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test/yukicoder/772.test.cpp
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- Last update: 2024-04-27 11:55:26+09:00
- Problem: https://yukicoder.me/problems/no/772
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Code
#define PROBLEM "https://yukicoder.me/problems/no/772"
#include "my_template.hpp"
#include "other/io.hpp"
#include "graph/ds/link_cut_tree.hpp"
#include "ds/removable_queue.hpp"
struct Node {
using np = Node *;
struct VX {
bool is_edge = false;
ll x = 0; // 頂点なら X[v], 辺なら長さ
};
// (wt, light edge の接続先)
struct MX {
Removable_Queue<pq<pair<ll, int>>> que;
ll sm = 0;
ll dist_sum = 0;
};
struct X {
ll wt_sum;
ll length; // heavy path len
ll sum1, sum2; // heavy path の端点からの dist sum
};
Node *l, *r, *p;
int idx, size; // size は heavy path の頂点数
bool rev;
VX vx;
MX mx;
X x;
Node(int i = 0)
: l(nullptr), r(nullptr), p(nullptr), idx(i), size(1), rev(0) {}
void update() {
size = 1;
x.wt_sum = (vx.is_edge ? 0 : vx.x);
x.wt_sum += mx.sm;
if (l) {
size += l->size;
x.wt_sum += l->x.wt_sum;
}
if (r) {
size += r->size;
x.wt_sum += r->x.wt_sum;
}
ll l_len = (l ? l->x.length : 0);
ll m_len = (vx.is_edge ? vx.x : 0);
ll r_len = (r ? r->x.length : 0);
x.length = l_len + m_len + r_len;
x.sum1 = 0, x.sum2 = 0;
x.sum1 += mx.sm * (l_len + m_len) + mx.dist_sum;
x.sum2 += mx.sm * (r_len + m_len) + mx.dist_sum;
x.sum1 += (vx.is_edge ? 0 : vx.x * l_len);
x.sum2 += (vx.is_edge ? 0 : vx.x * r_len);
if (l) {
x.sum1 += l->x.sum1;
x.sum2 += l->x.sum2 + (m_len + r_len) * l->x.wt_sum;
}
if (r) {
x.sum2 += r->x.sum2;
x.sum1 += r->x.sum1 + (m_len + l_len) * r->x.wt_sum;
}
}
void push() {
if (rev) {
if (l) l->reverse();
if (r) r->reverse();
rev = 0;
}
}
// data の reverse も行う
void reverse() {
rev ^= 1;
swap(l, r);
swap(x.sum1, x.sum2);
}
// LCT 内で expose, update を行うのでここは変更だけ
void set(VX x) { vx = x; }
// c がこの時点では update されていないかもしれないが, x は正常なものが入る
// c->x 等は使わないように注意する
// c->idx を持っておくと探索できることがある
void add_light(Node *c) {
auto x = c->x;
mx.sm += x.wt_sum;
mx.que.push(mp(x.wt_sum, c->idx));
mx.dist_sum += x.sum1;
}
void erase_light(Node *c) {
auto x = c->x;
mx.sm -= x.wt_sum;
mx.que.remove(mp(x.wt_sum, c->idx));
mx.dist_sum -= x.sum1;
}
void change_light(np a, np b) {
auto sm = b->x.wt_sum;
mx.que.remove(mp(sm, a->idx));
mx.que.push(mp(sm, b->idx));
}
};
void solve() {
LL(N, Q);
Link_Cut_Tree<Node> LCT(N + Q);
vi X(N, 1);
FOR(i, N) { LCT.set(i, {false, 1}); }
int pid = N;
ll SUM_ANS = 0;
auto read_vertex = [&]() -> ll {
LL(x);
return (x - 1 + SUM_ANS) % N;
};
auto solve_1 = [&](int a, int b, int c) -> void {
int idx = pid++;
LCT.set(idx, {true, c});
LCT.link(a, idx), LCT.link(b, idx);
};
auto solve_2 = [&](int a, int b) -> void {
int c = LCT.jump(a, b, 1);
LCT.cut(a, c), LCT.cut(b, c);
};
auto solve_3 = [&](int a) -> ll {
X[a] ^= 1;
LCT.set(a, {false, X[a]});
LCT.evert(a);
ll total = LCT[a]->x.wt_sum;
if (total == 0) return 0;
ll half = ceil<ll>(total, 2);
// half 以上の重みを持つ subtree で topological 順で極大なところ
using np = typename decltype(LCT)::np;
auto dfs = [&](auto &dfs, np c, ll need) -> np {
c->push();
assert(c->x.wt_sum >= need);
// ll a = (c->l ? c->l->x.wt_sum : 0);
ll b = (c->r ? c->r->x.wt_sum : 0);
ll me = (c->vx.is_edge ? 0 : c->vx.x);
ll mid = c->mx.sm;
if (me + mid + b >= need) {
if (b >= need) { return dfs(dfs, c->r, need); }
if (mid >= half) {
auto [val, idx] = c->mx.que.top();
if (val >= half) return dfs(dfs, LCT[idx], half);
}
return c;
}
return dfs(dfs, c->l, need - (me + mid + b));
};
np c = dfs(dfs, LCT[a], half);
LCT.evert(c);
return c->x.sum1;
};
FOR(q, Q) {
INT(t);
if (t == 1) {
ll a = read_vertex();
ll b = read_vertex();
LL(c);
solve_1(a, b, c);
}
if (t == 2) {
ll a = read_vertex();
ll b = read_vertex();
solve_2(a, b);
}
if (t == 3) {
ll a = read_vertex();
ll ans = solve_3(a);
print(ans);
SUM_ANS += ans;
SUM_ANS %= N;
}
}
}
signed main() {
solve();
return 0;
}#line 1 "test/yukicoder/772.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/772"
#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
// https://codeforces.com/blog/entry/96344
#pragma GCC optimize("Ofast,unroll-loops")
// いまの CF だとこれ入れると動かない？
// #pragma GCC target("avx2,popcnt")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;
using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
#define vv(type, name, h, ...) \
vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) \
vector<vector<vector<type>>> name( \
h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
vector<vector<vector<vector<type>>>> name( \
a, vector<vector<vector<type>>>( \
b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#define FOR_subset(t, s) \
for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define stoi stoll
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T>
T floor(T a, T b) {
return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
T q = floor(x, y);
return {q, x - q * y};
}
template <typename T, typename U>
T SUM(const vector<U> &A) {
T sm = 0;
for (auto &&a: A) sm += a;
return sm;
}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) \
sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()
template <typename T>
T POP(deque<T> &que) {
T a = que.front();
que.pop_front();
return a;
}
template <typename T>
T POP(pq<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(pqg<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(vc<T> &que) {
T a = que.back();
que.pop_back();
return a;
}
template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
if (check_ok) assert(check(ok));
while (abs(ok - ng) > 1) {
auto x = (ng + ok) / 2;
(check(x) ? ok : ng) = x;
}
return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
FOR(iter) {
double x = (ok + ng) / 2;
(check(x) ? ok : ng) = x;
}
return (ok + ng) / 2;
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
vc<int> A(S.size());
FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
return A;
}
template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
int N = A.size();
vector<T> B(N + 1);
FOR(i, N) { B[i + 1] = B[i] + A[i]; }
if (off == 0) B.erase(B.begin());
return B;
}
// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
vector<int> ids(len(A));
iota(all(ids), 0);
sort(all(ids),
[&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
return ids;
}
// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
vc<T> B(len(I));
FOR(i, len(I)) B[i] = A[I[i]];
return B;
}
#endif
#line 1 "other/io.hpp"
#define FASTIO
#include <unistd.h>
// https://judge.yosupo.jp/submission/21623
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;
struct Pre {
char num[10000][4];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i][j] = n % 10 | '0';
n /= 10;
}
}
}
} constexpr pre;
inline void load() {
memcpy(ibuf, ibuf + pil, pir - pil);
pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
pil = 0;
if (pir < SZ) ibuf[pir++] = '\n';
}
inline void flush() {
fwrite(obuf, 1, por, stdout);
por = 0;
}
void rd(char &c) {
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
}
void rd(string &x) {
x.clear();
char c;
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
do {
x += c;
if (pil == pir) load();
c = ibuf[pil++];
} while (!isspace(c));
}
template <typename T>
void rd_real(T &x) {
string s;
rd(s);
x = stod(s);
}
template <typename T>
void rd_integer(T &x) {
if (pil + 100 > pir) load();
char c;
do
c = ibuf[pil++];
while (c < '-');
bool minus = 0;
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (c == '-') { minus = 1, c = ibuf[pil++]; }
}
x = 0;
while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (minus) x = -x;
}
}
void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }
template <class T, class U>
void rd(pair<T, U> &p) {
return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
rd(x);
rd_tuple<N + 1>(t);
}
}
template <class... T>
void rd(tuple<T...> &tpl) {
rd_tuple(tpl);
}
template <size_t N = 0, typename T>
void rd(array<T, N> &x) {
for (auto &d: x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
for (auto &d: x) rd(d);
}
void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
rd(h), read(t...);
}
void wt(const char c) {
if (por == SZ) flush();
obuf[por++] = c;
}
void wt(const string s) {
for (char c: s) wt(c);
}
void wt(const char *s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++) wt(s[i]);
}
template <typename T>
void wt_integer(T x) {
if (por > SZ - 100) flush();
if (x < 0) { obuf[por++] = '-', x = -x; }
int outi;
for (outi = 96; x >= 10000; outi -= 4) {
memcpy(out + outi, pre.num[x % 10000], 4);
x /= 10000;
}
if (x >= 1000) {
memcpy(obuf + por, pre.num[x], 4);
por += 4;
} else if (x >= 100) {
memcpy(obuf + por, pre.num[x] + 1, 3);
por += 3;
} else if (x >= 10) {
int q = (x * 103) >> 10;
obuf[por] = q | '0';
obuf[por + 1] = (x - q * 10) | '0';
por += 2;
} else
obuf[por++] = x | '0';
memcpy(obuf + por, out + outi + 4, 96 - outi);
por += 96 - outi;
}
template <typename T>
void wt_real(T x) {
ostringstream oss;
oss << fixed << setprecision(15) << double(x);
string s = oss.str();
wt(s);
}
void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }
template <class T, class U>
void wt(const pair<T, U> val) {
wt(val.first);
wt(' ');
wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) { wt(' '); }
const auto x = std::get<N>(t);
wt(x);
wt_tuple<N + 1>(t);
}
}
template <class... T>
void wt(tuple<T...> tpl) {
wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt(' ');
wt(val[i]);
}
}
template <class T>
void wt(const vector<T> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt(' ');
wt(val[i]);
}
}
void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
wt(head);
if (sizeof...(Tail)) wt(' ');
print(forward<Tail>(tail)...);
}
// gcc expansion. called automaticall after main.
void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio
using fastio::read;
using fastio::print;
using fastio::flush;
#define INT(...) \
int __VA_ARGS__; \
read(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
read(__VA_ARGS__)
#define U32(...) \
u32 __VA_ARGS__; \
read(__VA_ARGS__)
#define U64(...) \
u64 __VA_ARGS__; \
read(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
read(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
read(name)
#define VV(type, name, h, w) \
vector<vector<type>> name(h, vector<type>(w)); \
read(name)
void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 4 "test/yukicoder/772.test.cpp"
#line 1 "graph/ds/link_cut_tree.hpp"
/*
各 heavy path を head が左, tail が右となるように splay tree で持つ.
ユーザーが直接呼ぶ可能性があるものだけ int でも実装.
LCT 外で探索するときなど，push を忘れないように注意.
*/
template <typename Node>
struct Link_Cut_Tree {
using np = Node *;
int n;
vc<Node> nodes;
Link_Cut_Tree(int n = 0) : n(n), nodes(n) { FOR(i, n) nodes[i] = Node(i); }
Node *operator[](int v) { return &nodes[v]; }
// underlying tree の根
Node *get_root(Node *c) {
expose(c);
c->push();
while (c->l) {
c = c->l;
c->push();
}
splay(c);
return c;
}
// underlying tree の根
int get_root(int c) { return get_root(&nodes[c])->idx; }
// parent(c)==p となるように link.
void link(Node *c, Node *p) {
evert(c);
expose(p);
p->push();
// no edge -> heavy edge
assert(!(c->p));
assert(!(p->r));
c->p = p;
p->r = c;
p->update();
}
// parent(c)==p となるように link.
void link(int c, int p) { return link(&nodes[c], &nodes[p]); }
void cut(Node *a, Node *b) {
evert(a);
expose(b);
assert(!b->p);
assert((b->l) == a);
// heavy edge -> no edge
b->l->p = nullptr;
b->l = nullptr;
b->update();
}
void cut(int a, int b) { return cut(&nodes[a], &nodes[b]); }
// c を underlying tree の根とする.
// c は splay tree の根にもなる.
// c は push 済になる
void evert(Node *c) {
expose(c);
c->reverse();
c->push();
}
// c を underlying tree の根とする.
// c は splay tree の根にもなる.
void evert(int c) { evert(&nodes[c]); }
Node *lca(Node *u, Node *v) {
assert(get_root(u) == get_root(v));
expose(u);
return expose(v);
}
int lca(int u, int v) { return lca(&nodes[u], &nodes[v])->idx; }
// 辺の個数
int dist(int u, int v) {
evert(u), expose(v);
return ((*this)[v]->size) - 1;
}
Node *jump(Node *u, Node *v, int k) {
evert(v);
expose(u);
assert(0 <= k && k < (u->size));
while (1) {
u->push();
int rs = (u->r ? u->r->size : 0);
if (k < rs) {
u = u->r;
continue;
}
if (k == rs) { break; }
k -= rs + 1;
u = u->l;
}
splay(u);
return u;
}
int jump(int u, int v, int k) {
auto c = jump((*this)[u], (*this)[v], k);
return c->idx;
}
// [root, c] がひとつの splay tree になるように変更する.
// c が右端で splay tree の根という状態になる.
// path query はこの状態で c の data を見る.
// c は push 済になる
virtual Node *expose(Node *c) {
Node *now = c;
Node *rp = nullptr; // 今まで作ったパス
while (now) {
splay(now);
// heavy -> light, light -> heavy.
if (now->r) { now->add_light(now->r); }
if (rp) { now->erase_light(rp); }
now->r = rp;
now->update();
rp = now;
now = now->p;
}
splay(c);
return rp;
}
// [root, c] がひとつの splay tree になるように変更する.
// c が右端で splay tree の根という状態になる.
// path query はこの状態で c の data を見る.
int expose(int c) {
Node *x = expose(&nodes[c]);
if (!x) return -1;
return x->idx;
}
Node *get_parent(Node *x) {
expose(x);
if (!x->l) return nullptr;
x = x->l;
while (x->r) x = x->r;
return x;
}
int get_parent(int x) {
Node *p = get_parent((*this)[x]);
return (p ? p->idx : -1);
}
void set(Node *c, typename Node::VX x) {
evert(c);
c->set(x);
}
void set(int c, typename Node::VX x) { set((*this)[c], x); }
typename Node::X prod_path(int a, int b) {
evert(a), expose(b);
return (*this)[b]->x;
}
// subtree 用の node を使う
typename Node::X prod_subtree(int v, int root) {
static_assert(Node::NODE_FOR_SUBTREE);
if (v == root) {
evert(root);
return (*this)[root]->x;
}
root = jump(v, root, 1);
cut(v, root);
typename Node::X res = (*this)[v]->x;
link(v, root);
return res;
}
vc<int> collect_heavy_path(int v) {
np c = (*this)[v];
while (!is_root(c)) c = c->p;
vc<int> res;
auto dfs = [&](auto &dfs, np c, bool rev) -> void {
if (!rev) {
if (c->l) dfs(dfs, c->l, rev ^ c->rev);
res.eb(c->idx);
if (c->r) dfs(dfs, c->r, rev ^ c->rev);
} else {
if (c->r) dfs(dfs, c->r, rev ^ c->rev);
res.eb(c->idx);
if (c->l) dfs(dfs, c->l, rev ^ c->rev);
}
};
dfs(dfs, c, false);
return res;
}
void debug() {
print("p, l, r, rev");
auto f = [&](np c) -> int { return (c ? c->idx : -1); };
FOR(i, len(nodes)) {
print(i, ",", f((*this)[i]->p), f((*this)[i]->l), f((*this)[i]->r),
(*this)[i]->rev);
}
FOR(i, len(nodes)) {
np c = (*this)[i];
if (c->l) assert(c->l->p == c);
if (c->r) assert(c->r->p == c);
}
}
private:
// splay tree 内で完結する操作. 特に heavy, light 構造は変わらない.
// light pointer は rotate 内でケア
// c は push 済になる
void splay(Node *c) {
c->push();
while (!is_root(c)) {
Node *p = c->p;
Node *pp = (p ? p->p : nullptr);
if (state(p) == 0) {
p->push(), c->push();
rotate(c);
}
elif (state(c) == state(p)) {
pp->push(), p->push(), c->push();
rotate(p);
rotate(c);
}
else {
pp->push(), p->push(), c->push();
rotate(c);
rotate(c);
}
}
}
// パスを表す splay tree の根になっているかどうか
// underlying tree ではない
bool is_root(Node *c) { return state(c) == 0; }
// splay tree 内で完結する操作. 特に heavy, light 構造は変わらない.
// light edge のポインタは変更されうる
void rotate(Node *n) {
// n を根に近づける
Node *pp, *p, *c;
p = n->p;
pp = p->p;
if (p->l == n) {
c = n->r;
n->r = p;
p->l = c;
} else {
c = n->l;
n->l = p;
p->r = c;
}
p->update(), n->update();
if (pp) {
if (pp->l == p) pp->l = n;
elif (pp->r == p) pp->r = n;
else {
// light edge pointer が (pp-p) から (pp-n) に変わる
pp->change_light(p, n);
}
}
n->p = pp;
p->p = n;
if (c) c->p = p;
}
inline int state(Node *n) {
if (!n->p) return 0;
if (n->p->l == n) return 1;
if (n->p->r == n) return -1;
return 0;
}
};
#line 6 "test/yukicoder/772.test.cpp"
#line 2 "ds/removable_queue.hpp"
template <typename QUE_TYPE>
struct Removable_Queue {
using QUE = QUE_TYPE;
using T = typename QUE::value_type;
QUE que, rm_que;
Removable_Queue() {}
Removable_Queue(vc<T>& dat) : que(all(dat)) {}
void push(T x) { que.push(x); }
int size() { return len(que) - len(rm_que); }
bool empty() { return size() == 0; }
T pop() {
refresh();
return POP(que);
}
T top() {
refresh();
return que.top();
}
void remove(T x) { rm_que.push(x); }
private:
void refresh() {
while (len(rm_que) && rm_que.top() == que.top()) {
rm_que.pop(), que.pop();
}
}
};
#line 8 "test/yukicoder/772.test.cpp"
struct Node {
using np = Node *;
struct VX {
bool is_edge = false;
ll x = 0; // 頂点なら X[v], 辺なら長さ
};
// (wt, light edge の接続先)
struct MX {
Removable_Queue<pq<pair<ll, int>>> que;
ll sm = 0;
ll dist_sum = 0;
};
struct X {
ll wt_sum;
ll length; // heavy path len
ll sum1, sum2; // heavy path の端点からの dist sum
};
Node *l, *r, *p;
int idx, size; // size は heavy path の頂点数
bool rev;
VX vx;
MX mx;
X x;
Node(int i = 0)
: l(nullptr), r(nullptr), p(nullptr), idx(i), size(1), rev(0) {}
void update() {
size = 1;
x.wt_sum = (vx.is_edge ? 0 : vx.x);
x.wt_sum += mx.sm;
if (l) {
size += l->size;
x.wt_sum += l->x.wt_sum;
}
if (r) {
size += r->size;
x.wt_sum += r->x.wt_sum;
}
ll l_len = (l ? l->x.length : 0);
ll m_len = (vx.is_edge ? vx.x : 0);
ll r_len = (r ? r->x.length : 0);
x.length = l_len + m_len + r_len;
x.sum1 = 0, x.sum2 = 0;
x.sum1 += mx.sm * (l_len + m_len) + mx.dist_sum;
x.sum2 += mx.sm * (r_len + m_len) + mx.dist_sum;
x.sum1 += (vx.is_edge ? 0 : vx.x * l_len);
x.sum2 += (vx.is_edge ? 0 : vx.x * r_len);
if (l) {
x.sum1 += l->x.sum1;
x.sum2 += l->x.sum2 + (m_len + r_len) * l->x.wt_sum;
}
if (r) {
x.sum2 += r->x.sum2;
x.sum1 += r->x.sum1 + (m_len + l_len) * r->x.wt_sum;
}
}
void push() {
if (rev) {
if (l) l->reverse();
if (r) r->reverse();
rev = 0;
}
}
// data の reverse も行う
void reverse() {
rev ^= 1;
swap(l, r);
swap(x.sum1, x.sum2);
}
// LCT 内で expose, update を行うのでここは変更だけ
void set(VX x) { vx = x; }
// c がこの時点では update されていないかもしれないが, x は正常なものが入る
// c->x 等は使わないように注意する
// c->idx を持っておくと探索できることがある
void add_light(Node *c) {
auto x = c->x;
mx.sm += x.wt_sum;
mx.que.push(mp(x.wt_sum, c->idx));
mx.dist_sum += x.sum1;
}
void erase_light(Node *c) {
auto x = c->x;
mx.sm -= x.wt_sum;
mx.que.remove(mp(x.wt_sum, c->idx));
mx.dist_sum -= x.sum1;
}
void change_light(np a, np b) {
auto sm = b->x.wt_sum;
mx.que.remove(mp(sm, a->idx));
mx.que.push(mp(sm, b->idx));
}
};
void solve() {
LL(N, Q);
Link_Cut_Tree<Node> LCT(N + Q);
vi X(N, 1);
FOR(i, N) { LCT.set(i, {false, 1}); }
int pid = N;
ll SUM_ANS = 0;
auto read_vertex = [&]() -> ll {
LL(x);
return (x - 1 + SUM_ANS) % N;
};
auto solve_1 = [&](int a, int b, int c) -> void {
int idx = pid++;
LCT.set(idx, {true, c});
LCT.link(a, idx), LCT.link(b, idx);
};
auto solve_2 = [&](int a, int b) -> void {
int c = LCT.jump(a, b, 1);
LCT.cut(a, c), LCT.cut(b, c);
};
auto solve_3 = [&](int a) -> ll {
X[a] ^= 1;
LCT.set(a, {false, X[a]});
LCT.evert(a);
ll total = LCT[a]->x.wt_sum;
if (total == 0) return 0;
ll half = ceil<ll>(total, 2);
// half 以上の重みを持つ subtree で topological 順で極大なところ
using np = typename decltype(LCT)::np;
auto dfs = [&](auto &dfs, np c, ll need) -> np {
c->push();
assert(c->x.wt_sum >= need);
// ll a = (c->l ? c->l->x.wt_sum : 0);
ll b = (c->r ? c->r->x.wt_sum : 0);
ll me = (c->vx.is_edge ? 0 : c->vx.x);
ll mid = c->mx.sm;
if (me + mid + b >= need) {
if (b >= need) { return dfs(dfs, c->r, need); }
if (mid >= half) {
auto [val, idx] = c->mx.que.top();
if (val >= half) return dfs(dfs, LCT[idx], half);
}
return c;
}
return dfs(dfs, c->l, need - (me + mid + b));
};
np c = dfs(dfs, LCT[a], half);
LCT.evert(c);
return c->x.sum1;
};
FOR(q, Q) {
INT(t);
if (t == 1) {
ll a = read_vertex();
ll b = read_vertex();
LL(c);
solve_1(a, b, c);
}
if (t == 2) {
ll a = read_vertex();
ll b = read_vertex();
solve_2(a, b);
}
if (t == 3) {
ll a = read_vertex();
ll ans = solve_3(a);
print(ans);
SUM_ANS += ans;
SUM_ANS %= N;
}
}
}
signed main() {
solve();
return 0;
}