#line 1 "verify/binary-search-tree/UNIT_rbst_segment_tree.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#line 2 "template/template.hpp"
// repo: https://github.com/kumacs/library-cpp
// docs: https://kumacs.github.io/library-cpp
#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 10 "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 12 "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 14 "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 "binary-search-tree/rbst-base.hpp"
template <class Node>
struct RBSTBase {
using Ptr = Node*;
template <typename... Args>
inline Ptr my_new(Args... args) {
return new Node(args...);
}
inline void my_del(Ptr t) { delete t; }
inline Ptr make_tree() const { return nullptr; }
int size(Ptr t) const { return count(t); }
Ptr merge(Ptr l, Ptr r) {
if (!l || !r) return l ? l : r;
if (int((rng() * (l->cnt + r->cnt)) >> 32) < l->cnt) {
push(l);
l->r = merge(l->r, r);
return update(l);
} else {
push(r);
r->l = merge(l, r->l);
return update(r);
}
}
pair<Ptr, Ptr> split(Ptr t, int k) {
if (!t) return {nullptr, nullptr};
push(t);
if (k <= count(t->l)) {
auto s = split(t->l, k);
t->l = s.second;
return {s.first, update(t)};
} else {
auto s = split(t->r, k - count(t->l) - 1);
t->r = s.first;
return {update(t), s.second};
}
}
Ptr build(int l, int r, const vector<decltype(Node::key)>& v) {
if (l + 1 == r) return my_new(v[l]);
int m = (l + r) >> 1;
Ptr pm = my_new(v[m]);
if (l < m) pm->l = build(l, m, v);
if (m + 1 < r) pm->r = build(m + 1, r, v);
return update(pm);
}
Ptr build(const vector<decltype(Node::key)>& v) {
return build(0, (int)v.size(), v);
}
template <typename... Args>
void insert(Ptr& t, int k, const Args&... args) {
auto x = split(t, k);
t = merge(merge(x.first, my_new(args...)), x.second);
}
void erase(Ptr& t, int k) {
auto x = split(t, k);
auto y = split(x.second, 1);
my_del(y.first);
t = merge(x.first, y.second);
}
protected:
static uint64_t rng() {
static uint64_t x_ = 123456789ull;
return x_ ^= x_ << 7, x_ ^= x_ >> 9, x_ & 0xFFFFFFFFull;
}
inline int count(const Ptr t) const { return t ? t->cnt : 0; }
virtual void push(Ptr) = 0;
virtual Ptr update(Ptr) = 0;
};
/**
* @brief Randomized Binary Search Tree (基底クラス)
* @docs docs/binary-search-tree/rbst-base.md
*/
#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 4 "binary-search-tree/rbst-segment-tree.hpp"
template <class M>
REQUIRES(Monoid<M>)
struct RBSTSegmentTreeNode {
using T = M::value_type;
typename RBSTBase<RBSTSegmentTreeNode>::Ptr l, r;
int cnt;
T key, sum, rev_sum;
bool rev;
RBSTSegmentTreeNode(const T& t = M::e()) : l(), r(), cnt(1), key(t), sum(t), rev_sum(t), rev(false) {}
};
template <class M>
REQUIRES(Monoid<M>)
struct RBSTSegmentTree : RBSTBase<RBSTSegmentTreeNode<M>> {
using T = M::value_type;
using Node = RBSTSegmentTreeNode<M>;
using base = RBSTBase<Node>;
using base::merge;
using base::split;
using typename base::Ptr;
RBSTSegmentTree() = default;
T get(Ptr& t, int k) {
auto x = split(t, k);
auto y = split(x.second, 1);
T v = y.first->key;
t = merge(x.first, merge(y.first, y.second));
return v;
}
void set(Ptr& t, int k, T v) {
auto x = split(t, k);
auto y = split(x.second, 1);
y.first->key = v;
update(y.first);
t = merge(x.first, merge(y.first, y.second));
}
T prod(Ptr& t, int l, int r) {
if (l >= r) return M::e();
auto x = split(t, l);
auto y = split(x.second, r - l);
auto ret = y.first->sum;
t = merge(x.first, merge(y.first, y.second));
return ret;
}
void reverse(Ptr& t, int l, int r) {
if (l >= r) return;
auto x = split(t, l);
auto y = split(x.second, r - l);
toggle(y.first);
t = merge(x.first, merge(y.first, y.second));
}
protected:
Ptr update(Ptr t) override {
t->cnt = 1;
t->sum = t->rev_sum = t->key;
if (t->l) {
t->cnt += t->l->cnt;
t->sum = M::op(t->l->sum, t->sum);
t->rev_sum = M::op(t->rev_sum, t->l->rev_sum);
}
if (t->r) {
t->cnt += t->r->cnt;
t->sum = M::op(t->sum, t->r->sum);
t->rev_sum = M::op(t->r->rev_sum, t->rev_sum);
}
return t;
}
void push(Ptr t) override {
if (!t->rev) return;
if (t->l) toggle(t->l);
if (t->r) toggle(t->r);
t->rev = false;
}
private:
void toggle(Ptr t) {
swap(t->l, t->r);
swap(t->sum, t->rev_sum);
t->rev ^= true;
}
};
/**
* @brief 挿入/削除の可能なセグメント木 (乱択二分探索木)
* @docs docs/binary-search-tree/rbst-segment-tree.md
*/
#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 6 "verify/binary-search-tree/UNIT_rbst_segment_tree.test.cpp"
struct StringMonoid {
using value_type = string;
static string op(const string& x, const string& y) { return x + y; }
static string e() { return ""; }
};
void test() {
vector<string> a = {"a", "bc", "d"};
RBSTSegmentTree<StringMonoid> seg;
auto t = seg.build(a);
rep(loop, 0, 10000) {
int type = XORShift::xor32() % 5;
if (a.empty()) type = 0;
if (type == 0) {
int k = XORShift::xor32() % (a.size() + 1);
string x = to_string(XORShift::xor32() % 10);
a.insert(a.begin() + k, x);
seg.insert(t, k, x);
} else if (type == 1) {
int k = XORShift::xor32() % a.size();
a.erase(a.begin() + k);
seg.erase(t, k);
} else if (type == 2) {
int k = XORShift::xor32() % a.size();
string x = to_string(XORShift::xor32() % 10);
a[k] = x;
seg.set(t, k, x);
} else if (type == 3) {
int k = XORShift::xor32() % a.size();
assert(seg.get(t, k) == a[k]);
} else {
int l = XORShift::xor32() % (a.size() + 1);
int r = XORShift::xor32() % (a.size() + 1);
if (l > r) swap(l, r);
string expected;
rep(i, l, r) expected += a[i];
assert(seg.prod(t, l, r) == expected);
}
assert(seg.size(t) == (int)a.size());
assert(seg.prod(t, 0, 0) == "");
string expected;
for (const string& x : a) expected += x;
assert(seg.prod(t, 0, a.size()) == expected);
}
}
int main() {
test();
int a, b;
in(a, b);
out(a + b);
}
verify/binary-search-tree/UNIT_rbst_segment_tree.test.cpp