs.hash);
power = mul(power, rhs.power);
return *this;
}
friend RollingHashValue operator+(RollingHashValue lhs, RollingHashValue rhs) {
return lhs += rhs;
}
friend bool operator==(RollingHashValue lhs, RollingHashValue rhs) {
return lhs.hash == rhs.hash && lhs.power == rhs.power;
}
};
struct RollingHashValueReversible : RollingHashBase {
u64 hash, reverse_hash, power;
RollingHashValueReversible() : hash(0), reverse_hash(0), power(1) {}
RollingHashValueReversible(u64 h, u64 rh, u64 p) : hash(h), reverse_hash(rh), power(p) {}
template <class T>
static RollingHashValueReversible single(T v) {
u64 h = normalize(v);
return RollingHashValueReversible(h, h, base);
}
RollingHashValueReversible& operator+=(RollingHashValueReversible rhs) {
hash = add(mul(hash, rhs.power), rhs.hash);
reverse_hash = add(reverse_hash, mul(rhs.reverse_hash, power));
power = mul(power, rhs.power);
return *this;
}
RollingHashValueReversible reversed() const {
return RollingHashValueReversible(reverse_hash, hash, power);
}
friend RollingHashValueReversible operator+(RollingHashValueReversible lhs,
RollingHashValueReversible rhs) {
return lhs += rhs;
}
friend bool operator==(RollingHashValueReversible lhs, RollingHashValueReversible rhs) {
return lhs.hash == rhs.hash && lhs.reverse_hash == rhs.reverse_hash &&
lhs.power == rhs.power;
}
};
#line 4 "string/rolling-hash.hpp"
struct RollingHash : RollingHashBase {
vector<RollingHashValue> prefix;
RollingHash() : prefix(1) {}
template <class T>
RollingHash(const vector<T>& a) : RollingHash() {
for (auto v : a) push(v);
}
RollingHash(const string& s) : RollingHash() {
for (auto c : s) push(c);
}
template <class T>
void push(T v) { prefix.push_back(prefix.back() + RollingHashValue::single(v)); }
int size() const { return prefix.size() - 1; }
RollingHashValue slice(int l, int r) const {
assert(0 <= l && l <= r && r <= size());
u64 power = prefix[r - l].power;
return RollingHashValue(sub(prefix[r].hash, mul(prefix[l].hash, power)), power);
}
};
#line 2 "string/rolling-hash-segment-tree.hpp"
#line 2 "algebraic-structure/util.hpp"
#ifdef __cpp_concepts
#define REQUIRES(...) requires __VA_ARGS__
#else
#define REQUIRES(...)
#endif
#line 3 "algebraic-structure/magma.hpp"
#ifdef __cpp_concepts
template <class M>
concept Magma = requires(typename M::value_type x, typename M::value_type y) {
typename M::value_type;
{ M::op(x, y) } -> same_as<typename M::value_type>;
};
#endif
template <class T>
struct AddMagma {
using value_type = T;
static T op(T x, T y) { return x + y; }
};
template <class T>
struct MulMagma {
using value_type = T;
static T op(T x, T y) { return x * y; }
};
template <class T, T id>
struct MaxMagma {
using value_type = T;
static T op(T x, T y) { return x > y ? x : y; }
};
template <class T, T id>
struct MinMagma {
using value_type = T;
static T op(T x, T y) { return x < y ? x : y; }
};
#line 3 "algebraic-structure/monoid.hpp"
#ifdef __cpp_concepts
template <class M>
concept Monoid = Magma<M> && requires {
{ M::e() } -> same_as<typename M::value_type>;
};
#endif
template <class T>
struct AddMonoid {
using value_type = T;
static T op(T x, T y) { return x + y; }
static T e() { return T(0); }
};
template <class T>
struct MulMonoid {
using value_type = T;
static T op(T x, T y) { return x * y; }
static T e() { return T(1); }
};
template <class T, T id>
struct MaxMonoid {
using value_type = T;
static T op(T x, T y) { return x > y ? x : y; }
static T e() { return id; }
};
template <class T, T id>
struct MinMonoid {
using value_type = T;
static T op(T x, T y) { return x < y ? x : y; }
static T e() { return id; }
};
#line 3 "segment-tree/segment-tree.hpp"
template <class M>
REQUIRES(Monoid<M>)
struct SegmentTree {
using T = typename M::value_type;
private:
int _n, size, log;
vector<T> d;
void update(int p) { d[p] = M::op(d[2 * p], d[2 * p + 1]); }
public:
SegmentTree() : SegmentTree(0) {}
explicit SegmentTree(int sz) : SegmentTree(vector<T>(sz, M::e())) {}
explicit SegmentTree(const vector<T>& v) : _n(v.size()) {
size = 1, log = 0;
while (size < _n) size <<= 1, log++;
d.assign(2 * size, M::e());
for (int i = 0; i < _n; i++) d[size + i] = v[i];
for (int i = size - 1; i > 0; i--) update(i);
}
void clear() { fill(d.begin(), d.end(), M::e()); }
void set_without_update(int p, T v) { d[p + size] = v; }
void all_update() {
for (int i = size - 1; i > 0; i--) update(i);
}
T get(int p) {
assert(0 <= p && p <= _n);
return d[p + size];
}
void set(int p, T v) {
assert(0 <= p && p <= _n);
p += size;
d[p] = v;
for (int i = 1; i <= log; i++) update(p >> i);
}
void apply(int p, T v) {
assert(0 <= p && p <= _n);
p += size;
d[p] = M::op(d[p], v);
for (int i = 1; i <= log; i++) update(p >> i);
}
T all_prod() { return d[1]; }
T prod(int l, int r) {
if (l >= r) return M::e();
assert(0 <= l && l <= r && r <= _n);
T sl = M::e(), sr = M::e();
l += size, r += size;
while (l < r) {
if ((l & 1) != 0) sl = M::op(sl, d[l++]);
if ((r & 1) != 0) sr = M::op(d[--r], sr);
l >>= 1, r >>= 1;
}
return M::op(sl, sr);
}
template <bool (*f)(T)>
int max_right(int l) const {
return max_right(l, [](T x) { return f(x); });
}
template <class F>
int max_right(int l, F f) const {
assert(0 <= l && l <= size);
assert(f(M::e()));
if (l == _n) return _n;
l += size;
T s = M::e();
do {
while (l % 2 == 0) l >>= 1;
if (!f(M::op(s, d[l]))) {
while (l < size) {
l <<= 1;
if (f(M::op(s, d[l]))) s = M::op(s, d[l++]);
}
return l - size;
}
s = M::op(s, d[l++]);
} while ((l & -l) != l);
return _n;
}
template <bool (*f)(T)>
int min_left(int r) const {
return min_left(r, [](T x) { return f(x); });
}
template <class F>
int min_left(int r, F f) const {
assert(0 <= r && r <= _n);
assert(f(M::e()));
if (r == 0) return 0;
r += size;
T s = M::e();
do {
r--;
while (r > 1 && (r % 2)) r >>= 1;
if (!f(M::op(d[r], s))) {
while (r < size) {
r <<= 1, r++;
if (f(M::op(d[r], s))) s = M::op(d[r--], s);
}
return r + 1 - size;
}
s = M::op(d[r], s);
} while ((r & -r) != r);
return 0;
}
};
/**
* @brief Segment Tree
* @docs docs/segment-tree/segment-tree.md
*/
#line 2 "string/rolling-hash-monoid.hpp"
#line 4 "string/rolling-hash-monoid.hpp"
struct RollingHashMonoid {
using value_type = RollingHashValue;
static value_type op(value_type x, value_type y) { return x + y; }
static value_type e() { return value_type(); }
template <class T>
static value_type single(T v) {
return value_type::single(v);
}
template <class Sequence>
static vector<value_type> init(const Sequence& a) {
vector<value_type> v(a.size());
for (int i = 0; i < (int)a.size(); i++) v[i] = single(a[i]);
return v;
}
};
struct RollingHashMonoidReversible {
using value_type = RollingHashValueReversible;
static value_type op(value_type x, value_type y) { return x + y; }
static value_type e() { return value_type(); }
template <class T>
static value_type single(T v) {
return value_type::single(v);
}
template <class Sequence>
static vector<value_type> init(const Sequence& a) {
vector<value_type> v(a.size());
for (int i = 0; i < (int)a.size(); i++) v[i] = single(a[i]);
return v;
}
};
#line 5 "string/rolling-hash-segment-tree.hpp"
template <class Value = char>
struct RollingHashSegmentTree : SegmentTree<RollingHashMonoid> {
using M = RollingHashMonoid;
using SegTree = SegmentTree<M>;
RollingHashSegmentTree() : SegTree() {}
explicit RollingHashSegmentTree(const vector<Value>& a) : SegTree(M::init(a)) {}
explicit RollingHashSegmentTree(const string& s) : SegTree(M::init(s)) {}
void set(int p, Value v) { SegTree::set(p, M::single(v)); }
Value get(int p) { return RollingHashBase::restore<Value>(SegTree::get(p).hash); }
RollingHashValue prod(int l, int r) { return SegTree::prod(l, r); }
};
template <class Value = char>
struct RollingHashSegmentTreeReversible : SegmentTree<RollingHashMonoidReversible> {
using M = RollingHashMonoidReversible;
using SegTree = SegmentTree<M>;
RollingHashSegmentTreeReversible() : SegTree() {}
explicit RollingHashSegmentTreeReversible(const vector<Value>& a) : SegTree(M::init(a)) {}
explicit RollingHashSegmentTreeReversible(const string& s) : SegTree(M::init(s)) {}
void set(int p, Value v) { SegTree::set(p, M::single(v)); }
Value get(int p) { return RollingHashBase::restore<Value>(SegTree::get(p).hash); }
RollingHashValueReversible prod(int l, int r) { return SegTree::prod(l, r); }
};
#line 2 "util/xorshift.hpp"
namespace XORShift {
unsigned int xor32() {
static unsigned int x = 123456789u;
x ^= x << 13, x ^= x >> 17, x ^= x << 5;
return x;
}
unsigned long long xor64() {
static unsigned long long x = 123456789ull;
x ^= x << 13, x ^= x >> 7, x ^= x << 17;
return x;
}
}; // namespace XORShift
/**
* @brief XOR shift
*/
#line 7 "verify/string/UNIT_rolling_hash.test.cpp"
void check_static(const vector<int>& a) {
RollingHash hash(a);
RollingHashSegmentTree<int> seg(a);
assert(hash.size() == (int)a.size());
for (int l = 0; l <= (int)a.size(); l++) {
for (int r = l; r <= (int)a.size(); r++) {
RollingHash direct(vector<int>(a.begin() + l, a.begin() + r));
assert(hash.slice(l, r) == direct.slice(0, r - l));
assert(seg.prod(l, r) == hash.slice(l, r));
}
}
for (int l = 0; l <= (int)a.size(); l++) {
for (int m = l; m <= (int)a.size(); m++) {
for (int r = m; r <= (int)a.size(); r++) {
assert(hash.slice(l, m) + hash.slice(m, r) == hash.slice(l, r));
}
}
}
}
void test_value() {
static_assert(sizeof(RollingHashValue) == 2 * sizeof(uint64_t));
static_assert(sizeof(RollingHashValueReversible) == 3 * sizeof(uint64_t));
RollingHashBase::base = 911382323;
assert(RollingHashValue() == RollingHashValue(0, 1));
assert(RollingHashValue::single(-1).hash == RollingHashBase::MOD - 1);
assert(RollingHashValue::single(0).hash == 0);
assert(RollingHashValue::single(1).hash == 1);
RollingHash zero(vector<int>{0});
RollingHash zeros(vector<int>{0, 0});
assert(zero.slice(0, 1).hash == zeros.slice(0, 2).hash);
assert(zero.slice(0, 1) != zeros.slice(0, 2));
for (long long v :
{numeric_limits<long long>::min(), -(long long)RollingHashBase::MOD - 1, -1ll, 0ll, 1ll,
(long long)RollingHashBase::MOD, numeric_limits<long long>::max()}) {
RollingHashBase::i128 expected = RollingHashBase::i128(v) % RollingHashBase::MOD;
if (expected < 0) expected += RollingHashBase::MOD;
assert(RollingHashBase::normalize(v) == RollingHashBase::u64(expected));
}
assert(RollingHashBase::restore<int>(RollingHashBase::normalize(numeric_limits<int>::min())) ==
numeric_limits<int>::min());
assert(RollingHashBase::restore<int>(RollingHashBase::normalize(numeric_limits<int>::max())) ==
numeric_limits<int>::max());
auto x = RollingHashValueReversible::single(-1);
assert(x.hash == RollingHashBase::MOD - 1);
assert(x.hash == x.reverse_hash);
assert(x.reversed() == x);
}
void test_static() {
check_static({});
check_static({0});
check_static({-3, 0, 1, -1, 1000000000, -1000000000});
string s = "abracadabra";
RollingHash hash(s);
RollingHashSegmentTree seg(s);
for (int l = 0; l <= (int)s.size(); l++)
for (int r = l; r <= (int)s.size(); r++) assert(seg.prod(l, r) == hash.slice(l, r));
}
void test_segment_tree() {
int n = 30;
vector<int> a(n);
for (int i = 0; i < n; i++) a[i] = int(XORShift::xor32() % 2001) - 1000;
RollingHashSegmentTree<int> seg(a);
for (int t = 0; t < 1000; t++) {
if (XORShift::xor32() & 1) {
int p = XORShift::xor32() % n;
a[p] = int(XORShift::xor32() % 2000000001) - 1000000000;
seg.set(p, a[p]);
assert(seg.get(p) == a[p]);
} else {
int l = XORShift::xor32() % (n + 1);
int r = XORShift::xor32() % (n + 1);
if (l > r) swap(l, r);
RollingHash hash(a);
assert(seg.prod(l, r) == hash.slice(l, r));
}
}
}
void test_reversible() {
vector<int> a = {-3, 0, 1, -1, 4, 0};
RollingHashSegmentTreeReversible<int> seg(a);
RollingHash hash(a);
for (int l = 0; l <= (int)a.size(); l++) {
for (int r = l; r <= (int)a.size(); r++) {
auto value = seg.prod(l, r);
vector<int> b(a.begin() + l, a.begin() + r);
reverse(b.begin(), b.end());
RollingHash reversed(b);
assert(value.hash == hash.slice(l, r).hash);
assert(value.reverse_hash == reversed.slice(0, b.size()).hash);
assert(value.power == hash.slice(l, r).power);
assert(value.reversed().hash == value.reverse_hash);
assert(value.reversed().reverse_hash == value.hash);
for (int m = l; m <= r; m++) {
auto left = seg.prod(l, m), right = seg.prod(m, r);
assert(left + right == value);
assert(value.reversed() == right.reversed() + left.reversed());
}
}
}
seg.set(2, -100);
a[2] = -100;
assert(seg.get(2) == a[2]);
RollingHash updated(a);
assert(seg.prod(0, a.size()).hash == updated.slice(0, a.size()).hash);
}
int main() {
test_value();
test_static();
test_segment_tree();
test_reversible();
int a, b;
in(a, b);
out(a + b);
}
verify/string/UNIT_rolling_hash.test.cpp
algebraic-structure/magma.hpp