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test/mytest_auxiliary_tree.test.cpp
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- Last update: 2026-02-03 05:22:52+08:00
- Problem: https://judge.yosupo.jp/problem/aplusb
- Link: View error logs on GitHub Actions
Depends on
default/t.cpp
- ds/RMQ.cpp
- enumerate/enumerate_bit.cpp
- enumerate/enumerate_label_tree.cpp
- enumerate/enumerate_twelvefold.cpp
- enumerate/enumerate_unlabel_rooted_tree.cpp
- tree/LCA.cpp
- tree/auxiliary_tree.cpp
- tree/prufer_recover.cpp
Code
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#include "../default/t.cpp"
#include "../tree/prufer_recover.cpp"
#include "../enumerate/enumerate_bit.cpp"
#include "../enumerate/enumerate_twelvefold.cpp"
#include "../enumerate/enumerate_label_tree.cpp"
#include "../enumerate/enumerate_unlabel_rooted_tree.cpp"
#include "../ds/RMQ.cpp"
#include "../tree/LCA.cpp"
#include "../tree/auxiliary_tree.cpp"
auto auxiliary_tree_brute_force(vvi g, vi vs, int root = 0) {
vc<bool> in_vs(size(g), false);
for(int v : vs) in_vs[v] = true;
vi old_id;
vc<pii> e;
vc<bool> is_critical_node;
auto dfs = [&](int v, int p, auto &self) -> int {
vi head;
for(int x : g[v]) {
if (x == p) continue;
int y = self(x, v, self);
if (y != -1) head.eb(y);
}
if (!in_vs[v] and ssize(head) <= 1)
return head.empty() ? -1 : head[0];
int i = size(old_id);
old_id.emplace_back(v);
is_critical_node.emplace_back(in_vs[v]);
for(int j : head)
e.emplace_back(i, j);
return i;
};
dfs(root, -1, dfs);
return tuple(e, old_id, is_critical_node);
}
void check(vector<vector<int>> g, int root) {
vc<pii> e;
for(int u = 0; u < ssize(g); u++)
for(int v : g[u])
if (u < v)
e.emplace_back(u, v);
auxiliary_tree aux(e, root);
auto check2 = [&](vi vs) {
auto [ep, old_id, crit] = aux.induced_tree(vs);
auto [ep2, old_id2, crit2] = auxiliary_tree_brute_force(g, vs, root);
assert(ssize(old_id) == ssize(old_id2));
assert(set(old_id.begin(), old_id.end()) ==
set(old_id2.begin(), old_id2.end()));
vi val = old_id;
ranges::sort(val);
vi mp(size(g), -1);
for(int i = 0; i < ssize(val); i++)
mp[val[i]] = i;
{
vi p(size(old_id));
for(int i = 0; i < ssize(p); i++)
p[i] = mp[old_id[i]];
for(auto &[u, v] : ep)
u = p[u], v = p[v];
vi tmp(size(old_id));
for(int i = 0; i < ssize(p); i++)
tmp[p[i]] = old_id[i];
old_id.swap(tmp);
vc<bool> tmp2(size(old_id));
for(int i = 0; i < ssize(p); i++)
tmp2[p[i]] = crit[i];
crit.swap(tmp2);
}
{
vi p(size(old_id2));
for(int i = 0; i < ssize(p); i++)
p[i] = mp[old_id2[i]];
for(auto &[u, v] : ep2)
u = p[u], v = p[v];
vi tmp(size(old_id2));
for(int i = 0; i < ssize(p); i++)
tmp[p[i]] = old_id2[i];
old_id2.swap(tmp);
vc<bool> tmp2(size(old_id2));
for(int i = 0; i < ssize(p); i++)
tmp2[p[i]] = crit2[i];
crit2.swap(tmp2);
}
ranges::sort(ep);
ranges::sort(ep2);
assert(old_id == old_id2);
assert(ep == ep2);
assert(crit == crit2);
};
mt19937 rng(clock);
const int n = ssize(g);
if (ssize(g) <= 15) {
for(int msk = 1; msk < (1 << n); msk++) {
vi vs;
for(int i = 0; i < n; i++)
if (msk >> i & 1)
vs.eb(i);
shuffle(vs.begin(), vs.end(), rng);
check2(vs);
}
} else {
for(int sz = 1; sz <= n; sz <<= 1) {
set<int> s;
while(ssize(s) != sz)
s.insert(rng() % n);
vi vs;
for(int x : s) vs.eb(x);
shuffle(vs.begin(), vs.end(), rng);
check2(vs);
}
}
}
auto random_relabel(vector<vector<int>> g) {
mt19937 rng(clock);
const int n = ssize(g);
vector<int> p(n);
iota(p.begin(), p.end(), 0);
shuffle(p.begin(), p.end(), rng);
vector<vector<int>> g2(n);
for(int u = 0; u < n; u++)
for(int v : g[u])
g2[p[u]].eb(p[v]);
return g2;
}
void a_plus_b() {
int a, b; cin >> a >> b;
cout << a + b << '\n';
}
int main() {
ios::sync_with_stdio(false), cin.tie(NULL);
mt19937 rng(clock);
for(int n = 1; n <= 6; n++) {
enumerate_label_tree(n, [&](vector<vector<int>> g) {
for(int r = 0; r < n; r++)
check(g, r);
});
}
for(int n = 7; n <= 8; n++) {
enumerate_unlabel_rooted_tree(n, [&](vector<vector<int>> g) {
for(int r = 0; r < n; r++)
check(g, r);
g = random_relabel(g);
for(int r = 0; r < n; r++)
check(g, r);
});
}
//path
for(int n = 1; n <= 100; n += 2) {
vector<vector<int>> g(n);
for(int i = 1; i < n; i++)
g[i].emplace_back(i - 1), g[i - 1].emplace_back(i);
check(g, 0);
check(random_relabel(g), rng() % n);
}
//star
for(int n = 2; n <= 100; n += 2) {
for(int root : {0, n / 2, n - 1}) {
vector<vector<int>> g(n);
for(int i = 0; i < n; i++)
if (i != root)
g[root].emplace_back(i), g[i].emplace_back(root);
check(g, root);
check(g, root == 0);
}
}
//almost path
for(int tc = 0; tc < 10; tc++) {
int n = 5'000;
vector<vector<int>> g(n);
for(int v = 1; v < n; v++) {
int x = rng() % min(v, 5);
g[v].emplace_back(x), g[x].emplace_back(v);
}
for(int r : {0, n / 2, n - 1})
check(g, r);
g = random_relabel(g);
for(int r : {0, n / 2, n - 1})
check(g, r);
}
a_plus_b();
return 0;
}#line 1 "test/mytest_auxiliary_tree.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#line 1 "default/t.cpp"
#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 <variant>
#include <bit>
#include <compare>
#include <concepts>
#include <numbers>
#include <ranges>
#include <span>
#define INT128_MAX (__int128)(((unsigned __int128) 1 << ((sizeof(__int128) * __CHAR_BIT__) - 1)) - 1)
#define INT128_MIN (-INT128_MAX - 1)
#define pb push_back
#define eb emplace_back
#define clock chrono::steady_clock::now().time_since_epoch().count()
using namespace std;
template<size_t I = 0, typename... args>
ostream& print_tuple(ostream& os, const tuple<args...> tu) {
os << get<I>(tu);
if constexpr (I + 1 != sizeof...(args)) {
os << ' ';
print_tuple<I + 1>(os, tu);
}
return os;
}
template<typename... args>
ostream& operator<<(ostream& os, const tuple<args...> tu) {
return print_tuple(os, tu);
}
template<class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2> pr) {
return os << pr.first << ' ' << pr.second;
}
template<class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N> &arr) {
for(size_t i = 0; T x : arr) {
os << x;
if (++i != N) os << ' ';
}
return os;
}
template<class T>
ostream& operator<<(ostream& os, const vector<T> &vec) {
for(size_t i = 0; T x : vec) {
os << x;
if (++i != size(vec)) os << ' ';
}
return os;
}
template<class T>
ostream& operator<<(ostream& os, const set<T> &s) {
for(size_t i = 0; T x : s) {
os << x;
if (++i != size(s)) os << ' ';
}
return os;
}
template<class T>
ostream& operator<<(ostream& os, const multiset<T> &s) {
for(size_t i = 0; T x : s) {
os << x;
if (++i != size(s)) os << ' ';
}
return os;
}
template<class T1, class T2>
ostream& operator<<(ostream& os, const map<T1, T2> &m) {
for(size_t i = 0; pair<T1, T2> x : m) {
os << x.first << " : " << x.second;
if (++i != size(m)) os << ", ";
}
return os;
}
#ifdef DEBUG
#define dbg(...) cerr << '(', _do(#__VA_ARGS__), cerr << ") = ", _do2(__VA_ARGS__)
template<typename T> void _do(T &&x) { cerr << x; }
template<typename T, typename ...S> void _do(T &&x, S&&...y) { cerr << x << ", "; _do(y...); }
template<typename T> void _do2(T &&x) { cerr << x << endl; }
template<typename T, typename ...S> void _do2(T &&x, S&&...y) { cerr << x << ", "; _do2(y...); }
#else
#define dbg(...)
#endif
using ll = long long;
using ull = unsigned long long;
using ldb = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
template<typename T> using vc = vector<T>;
template<typename T> using vvc = vc<vc<T>>;
template<typename T> using vvvc = vc<vvc<T>>;
using vi = vc<int>;
using vll = vc<ll>;
using vvi = vvc<int>;
using vvll = vvc<ll>;
template<typename T> using min_heap = priority_queue<T, vc<T>, greater<T>>;
template<typename T> using max_heap = priority_queue<T>;
template<typename R, typename F, typename... Args>
concept R_invocable = requires(F&& f, Args&&... args) {
{ std::invoke(std::forward<F>(f), std::forward<Args>(args)...) } -> std::same_as<R>;
};
template<ranges::forward_range rng, class T = ranges::range_value_t<rng>, typename F>
requires R_invocable<T, F, T, T>
void pSum(rng &&v, F f) {
if (!v.empty())
for(T p = *v.begin(); T &x : v | views::drop(1))
x = p = f(p, x);
}
template<ranges::forward_range rng, class T = ranges::range_value_t<rng>>
void pSum(rng &&v) {
if (!v.empty())
for(T p = *v.begin(); T &x : v | views::drop(1))
x = p = p + x;
}
template<ranges::forward_range rng>
void Unique(rng &v) {
ranges::sort(v);
v.resize(unique(v.begin(), v.end()) - v.begin());
}
template<ranges::random_access_range rng>
rng invPerm(rng p) {
rng ret = p;
for(int i = 0; i < ssize(p); i++)
ret[p[i]] = i;
return ret;
}
template<ranges::random_access_range rng>
vi argSort(rng p) {
vi id(size(p));
iota(id.begin(), id.end(), 0);
ranges::sort(id, {}, [&](int i) { return pair(p[i], i); });
return id;
}
template<ranges::random_access_range rng, class T = ranges::range_value_t<rng>, typename F>
requires invocable<F, T&>
vi argSort(rng p, F proj) {
vi id(size(p));
iota(id.begin(), id.end(), 0);
ranges::sort(id, {}, [&](int i) { return pair(proj(p[i]), i); });
return id;
}
template<bool directed>
vvi read_graph(int n, int m, int base) {
vvi g(n);
for(int i = 0; i < m; i++) {
int u, v; cin >> u >> v;
u -= base, v -= base;
g[u].emplace_back(v);
if constexpr (!directed)
g[v].emplace_back(u);
}
return g;
}
template<bool directed>
vvi adjacency_list(int n, vc<pii> e, int base) {
vvi g(n);
for(auto [u, v] : e) {
u -= base, v -= base;
g[u].emplace_back(v);
if constexpr (!directed)
g[v].emplace_back(u);
}
return g;
}
template<class T>
void setBit(T &msk, int bit, bool x) { (msk &= ~(T(1) << bit)) |= T(x) << bit; }
template<class T> void onBit(T &msk, int bit) { setBit(msk, bit, true); }
template<class T> void offBit(T &msk, int bit) { setBit(msk, bit, false); }
template<class T> void flipBit(T &msk, int bit) { msk ^= T(1) << bit; }
template<class T> bool getBit(T msk, int bit) { return msk >> bit & T(1); }
template<class T>
T floorDiv(T a, T b) {
if (b < 0) a *= -1, b *= -1;
return a >= 0 ? a / b : (a - b + 1) / b;
}
template<class T>
T ceilDiv(T a, T b) {
if (b < 0) a *= -1, b *= -1;
return a >= 0 ? (a + b - 1) / b : a / b;
}
template<class T> bool chmin(T &a, T b) { return a > b ? a = b, 1 : 0; }
template<class T> bool chmax(T &a, T b) { return a < b ? a = b, 1 : 0; }
#line 1 "tree/prufer_recover.cpp"
//empty vector would be assumed to be n = 2
vc<pii> prufer_recover(vi prufer_code) {
const int n = ssize(prufer_code) + 2;
assert(prufer_code.empty() or (ranges::min(prufer_code) >= 0 and ranges::max(prufer_code) < n));
vi d(n, 1);
for(int x : prufer_code) d[x]++;
min_heap<int> leaf;
for(int v = 0; v < n; v++)
if (d[v] == 1)
leaf.emplace(v);
vc<pii> edges;
for(int x : prufer_code) {
int v = leaf.top(); leaf.pop();
edges.emplace_back(v, x);
if (--d[x] == 1)
leaf.emplace(x);
}
int v = leaf.top(); leaf.pop();
edges.emplace_back(v, leaf.top());
return edges;
}
#line 1 "enumerate/enumerate_bit.cpp"
template<typename F, typename INT>
requires invocable<F, INT>
void enumerate_subset(INT msk, F f) {
for(INT x = msk; x > 0; x = (x - 1) & msk)
f(x);
f(0);
}
#line 1 "enumerate/enumerate_twelvefold.cpp"
//#include "enumerate/bit.cpp"
template<typename F>
requires invocable<F, vector<int>>
void enumerate_cartesian_power(int n, int k, F f) {
assert(min(n, k) >= 0);
vector<int> p(k);
auto dfs = [&](int i, auto &self) -> void {
if (i == k) {
f(p);
} else {
for(int x = 0; x < n; x++) {
p[i] = x;
self(i + 1, self);
}
}
};
dfs(0, dfs);
}
template<typename F>
requires invocable<F, vector<int>>
void enumerate_permutation(int n, F f) {
assert(n >= 0);
vector<int> p(n);
iota(p.begin(), p.end(), 0);
do { f(p); } while(next_permutation(p.begin(), p.end()));
}
template<typename F>
requires invocable<F, vector<int>>
void enumerate_combination(int n, int k, F f) {
assert(min(n, k) >= 0);
vector<int> p;
auto dfs = [&](auto &self) -> void {
if (ssize(p) == k) {
f(p);
} else {
for(int x = (p.empty() ? 0 : p.back() + 1); x + k - ssize(p) <= n; x++) {
p.emplace_back(x);
self(self);
p.pop_back();
}
}
};
dfs(dfs);
}
template<typename F>
requires invocable<F, vector<int>>
void enumerate_set_partition(int n, F f) {
assert(n >= 0);
vector<int> p;
int msk = (1 << n) - 1;
auto dfs = [&](auto &self) -> void {
if (msk == 0) {
f(p);
} else {
int x = msk & (-msk);
msk ^= x;
enumerate_subset(msk, [&](int sub) {
p.emplace_back(sub | x);
msk ^= sub;
self(self);
msk ^= sub;
p.pop_back();
});
msk ^= x;
}
};
dfs(dfs);
}
template<typename F>
requires invocable<F, vector<int>>
void enumerate_multisubset(int n, int sum, F f) {
assert(min(n, sum) >= 0);
vector<int> p(n);
auto dfs = [&](int i, auto &self) -> void {
if (i == n) {
if (sum == 0) f(p);
} else {
for(int x = sum; x >= 0; x--) {
p[i] = x, sum -= x;
self(i + 1, self);
sum += x;
}
}
};
dfs(0, dfs);
}
template<typename F>
requires invocable<F, vector<int>>
void enumerate_integer_partition(int n, F f) {
assert(n >= 0);
vector<int> p;
auto dfs = [&](int s, auto &self) -> void {
if (s == 0) {
f(p);
} else {
for(int x = (p.empty() ? s : min(p.back(), s)); x > 0; x--) {
p.emplace_back(x);
self(s - x, self);
p.pop_back();
}
}
};
dfs(n, dfs);
}
#line 1 "enumerate/enumerate_label_tree.cpp"
//#include "tree/prufer_recover.cpp"
//#include "enumerate/enumerate_bit.cpp"
//#include "enumerate/enumerate_twelvefold.cpp"
template<typename F>
requires invocable<F, vector<vector<int>>>
void enumerate_label_tree(int n, F f) {
assert(n > 0);
if (n == 1) {
f(vector<vector<int>>(1));
} else {
enumerate_cartesian_power(n, n - 2, [n, f](vector<int> a) {
f(adjacency_list<false>(n, prufer_recover(a), 0));
});
}
}
#line 1 "enumerate/enumerate_unlabel_rooted_tree.cpp"
//number of unlabel rooted tree (1-based)
//1, 1, 2, 4, 9,
//20, 48, 115, 286, 719,
//1842, 4766, 12486, 32973, 87811,
//235381, 634847, 1721159, 4688676, 12826228,
//35221832, 97055181, 268282855, 743724984, 2067174645
//root is 0
template<typename F>
requires invocable<F, vector<vector<int>>>
void enumerate_unlabel_rooted_tree(int n, F f) {
const int LIM = 25;
assert(0 < n and n <= LIM);
vector hash(1, array<int, LIM>{-1});
array<int, LIM + 2> st;
fill(st.begin(), st.end(), INT_MAX);
st[0] = -1, st[1] = 0;
auto size = [&](int id) {
int r = 1;
while(st[r] <= id) r++;
return r - 1;
};
for(int m = 2; m <= n; m++) {
st[m] = ssize(hash);
array<int, LIM> h;
int nxt = 0;
auto dfs = [&](int pre_id, int sum, auto &self) -> void {
if (sum == 0) {
h[nxt++] = -1;
hash.emplace_back(h);
nxt--;
} else {
for(int x = min(pre_id, st[sum + 1] - 1); x >= 0; x--) {
h[nxt++] = x;
self(x, sum - size(x), self);
nxt--;
}
}
};
dfs(INT_MAX, m - 1, dfs);
}
st[n + 1] = ssize(hash);
for(int id = st[n]; id < st[n + 1]; id++) {
vector<vector<int>> g(n);
int nxt = 0;
auto dfs = [&](int v, int id, auto &self) -> void {
if (id == 0) return;
for(int i = 0; hash[id][i] != -1; i++) {
g[v].emplace_back(nxt), g[nxt].emplace_back(v);
self(nxt++, hash[id][i], self);
}
};
dfs(nxt++, id, dfs);
f(g);
}
}
#line 1 "ds/RMQ.cpp"
template<class T>
struct RMQ {
uint64_t size;
vector<T> base;
vector<vector<T>> table;
vector<uint32_t> msk;
static const int lgw = 5;
static const int w = 1 << lgw;
RMQ(vector<T> _base) : size(ssize(_base)), base(_base), msk(size) {
msk.back() = 1;
for(int i = size - 2; i >= 0; i--) {
msk[i] = msk[i + 1] << 1;
while(msk[i] != 0 and base[i + countr_zero(msk[i])] >= base[i])
msk[i] ^= 1u << countr_zero(msk[i]);
msk[i] |= 1u;
}
table = vector(bit_width(size >> lgw), vector<T>(size >> lgw));
if (!table.empty())
for(uint64_t i = 0; i + w <= size; i += w)
table[0][i >> lgw] = base[i + bit_width(msk[i]) - 1];
for(int i = 1; i < ssize(table); i++)
for(uint64_t j = 0; j < (size >> lgw); j++)
if (j + (1 << (i - 1)) < (size >> lgw))
table[i][j] = min(table[i - 1][j], table[i - 1][j + (1 << (i - 1))]);
else
table[i][j] = table[i - 1][j];
}
T query(int l, int r) {
if (l >= r) {
return numeric_limits<T>::max();
} else if (r - l <= w) {
return base[l + bit_width(msk[l] & (~0u >> (w - (r - l)))) - 1];
} else {
T ret = min(query(l, l + w), query(r - w, r));
l = (l + w) >> lgw, r >>= lgw;
if (l == r) return ret;
int range = bit_width((unsigned)(r - l)) - 1;
return min({ret, table[range][l], table[range][r - (1 << range)]});
}
}
};
#line 1 "tree/LCA.cpp"
//#include "ds/RMQ.cpp"
struct LCA {
vi dep, tin, tout, mp;
RMQ<int> rmq;
vi precomp(vc<pii> &e, int root) {
const int n = ssize(e) + 1;
dep = tin = tout = mp = vi(n);
vi sz(n, 1), p(n), ord;
{
vi d(n);
for(auto &[u, v] : e)
p[u] ^= v, p[v] ^= u, d[u]++, d[v]++;
d[root] = 0, p[root] = root;
ord.reserve(n - 1);
for(int i = 0; i < n; i++) {
int v = i;
while(d[v] == 1) {
ord.emplace_back(v);
sz[p[v]] += sz[v];
d[v] = 0, d[p[v]]--, p[p[v]] ^= v;
v = p[v];
}
}
}
vi dfn(n);
{
vi nxt(n, 1);
for(int v : ord | views::reverse) {
dfn[v] = nxt[p[v]], nxt[p[v]] += sz[v];
nxt[v] = dfn[v] + 1;
dep[v] = dep[p[v]] + 1;
}
vi().swap(ord);
vi().swap(sz);
}
vi init(2 * n - 1);
{
vi dfn_ord = invPerm(std::move(dfn));
int nxt = 0, pre = root;
for(int v : dfn_ord) {
while(pre != p[v]) {
pre = p[pre], tout[pre] = nxt;
init[nxt++] = pre;
}
tin[v] = tout[v] = nxt;
init[nxt++] = pre = v;
}
while(pre != root) {
pre = p[pre], tout[pre] = nxt;
init[nxt++] = pre;
}
}
{
vi f(n);
for(int x : dep) f[x]++;
pSum(f);
vi rank(n);
for(int v = 0; v < n; v++) {
rank[v] = --f[dep[v]];
mp[rank[v]] = v;
}
for(int &v : init) v = rank[v];
}
return init;
}
LCA(vc<pii> e, int root = 0) : rmq(precomp(e, root)) {}
int lca(int u, int v) {
if (tin[u] > tin[v]) swap(u, v);
return mp[rmq.query(tin[u], tout[v] + 1)];
}
int dis(int u, int v) {
return dep[u] + dep[v] - 2 * dep[lca(u, v)];
}
bool is_ancestor_of(int u, int v) {
return tin[u] <= tin[v] and tout[v] <= tout[u];
}
};
#line 1 "tree/auxiliary_tree.cpp"
//#include "ds/RMQ.cpp"
//#include "tree/LCA.cpp"
struct auxiliary_tree {
LCA lca;
auxiliary_tree(vc<pii> e, int root = 0) : lca(e, root) {}
auto induced_tree(vi vs) {
const int P = 10;
auto proj = [&](int v) { return lca.tin[v]; };
if (ssize(vs) < (1 << P) / P) {
ranges::sort(vs, {}, proj);
} else {
int mx = proj(ranges::max(vs, {}, proj));
for(int i = 0; mx > 0; i++, mx >>= P){
array<int, (1 << P) + 1> f = {};
for(int v : vs)
f[(proj(v) >> (i * P) & ((1 << P) - 1)) + 1]++;
pSum(f);
vi nxt(size(vs));
for(int v : vs)
nxt[f[proj(v) >> (i * P) & ((1 << P) - 1)]++] = v;
vs.swap(nxt);
}
}
vi s, old_id;
vc<bool> is_critical_node;
auto push_new_vertex = [&](int v, bool critical = true) {
s.emplace_back(ssize(old_id));
old_id.emplace_back(v);
is_critical_node.emplace_back(critical);
};
if (int v = lca.lca(vs[0], vs.back()); v != vs[0])
push_new_vertex(v, false);
vc<pii> e;
for(int v : vs) {
if (s.empty() or lca.is_ancestor_of(old_id[s.back()], v)) {
push_new_vertex(v);
} else {
int last_pop = -1;
do {
int j = s.back(); s.pop_back();
if (last_pop != -1)
e.emplace_back(j, last_pop);
last_pop = j;
} while(!lca.is_ancestor_of(old_id[s.back()], v));
if (int x = lca.lca(old_id[last_pop], v); x != old_id[s.back()])
push_new_vertex(x, false);
e.emplace_back(s.back(), last_pop);
push_new_vertex(v);
}
}
for(int i = 1; i < ssize(s); i++)
e.emplace_back(s[i - 1], s[i]);
return tuple(e, old_id, is_critical_node);
}
};
#line 12 "test/mytest_auxiliary_tree.test.cpp"
auto auxiliary_tree_brute_force(vvi g, vi vs, int root = 0) {
vc<bool> in_vs(size(g), false);
for(int v : vs) in_vs[v] = true;
vi old_id;
vc<pii> e;
vc<bool> is_critical_node;
auto dfs = [&](int v, int p, auto &self) -> int {
vi head;
for(int x : g[v]) {
if (x == p) continue;
int y = self(x, v, self);
if (y != -1) head.eb(y);
}
if (!in_vs[v] and ssize(head) <= 1)
return head.empty() ? -1 : head[0];
int i = size(old_id);
old_id.emplace_back(v);
is_critical_node.emplace_back(in_vs[v]);
for(int j : head)
e.emplace_back(i, j);
return i;
};
dfs(root, -1, dfs);
return tuple(e, old_id, is_critical_node);
}
void check(vector<vector<int>> g, int root) {
vc<pii> e;
for(int u = 0; u < ssize(g); u++)
for(int v : g[u])
if (u < v)
e.emplace_back(u, v);
auxiliary_tree aux(e, root);
auto check2 = [&](vi vs) {
auto [ep, old_id, crit] = aux.induced_tree(vs);
auto [ep2, old_id2, crit2] = auxiliary_tree_brute_force(g, vs, root);
assert(ssize(old_id) == ssize(old_id2));
assert(set(old_id.begin(), old_id.end()) ==
set(old_id2.begin(), old_id2.end()));
vi val = old_id;
ranges::sort(val);
vi mp(size(g), -1);
for(int i = 0; i < ssize(val); i++)
mp[val[i]] = i;
{
vi p(size(old_id));
for(int i = 0; i < ssize(p); i++)
p[i] = mp[old_id[i]];
for(auto &[u, v] : ep)
u = p[u], v = p[v];
vi tmp(size(old_id));
for(int i = 0; i < ssize(p); i++)
tmp[p[i]] = old_id[i];
old_id.swap(tmp);
vc<bool> tmp2(size(old_id));
for(int i = 0; i < ssize(p); i++)
tmp2[p[i]] = crit[i];
crit.swap(tmp2);
}
{
vi p(size(old_id2));
for(int i = 0; i < ssize(p); i++)
p[i] = mp[old_id2[i]];
for(auto &[u, v] : ep2)
u = p[u], v = p[v];
vi tmp(size(old_id2));
for(int i = 0; i < ssize(p); i++)
tmp[p[i]] = old_id2[i];
old_id2.swap(tmp);
vc<bool> tmp2(size(old_id2));
for(int i = 0; i < ssize(p); i++)
tmp2[p[i]] = crit2[i];
crit2.swap(tmp2);
}
ranges::sort(ep);
ranges::sort(ep2);
assert(old_id == old_id2);
assert(ep == ep2);
assert(crit == crit2);
};
mt19937 rng(clock);
const int n = ssize(g);
if (ssize(g) <= 15) {
for(int msk = 1; msk < (1 << n); msk++) {
vi vs;
for(int i = 0; i < n; i++)
if (msk >> i & 1)
vs.eb(i);
shuffle(vs.begin(), vs.end(), rng);
check2(vs);
}
} else {
for(int sz = 1; sz <= n; sz <<= 1) {
set<int> s;
while(ssize(s) != sz)
s.insert(rng() % n);
vi vs;
for(int x : s) vs.eb(x);
shuffle(vs.begin(), vs.end(), rng);
check2(vs);
}
}
}
auto random_relabel(vector<vector<int>> g) {
mt19937 rng(clock);
const int n = ssize(g);
vector<int> p(n);
iota(p.begin(), p.end(), 0);
shuffle(p.begin(), p.end(), rng);
vector<vector<int>> g2(n);
for(int u = 0; u < n; u++)
for(int v : g[u])
g2[p[u]].eb(p[v]);
return g2;
}
void a_plus_b() {
int a, b; cin >> a >> b;
cout << a + b << '\n';
}
int main() {
ios::sync_with_stdio(false), cin.tie(NULL);
mt19937 rng(clock);
for(int n = 1; n <= 6; n++) {
enumerate_label_tree(n, [&](vector<vector<int>> g) {
for(int r = 0; r < n; r++)
check(g, r);
});
}
for(int n = 7; n <= 8; n++) {
enumerate_unlabel_rooted_tree(n, [&](vector<vector<int>> g) {
for(int r = 0; r < n; r++)
check(g, r);
g = random_relabel(g);
for(int r = 0; r < n; r++)
check(g, r);
});
}
//path
for(int n = 1; n <= 100; n += 2) {
vector<vector<int>> g(n);
for(int i = 1; i < n; i++)
g[i].emplace_back(i - 1), g[i - 1].emplace_back(i);
check(g, 0);
check(random_relabel(g), rng() % n);
}
//star
for(int n = 2; n <= 100; n += 2) {
for(int root : {0, n / 2, n - 1}) {
vector<vector<int>> g(n);
for(int i = 0; i < n; i++)
if (i != root)
g[root].emplace_back(i), g[i].emplace_back(root);
check(g, root);
check(g, root == 0);
}
}
//almost path
for(int tc = 0; tc < 10; tc++) {
int n = 5'000;
vector<vector<int>> g(n);
for(int v = 1; v < n; v++) {
int x = rng() % min(v, 5);
g[v].emplace_back(x), g[x].emplace_back(v);
}
for(int r : {0, n / 2, n - 1})
check(g, r);
g = random_relabel(g);
for(int r : {0, n / 2, n - 1})
check(g, r);
}
a_plus_b();
return 0;
}