#line 1 "verify/verify-yosupo-ds/yosupo-offline-dynamic-connectivity.test.cpp"
#define PROBLEM \
"https://judge.yosupo.jp/problem/dynamic_graph_vertex_add_component_sum"
#line 2 "template/template.hpp"
using namespace std;
// intrinstic
#include <immintrin.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
// utility
#line 1 "template/util.hpp"
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;
template <typename T, typename U>
struct P : pair<T, U> {
template <typename... Args>
P(Args... args) : pair<T, U>(args...) {}
using pair<T, U>::first;
using pair<T, U>::second;
P &operator+=(const P &r) {
first += r.first;
second += r.second;
return *this;
}
P &operator-=(const P &r) {
first -= r.first;
second -= r.second;
return *this;
}
P &operator*=(const P &r) {
first *= r.first;
second *= r.second;
return *this;
}
template <typename S>
P &operator*=(const S &r) {
first *= r, second *= r;
return *this;
}
P operator+(const P &r) const { return P(*this) += r; }
P operator-(const P &r) const { return P(*this) -= r; }
P operator*(const P &r) const { return P(*this) *= r; }
template <typename S>
P operator*(const S &r) const {
return P(*this) *= r;
}
P operator-() const { return P{-first, -second}; }
};
using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;
constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;
template <typename T>
int sz(const T &t) {
return t.size();
}
template <typename T, typename U>
inline bool amin(T &x, U y) {
return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T>
inline T Max(const vector<T> &v) {
return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
return accumulate(begin(v), end(v), 0LL);
}
template <typename T>
int lb(const vector<T> &v, const T &a) {
return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
return upper_bound(begin(v), end(v), a) - begin(v);
}
constexpr long long TEN(int n) {
long long ret = 1, x = 10;
for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
return ret;
}
template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
return make_pair(t, u);
}
template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
vector<T> ret(v.size() + 1);
if (rev) {
for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
} else {
for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
}
return ret;
};
template <typename T>
vector<T> mkuni(const vector<T> &v) {
vector<T> ret(v);
sort(ret.begin(), ret.end());
ret.erase(unique(ret.begin(), ret.end()), ret.end());
return ret;
}
template <typename F>
vector<int> mkord(int N, F f) {
vector<int> ord(N);
iota(begin(ord), end(ord), 0);
sort(begin(ord), end(ord), f);
return ord;
}
template <typename T>
vector<int> mkinv(vector<T> &v) {
int max_val = *max_element(begin(v), end(v));
vector<int> inv(max_val + 1, -1);
for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
return inv;
}
vector<int> mkiota(int n) {
vector<int> ret(n);
iota(begin(ret), end(ret), 0);
return ret;
}
template <typename T>
T mkrev(const T &v) {
T w{v};
reverse(begin(w), end(w));
return w;
}
template <typename T>
bool nxp(vector<T> &v) {
return next_permutation(begin(v), end(v));
}
// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
vector<vector<T>> ret;
vector<T> v;
auto dfs = [&](auto rc, int i) -> void {
if (i == (int)a.size()) {
ret.push_back(v);
return;
}
for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
};
dfs(dfs, 0);
return ret;
}
// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
T res = I;
for (; n; f(a = a * a), n >>= 1) {
if (n & 1) f(res = res * a);
}
return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I) {
return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}
} // namespace Nyaan
#line 58 "template/template.hpp"
// bit operation
#line 1 "template/bitop.hpp"
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
return _mm_popcnt_u64(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
} // namespace Nyaan
#line 61 "template/template.hpp"
// inout
#line 1 "template/inout.hpp"
namespace Nyaan {
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (auto &x : v) is >> x;
return is;
}
istream &operator>>(istream &is, __int128_t &x) {
string S;
is >> S;
x = 0;
int flag = 0;
for (auto &c : S) {
if (c == '-') {
flag = true;
continue;
}
x *= 10;
x += c - '0';
}
if (flag) x = -x;
return is;
}
istream &operator>>(istream &is, __uint128_t &x) {
string S;
is >> S;
x = 0;
for (auto &c : S) {
x *= 10;
x += c - '0';
}
return is;
}
ostream &operator<<(ostream &os, __int128_t x) {
if (x == 0) return os << 0;
if (x < 0) os << '-', x = -x;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
if (x == 0) return os << 0;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
cin >> t;
in(u...);
}
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...);
}
struct IoSetupNya {
IoSetupNya() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetupnya;
} // namespace Nyaan
#line 64 "template/template.hpp"
// debug
#line 1 "template/debug.hpp"
namespace DebugImpl {
template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
U, typename conditional<false, typename U::iterator, void>::type>
: true_type {};
template <typename U>
struct is_specialize<
U, typename conditional<false, decltype(U::first), void>::type>
: true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};
void dump(const char& t) { cerr << t; }
void dump(const string& t) { cerr << t; }
void dump(const bool& t) { cerr << (t ? "true" : "false"); }
void dump(__int128_t t) {
if (t == 0) cerr << 0;
if (t < 0) cerr << '-', t = -t;
string S;
while (t) S.push_back('0' + t % 10), t /= 10;
reverse(begin(S), end(S));
cerr << S;
}
void dump(__uint128_t t) {
if (t == 0) cerr << 0;
string S;
while (t) S.push_back('0' + t % 10), t /= 10;
reverse(begin(S), end(S));
cerr << S;
}
template <typename U,
enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
cerr << t;
}
template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
string res;
if (t == Nyaan::inf) res = "inf";
if constexpr (is_signed<T>::value) {
if (t == -Nyaan::inf) res = "-inf";
}
if constexpr (sizeof(T) == 8) {
if (t == Nyaan::infLL) res = "inf";
if constexpr (is_signed<T>::value) {
if (t == -Nyaan::infLL) res = "-inf";
}
}
if (res.empty()) res = to_string(t);
cerr << res;
}
template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);
template <typename T>
void dump(const T& t,
enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
cerr << "[ ";
for (auto it = t.begin(); it != t.end();) {
dump(*it);
cerr << (++it == t.end() ? "" : ", ");
}
cerr << " ]";
}
template <typename T, typename U>
void dump(const pair<T, U>& t) {
cerr << "( ";
dump(t.first);
cerr << ", ";
dump(t.second);
cerr << " )";
}
template <typename T>
void dump(const pair<T*, int>& t) {
cerr << "[ ";
for (int i = 0; i < t.second; i++) {
dump(t.first[i]);
cerr << (i == t.second - 1 ? "" : ", ");
}
cerr << " ]";
}
void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
cerr << " ";
dump(head);
if (sizeof...(tail) != 0) cerr << ",";
trace(forward<Tail>(tail)...);
}
} // namespace DebugImpl
#ifdef NyaanDebug
#define trc(...) \
do { \
cerr << "## " << #__VA_ARGS__ << " = "; \
DebugImpl::trace(__VA_ARGS__); \
} while (0)
#else
#define trc(...) (void(0))
#endif
#ifdef NyaanLocal
#define trc2(...) \
do { \
cerr << "## " << #__VA_ARGS__ << " = "; \
DebugImpl::trace(__VA_ARGS__); \
} while (0)
#else
#define trc2(...) (void(0))
#endif
#line 67 "template/template.hpp"
// macro
#line 1 "template/macro.hpp"
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...) \
int __VA_ARGS__; \
in(__VA_ARGS__)
#define inl(...) \
long long __VA_ARGS__; \
in(__VA_ARGS__)
#define ins(...) \
string __VA_ARGS__; \
in(__VA_ARGS__)
#define in2(s, t) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i]); \
}
#define in3(s, t, u) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i]); \
}
#define in4(s, t, u, v) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i], v[i]); \
}
#define die(...) \
do { \
Nyaan::out(__VA_ARGS__); \
return; \
} while (0)
#line 70 "template/template.hpp"
namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
#line 5 "verify/verify-yosupo-ds/yosupo-offline-dynamic-connectivity.test.cpp"
//
#line 2 "graph/offline-dynamic-connectivity.hpp"
#line 2 "data-structure/rollback-union-find.hpp"
struct RollbackUnionFind {
vector<int> data;
stack<pair<int, int> > history;
int inner_snap;
RollbackUnionFind(int sz) : inner_snap(0) { data.assign(sz, -1); }
bool unite(int x, int y) {
x = find(x), y = find(y);
history.emplace(x, data[x]);
history.emplace(y, data[y]);
if (x == y) return false;
if (data[x] > data[y]) swap(x, y);
data[x] += data[y];
data[y] = x;
return true;
}
int find(int k) {
if (data[k] < 0) return k;
return find(data[k]);
}
int same(int x, int y) { return find(x) == find(y); }
int size(int k) { return (-data[find(k)]); }
void undo() {
data[history.top().first] = history.top().second;
history.pop();
data[history.top().first] = history.top().second;
history.pop();
}
void snapshot() { inner_snap = int(history.size() >> 1); }
int get_state() { return int(history.size() >> 1); }
void rollback(int state = -1) {
if (state == -1) state = inner_snap;
state <<= 1;
assert(state <= (int)history.size());
while (state < (int)history.size()) undo();
}
};
/**
* @brief RollbackつきUnion Find
* @docs docs/data-structure/rollback-union-find.md
*/
#line 2 "hashmap/hashmap.hpp"
#line 2 "hashmap/hashmap-base.hpp"
#line 4 "hashmap/hashmap-base.hpp"
using namespace std;
namespace HashMapImpl {
using u32 = uint32_t;
using u64 = uint64_t;
template <typename Key, typename Data>
struct HashMapBase;
template <typename Key, typename Data>
struct itrB
: iterator<bidirectional_iterator_tag, Data, ptrdiff_t, Data*, Data&> {
using base =
iterator<bidirectional_iterator_tag, Data, ptrdiff_t, Data*, Data&>;
using ptr = typename base::pointer;
using ref = typename base::reference;
u32 i;
HashMapBase<Key, Data>* p;
explicit constexpr itrB() : i(0), p(nullptr) {}
explicit constexpr itrB(u32 _i, HashMapBase<Key, Data>* _p) : i(_i), p(_p) {}
explicit constexpr itrB(u32 _i, const HashMapBase<Key, Data>* _p)
: i(_i), p(const_cast<HashMapBase<Key, Data>*>(_p)) {}
friend void swap(itrB& l, itrB& r) { swap(l.i, r.i), swap(l.p, r.p); }
friend bool operator==(const itrB& l, const itrB& r) { return l.i == r.i; }
friend bool operator!=(const itrB& l, const itrB& r) { return l.i != r.i; }
const ref operator*() const {
return const_cast<const HashMapBase<Key, Data>*>(p)->data[i];
}
ref operator*() { return p->data[i]; }
ptr operator->() const { return &(p->data[i]); }
itrB& operator++() {
assert(i != p->cap && "itr::operator++()");
do {
i++;
if (i == p->cap) break;
if (p->occupied_flag[i] && !p->deleted_flag[i]) break;
} while (true);
return (*this);
}
itrB operator++(int) {
itrB it(*this);
++(*this);
return it;
}
itrB& operator--() {
do {
i--;
if (p->occupied_flag[i] && !p->deleted_flag[i]) break;
assert(i != 0 && "itr::operator--()");
} while (true);
return (*this);
}
itrB operator--(int) {
itrB it(*this);
--(*this);
return it;
}
};
template <typename Key, typename Data>
struct HashMapBase {
using u32 = uint32_t;
using u64 = uint64_t;
using iterator = itrB<Key, Data>;
using itr = iterator;
protected:
template <typename K>
inline u64 randomized(const K& key) const {
return u64(key) ^ r;
}
template <typename K,
enable_if_t<is_same<K, Key>::value, nullptr_t> = nullptr,
enable_if_t<is_integral<K>::value, nullptr_t> = nullptr>
inline u32 inner_hash(const K& key) const {
return (randomized(key) * 11995408973635179863ULL) >> shift;
}
template <
typename K, enable_if_t<is_same<K, Key>::value, nullptr_t> = nullptr,
enable_if_t<is_integral<decltype(K::first)>::value, nullptr_t> = nullptr,
enable_if_t<is_integral<decltype(K::second)>::value, nullptr_t> = nullptr>
inline u32 inner_hash(const K& key) const {
u64 a = randomized(key.first), b = randomized(key.second);
a *= 11995408973635179863ULL;
b *= 10150724397891781847ULL;
return (a + b) >> shift;
}
template <typename K,
enable_if_t<is_same<K, Key>::value, nullptr_t> = nullptr,
enable_if_t<is_integral<typename K::value_type>::value, nullptr_t> =
nullptr>
inline u32 inner_hash(const K& key) const {
static constexpr u64 mod = (1LL << 61) - 1;
static constexpr u64 base = 950699498548472943ULL;
u64 res = 0;
for (auto& elem : key) {
__uint128_t x = __uint128_t(res) * base + (randomized(elem) & mod);
res = (x & mod) + (x >> 61);
}
__uint128_t x = __uint128_t(res) * base;
res = (x & mod) + (x >> 61);
if (res >= mod) res -= mod;
return res >> (shift - 3);
}
template <typename D = Data,
enable_if_t<is_same<D, Key>::value, nullptr_t> = nullptr>
inline u32 hash(const D& dat) const {
return inner_hash(dat);
}
template <
typename D = Data,
enable_if_t<is_same<decltype(D::first), Key>::value, nullptr_t> = nullptr>
inline u32 hash(const D& dat) const {
return inner_hash(dat.first);
}
template <typename D = Data,
enable_if_t<is_same<D, Key>::value, nullptr_t> = nullptr>
inline Key data_to_key(const D& dat) const {
return dat;
}
template <
typename D = Data,
enable_if_t<is_same<decltype(D::first), Key>::value, nullptr_t> = nullptr>
inline Key data_to_key(const D& dat) const {
return dat.first;
}
void reallocate(u32 ncap) {
vector<Data> ndata(ncap);
vector<bool> nf(ncap);
shift = 64 - __lg(ncap);
for (u32 i = 0; i < cap; i++) {
if (occupied_flag[i] && !deleted_flag[i]) {
u32 h = hash(data[i]);
while (nf[h]) h = (h + 1) & (ncap - 1);
ndata[h] = move(data[i]);
nf[h] = true;
}
}
data.swap(ndata);
occupied_flag.swap(nf);
cap = ncap;
occupied = s;
deleted_flag.resize(cap);
fill(std::begin(deleted_flag), std::end(deleted_flag), false);
}
inline bool extend_rate(u32 x) const { return x * 2 >= cap; }
inline bool shrink_rate(u32 x) const {
return HASHMAP_DEFAULT_SIZE < cap && x * 10 <= cap;
}
inline void extend() { reallocate(cap << 1); }
inline void shrink() { reallocate(cap >> 1); }
public:
u32 cap, s, occupied;
vector<Data> data;
vector<bool> occupied_flag, deleted_flag;
u32 shift;
static u64 r;
static constexpr uint32_t HASHMAP_DEFAULT_SIZE = 4;
explicit HashMapBase()
: cap(HASHMAP_DEFAULT_SIZE),
s(0),
occupied(0),
data(cap),
occupied_flag(cap),
deleted_flag(cap),
shift(64 - __lg(cap)) {}
itr begin() const {
u32 h = 0;
while (h != cap) {
if (occupied_flag[h] && !deleted_flag[h]) break;
h++;
}
return itr(h, this);
}
itr end() const { return itr(this->cap, this); }
friend itr begin(const HashMapBase& h) { return h.begin(); }
friend itr end(const HashMapBase& h) { return h.end(); }
itr find(const Key& key) const {
u32 h = inner_hash(key);
while (true) {
if (occupied_flag[h] == false) return this->end();
if (data_to_key(data[h]) == key) {
if (deleted_flag[h] == true) return this->end();
return itr(h, this);
}
h = (h + 1) & (cap - 1);
}
}
bool contain(const Key& key) const { return find(key) != this->end(); }
itr insert(const Data& d) {
u32 h = hash(d);
while (true) {
if (occupied_flag[h] == false) {
if (extend_rate(occupied + 1)) {
extend();
h = hash(d);
continue;
}
data[h] = d;
occupied_flag[h] = true;
++occupied, ++s;
return itr(h, this);
}
if (data_to_key(data[h]) == data_to_key(d)) {
if (deleted_flag[h] == true) {
data[h] = d;
deleted_flag[h] = false;
++s;
}
return itr(h, this);
}
h = (h + 1) & (cap - 1);
}
}
// tips for speed up :
// if return value is unnecessary, make argument_2 false.
itr erase(itr it, bool get_next = true) {
if (it == this->end()) return this->end();
s--;
if (!get_next) {
this->deleted_flag[it.i] = true;
if (shrink_rate(s)) shrink();
return this->end();
}
itr nxt = it;
nxt++;
this->deleted_flag[it.i] = true;
if (shrink_rate(s)) {
Data d = data[nxt.i];
shrink();
it = find(data_to_key(d));
}
return nxt;
}
itr erase(const Key& key) { return erase(find(key)); }
int count(const Key& key) { return find(key) == end() ? 0 : 1; }
bool empty() const { return s == 0; }
int size() const { return s; }
void clear() {
fill(std::begin(occupied_flag), std::end(occupied_flag), false);
fill(std::begin(deleted_flag), std::end(deleted_flag), false);
s = occupied = 0;
}
void reserve(int n) {
if (n <= 0) return;
n = 1 << min(23, __lg(n) + 2);
if (cap < u32(n)) reallocate(n);
}
};
template <typename Key, typename Data>
uint64_t HashMapBase<Key, Data>::r =
chrono::duration_cast<chrono::nanoseconds>(
chrono::high_resolution_clock::now().time_since_epoch())
.count();
} // namespace HashMapImpl
/**
* @brief Hash Map(base) (ハッシュマップ・基底クラス)
*/
#line 4 "hashmap/hashmap.hpp"
template <typename Key, typename Val>
struct HashMap : HashMapImpl::HashMapBase<Key, pair<Key, Val>> {
using base = typename HashMapImpl::HashMapBase<Key, pair<Key, Val>>;
using HashMapImpl::HashMapBase<Key, pair<Key, Val>>::HashMapBase;
using Data = pair<Key, Val>;
Val& operator[](const Key& k) {
typename base::u32 h = base::inner_hash(k);
while (true) {
if (base::occupied_flag[h] == false) {
if (base::extend_rate(base::occupied + 1)) {
base::extend();
h = base::hash(k);
continue;
}
base::data[h].first = k;
base::data[h].second = Val();
base::occupied_flag[h] = true;
++base::occupied, ++base::s;
return base::data[h].second;
}
if (base::data[h].first == k) {
if (base::deleted_flag[h] == true) {
base::data[h].second = Val();
base::deleted_flag[h] = false;
++base::s;
}
return base::data[h].second;
}
h = (h + 1) & (base::cap - 1);
}
}
typename base::itr emplace(const Key& key, const Val& val) {
return base::insert(Data(key, val));
}
};
/*
* @brief ハッシュマップ(連想配列)
* @docs docs/hashmap/hashmap.md
**/
#line 5 "graph/offline-dynamic-connectivity.hpp"
struct OffLineDynamicConnectivity {
int N, Q, segsz;
RollbackUnionFind uf;
vector<vector<pair<int, int>>> seg, qadd, qdel;
HashMap<pair<int, int>, pair<int, int>> cnt;
OffLineDynamicConnectivity(int n, int q)
: N(n), Q(q), uf(n), qadd(q), qdel(q) {
segsz = 1;
while (segsz < Q) segsz *= 2;
seg.resize(segsz * 2);
}
void add_edge(int t, int u, int v) { qadd[t].emplace_back(u, v); }
void del_edge(int t, int u, int v) { qdel[t].emplace_back(u, v); }
void build() {
for (int i = 0; i < Q; i++) {
for (auto& e : qadd[i]) {
auto& dat = cnt[e];
if (dat.second++ == 0) dat.first = i;
}
for (auto& e : qdel[i]) {
auto& dat = cnt[e];
if (--dat.second == 0) segment(e, dat.first, i);
}
}
for (auto& [e, dat] : cnt) {
if (dat.second != 0) segment(e, dat.first, Q);
}
}
template <typename ADD, typename DEL, typename QUERY>
void dfs(const ADD& add, const DEL& del, const QUERY& query, int id, int l,
int r) {
if (Q <= l) return;
int state = uf.get_state();
vector<pair<int, int>> es;
for (auto& [u, v] : seg[id]) {
if (!uf.same(u, v)) {
uf.unite(u, v);
add(u, v);
es.emplace_back(u, v);
}
}
if (l + 1 == r) {
query(l);
} else {
dfs(add, del, query, id * 2 + 0, l, (l + r) >> 1);
dfs(add, del, query, id * 2 + 1, (l + r) >> 1, r);
}
for (auto& [u, v] : es) del(u, v);
uf.rollback(state);
}
template <typename ADD, typename DEL, typename QUERY>
void run(const ADD& add, const DEL& del, const QUERY& query) {
dfs(add, del, query, 1, 0, segsz);
}
private:
void segment(pair<int, int>& e, int l, int r) {
int L = l + segsz;
int R = r + segsz;
while (L < R) {
if (L & 1) seg[L++].push_back(e);
if (R & 1) seg[--R].push_back(e);
L >>= 1, R >>= 1;
}
}
};
#line 2 "lct/link-cut-tree-subtree.hpp"
#line 2 "lct/reversible-bbst-base.hpp"
template <typename Tree, typename Node, typename T, T (*f)(T, T), T (*ts)(T)>
struct ReversibleBBST : Tree {
using Tree::merge;
using Tree::split;
using typename Tree::Ptr;
ReversibleBBST() = default;
virtual void toggle(Ptr t) {
if(!t) return;
swap(t->l, t->r);
t->sum = ts(t->sum);
t->rev ^= true;
}
T fold(Ptr &t, int a, int b) {
auto x = split(t, a);
auto y = split(x.second, b - a);
auto ret = sum(y.first);
t = merge(x.first, merge(y.first, y.second));
return ret;
}
void reverse(Ptr &t, int a, int b) {
auto x = split(t, a);
auto y = split(x.second, b - a);
toggle(y.first);
t = merge(x.first, merge(y.first, y.second));
}
Ptr update(Ptr t) override {
if (!t) return t;
t->cnt = 1;
t->sum = t->key;
if (t->l) t->cnt += t->l->cnt, t->sum = f(t->l->sum, t->sum);
if (t->r) t->cnt += t->r->cnt, t->sum = f(t->sum, t->r->sum);
return t;
}
protected:
inline T sum(const Ptr t) { return t ? t->sum : T(); }
void push(Ptr t) override {
if (!t) return;
if (t->rev) {
if (t->l) toggle(t->l);
if (t->r) toggle(t->r);
t->rev = false;
}
}
};
/**
* @brief 反転可能平衡二分木(基底クラス)
*/
#line 2 "lct/splay-base.hpp"
template <typename Node>
struct SplayTreeBase {
using Ptr = Node *;
template <typename... Args>
Ptr my_new(const Args &...args) {
return new Node(args...);
}
void my_del(Ptr p) { delete p; }
bool is_root(Ptr t) { return !(t->p) || (t->p->l != t && t->p->r != t); }
int size(Ptr t) const { return count(t); }
virtual void splay(Ptr t) {
if (!t) return;
push(t);
while (!is_root(t)) {
Ptr q = t->p;
if (is_root(q)) {
push(q), push(t);
rot(t);
} else {
Ptr r = q->p;
push(r), push(q), push(t);
if (pos(q) == pos(t))
rot(q), rot(t);
else
rot(t), rot(t);
}
}
}
Ptr get_left(Ptr t) {
while (t->l) push(t), t = t->l;
return t;
}
Ptr get_right(Ptr t) {
while (t->r) push(t), t = t->r;
return t;
}
pair<Ptr, Ptr> split(Ptr t, int k) {
if (!t) return {nullptr, nullptr};
if (k == 0) return {nullptr, t};
if (k == count(t)) return {t, nullptr};
push(t);
if (k <= count(t->l)) {
auto x = split(t->l, k);
t->l = x.second;
t->p = nullptr;
if (x.second) x.second->p = t;
return {x.first, update(t)};
} else {
auto x = split(t->r, k - count(t->l) - 1);
t->r = x.first;
t->p = nullptr;
if (x.first) x.first->p = t;
return {update(t), x.second};
}
}
Ptr merge(Ptr l, Ptr r) {
if (!l && !r) return nullptr;
if (!l) return splay(r), r;
if (!r) return splay(l), l;
splay(l), splay(r);
l = get_right(l);
splay(l);
l->r = r;
r->p = l;
update(l);
return l;
}
using Key = decltype(Node::key);
Ptr build(const vector<Key> &v) { return build(0, v.size(), v); }
Ptr build(int l, int r, const vector<Key> &v) {
if (l == r) return nullptr;
if (l + 1 == r) return my_new(v[l]);
return merge(build(l, (l + r) >> 1, v), build((l + r) >> 1, r, v));
}
template <typename... Args>
void insert(Ptr &t, int k, const Args &...args) {
splay(t);
auto x = split(t, k);
t = merge(merge(x.first, my_new(args...)), x.second);
}
void erase(Ptr &t, int k) {
splay(t);
auto x = split(t, k);
auto y = split(x.second, 1);
my_del(y.first);
t = merge(x.first, y.second);
}
virtual Ptr update(Ptr t) = 0;
protected:
inline int count(Ptr t) const { return t ? t->cnt : 0; }
virtual void push(Ptr t) = 0;
Ptr build(const vector<Ptr> &v) { return build(0, v.size(), v); }
Ptr build(int l, int r, const vector<Ptr> &v) {
if (l + 1 >= r) return v[l];
return merge(build(l, (l + r) >> 1, v), build((l + r) >> 1, r, v));
}
inline int pos(Ptr t) {
if (t->p) {
if (t->p->l == t) return -1;
if (t->p->r == t) return 1;
}
return 0;
}
virtual void rot(Ptr t) {
Ptr x = t->p, y = x->p;
if (pos(t) == -1) {
if ((x->l = t->r)) t->r->p = x;
t->r = x, x->p = t;
} else {
if ((x->r = t->l)) t->l->p = x;
t->l = x, x->p = t;
}
update(x), update(t);
if ((t->p = y)) {
if (y->l == x) y->l = t;
if (y->r == x) y->r = t;
}
}
};
/**
* @brief Splay Tree(base)
*/
#line 5 "lct/link-cut-tree-subtree.hpp"
template <typename T, T (*f)(T, T), T (*finv)(T, T)>
struct LinkCutForSubtreeNode {
using Node = LinkCutForSubtreeNode;
using Ptr = LinkCutForSubtreeNode*;
Ptr l, r, p;
T key, sum, sub;
int cnt;
bool rev;
LinkCutForSubtreeNode(const T& t = T())
: l(), r(), p(), key(t), sum(t), sub(T()), cnt(1), rev(false) {}
void add(Node* other) { sub = f(sub, other->sum); }
void erase(Node* other) { sub = finv(sub, other->sum); }
void merge(Node* n1, Node* n2) {
sum = f(f(n1 ? n1->sum : T(), key), f(sub, n2 ? n2->sum : T()));
}
};
template <typename T, T (*f)(T, T), T (*finv)(T, T)>
struct SplayTreeForLCSubtree
: ReversibleBBST<SplayTreeBase<LinkCutForSubtreeNode<T, f, finv>>,
LinkCutForSubtreeNode<T, f, finv>, T, nullptr, nullptr> {
using Node = LinkCutForSubtreeNode<T, f, finv>;
};
//
#line 2 "lct/link-cut-base.hpp"
template <typename Splay>
struct LinkCutBase : Splay {
using Node = typename Splay::Node;
using Ptr = Node*;
virtual Ptr expose(Ptr t) {
Ptr rp = nullptr;
for (Ptr cur = t; cur; cur = cur->p) {
this->splay(cur);
cur->r = rp;
this->update(cur);
rp = cur;
}
this->splay(t);
return rp;
}
virtual void link(Ptr u, Ptr v) {
evert(u);
expose(v);
u->p = v;
}
void cut(Ptr u, Ptr v) {
evert(u);
expose(v);
assert(u->p == v);
v->l = u->p = nullptr;
this->update(v);
}
void evert(Ptr t) {
expose(t);
this->toggle(t);
this->push(t);
}
Ptr lca(Ptr u, Ptr v) {
if (get_root(u) != get_root(v)) return nullptr;
expose(u);
return expose(v);
}
Ptr get_kth(Ptr x, int k) {
expose(x);
while (x) {
this->push(x);
if (x->r && x->r->sz > k) {
x = x->r;
} else {
if (x->r) k -= x->r->sz;
if (k == 0) return x;
k -= 1;
x = x->l;
}
}
return nullptr;
}
Ptr get_root(Ptr x) {
expose(x);
while (x->l) this->push(x), x = x->l;
return x;
}
Ptr get_parent(Ptr x) {
expose(x);
Ptr p = x->l;
if(p == nullptr) return nullptr;
while (true) {
this->push(p);
if (p->r == nullptr) return p;
p = p->r;
}
exit(1);
}
virtual void set_key(Ptr t, const decltype(Node::key)& key) {
this->splay(t);
t->key = key;
this->update(t);
}
virtual decltype(Node::key) get_key(Ptr t) { return t->key; }
decltype(Node::key) fold(Ptr u, Ptr v) {
evert(u);
expose(v);
return v->sum;
}
};
/**
* @brief Link/Cut Tree(base)
* @docs docs/lct/link-cut-tree.md
*/
#line 32 "lct/link-cut-tree-subtree.hpp"
template <typename T, T (*f)(T, T), T (*finv)(T, T)>
struct LinkCutTreeSubtreeQuery
: LinkCutBase<SplayTreeForLCSubtree<T, f, finv>> {
using base = LinkCutBase<SplayTreeForLCSubtree<T, f, finv>>;
using Node = typename base::Node;
using Ptr = typename base::Ptr;
Ptr expose(Ptr t) override {
Ptr rp = nullptr;
for (Ptr cur = t; cur; cur = cur->p) {
this->splay(cur);
if (cur->r) cur->add(cur->r);
cur->r = rp;
if (cur->r) cur->erase(cur->r);
this->update(cur);
rp = cur;
}
this->splay(t);
return rp;
}
void link(Ptr u, Ptr v) override {
this->evert(u);
this->expose(v);
u->p = v;
v->add(u);
}
void toggle(Ptr t) override {
if(!t) return;
swap(t->l, t->r);
t->rev ^= true;
}
Ptr update(Ptr t) override {
if (!t) return t;
t->cnt = 1 + this->count(t->l) + this->count(t->r);
t->merge(t->l, t->r);
return t;
}
void set_key(Ptr t, const T& key) override {
this->expose(t);
t->key = key;
this->update(t);
}
T subtree(Ptr t) {
this->expose(t);
return f(t->key, t->sub);
}
};
/**
* @brief 部分木クエリLink/Cut Tree
*/
#line 8 "verify/verify-yosupo-ds/yosupo-offline-dynamic-connectivity.test.cpp"
using namespace Nyaan;
ll add(ll a, ll b) { return a + b; }
ll sub(ll a, ll b) { return a - b; }
void Nyaan::solve() {
ini(N, Q);
vl a(N);
in(a);
vl cmd(Q), X(Q), Y(Q);
rep(i, Q) {
in(cmd[i], X[i]);
if (cmd[i] != 3) in(Y[i]);
if (cmd[i] < 2 and X[i] > Y[i]) swap(X[i], Y[i]);
}
using LCT = LinkCutTreeSubtreeQuery<ll, add, sub>;
LCT lct;
vector<LCT::Node*> vs(N);
rep(i, N) vs[i] = new LCT::Node(a[i]);
OffLineDynamicConnectivity dc(N, Q);
rep(i, Q) {
if (cmd[i] == 0) dc.add_edge(i, X[i], Y[i]);
if (cmd[i] == 1) dc.del_edge(i, X[i], Y[i]);
}
dc.build();
vl ans;
auto add = [&](int u, int v) { lct.link(vs[u], vs[v]); };
auto del = [&](int u, int v) { lct.cut(vs[u], vs[v]); };
auto query = [&](int i) {
if (cmd[i] == 2) {
ll k = lct.get_key(vs[X[i]]);
lct.set_key(vs[X[i]], k + Y[i]);
} else if (cmd[i] == 3) {
lct.evert(vs[X[i]]);
ans.emplace_back(lct.subtree(vs[X[i]]));
}
};
dc.run(add, del, query);
each(x, ans) out(x);
}
verify/verify-yosupo-ds/yosupo-offline-dynamic-connectivity.test.cpp