#pragma once
#include "../tree/euler-tour.hpp"
// https://smijake3.hatenablog.com/entry/2019/09/15/200200#%E3%82%BD%E3%83%BC%E3%83%882%E5%9B%9E%E3%81%AE%E6%96%B9%E6%B3%95
// https://nyaannyaan.github.io/library/tree/auxiliary-tree.hpp
template <class G> struct AuxiliaryTree {
G g;
EulerTour<G> et;
AuxiliaryTree(G &g) : g(g), et(g) {}
AuxiliaryTree(G &g, EulerTour<G> &et) : g(g), et(et) {}
// 頂点集合vsを受け取り
// {aux tree,vs:aux treeの頂点番号->gでの頂点番号}を返す
// aux tree : 親->子のみ含まれる
// N = size(g),M=size(vs)として
// 構築 O(N log N)
// クエリ O(M log M)
template <class T> pair<vector<vector<T>>, vector<T>> get(vector<T> vs) {
if(vs.empty())
return {};
auto comp = [&](T i, T j) { return et.in[i] < et.in[j]; };
sort(all(vs), comp);
for(int i = 1, sz = vs.size(); i < sz; i++) {
vs.push_back(et.lca(vs[i - 1], vs[i]));
}
sort(all(vs), comp);
vs.erase(unique(all(vs)), end(vs));
vector<vector<T>> aux(vs.size());
stack<T> st;
st.push(0);
rep(i, 1, vs.size()) {
while(et.out[vs[st.top()]] < et.in[vs[i]]) {
st.pop();
}
aux[st.top()].push_back(i);
st.push(i);
}
return {aux, vs};
}
};
#line 2 "other/fastio.hpp"
// ref: https://maspypy.com/library-checker-many-a-b , Nyaanさん
#line 2 "other/type-utils.hpp"
#include <bits/stdc++.h>
using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using vi = std::vector<int>;
using vii = std::vector<std::vector<int>>;
using pii = std::pair<int, int>;
using vl = std::vector<ll>;
using vll = std::vector<vl>;
using pll = std::pair<ll, ll>;
template <class T>
concept extended_integral =
std::integral<T> || std::same_as<std::remove_cv_t<T>, i128> ||
std::same_as<std::remove_cv_t<T>, u128>;
template <class T>
concept extended_signed_integral =
std::signed_integral<T> || std::same_as<std::remove_cv_t<T>, i128>;
template <class T>
concept extended_unsigned_integral =
std::unsigned_integral<T> || std::same_as<std::remove_cv_t<T>, u128>;
template <class T>
concept Streamable =
requires(std::ostream &os, T &x) { os << x; } || extended_integral<T>;
template <class mint>
concept is_modint = requires(mint &x) {
{ x.val() } -> std::convertible_to<int>;
};
#line 4 "other/fastio.hpp"
namespace fastio {
constexpr int SZ = 1 << 17;
constexpr int offset = 64;
constexpr int mod = 10000;
char in_buf[SZ];
int in_left{}, in_right{};
char out_buf[SZ];
char out_tmp[offset];
int out_right{};
struct Pre {
char num[4 * mod]{};
constexpr Pre() {
for(int i = 0; i < mod; ++i) {
for(int n = i, j = 3; j >= 0; --j, n /= 10)
num[4 * i + j] = '0' + n % 10;
}
}
constexpr const char *operator[](int i) const { return &num[4 * i]; }
} constexpr pre;
void load() {
memmove(in_buf, in_buf + in_left, in_right - in_left);
in_right += -in_left + std::fread(in_buf + in_right - in_left, 1,
SZ - (in_right - in_left), stdin);
in_left = 0;
if(in_right < SZ)
in_buf[in_right++] = '\n';
}
void read(char &c) {
do {
if(in_left == in_right)
load();
c = in_buf[in_left++];
} while(isspace(c));
}
void read(std::string &s) {
s.clear();
char c;
do {
if(in_left == in_right)
load();
c = in_buf[in_left++];
} while(isspace(c));
do {
s += c;
if(in_left == in_right)
load();
c = in_buf[in_left++];
} while(!isspace(c));
}
template <extended_integral T> void read(T &x) {
if(in_right - in_left < offset)
load();
char c;
do
c = in_buf[in_left++];
while(c < '-'); // \n:10 space:32 -:45 '0':48
bool minus{};
if constexpr(extended_signed_integral<T>) {
if(c == '-') {
c = in_buf[in_left++];
minus = true;
}
}
x = 0;
while(c >= '0') {
x = 10 * x + (c & 15);
c = in_buf[in_left++];
}
if constexpr(extended_signed_integral<T>) {
if(minus)
x = -x;
}
}
void flush() { fwrite(out_buf, 1, std::exchange(out_right, 0), stdout); }
void write_range(const char *c, int n) {
int pos{};
while(pos < n) {
if(out_right == SZ)
flush();
int len = std::min(n - pos, SZ - out_right);
memcpy(out_buf + out_right, c + pos, len);
out_right += len;
pos += len;
}
}
void write(char c) {
if(SZ == out_right)
flush();
out_buf[out_right++] = c;
}
void write(const char *c) { write_range(c, strlen(c)); }
void write(const std::string &s) { write_range(s.data(), s.size()); }
template <std::floating_point T> void write(T x) {
int n = std::snprintf(out_tmp, sizeof(out_tmp), "%.16g", x);
write_range(out_tmp, n);
}
void write(bool x) { write(x ? '1' : '0'); }
template <extended_integral T> void write(T x) {
if(x == 0) {
write('0');
}
if constexpr(extended_signed_integral<T>) {
if(x < 0) {
write('-');
x = -x;
}
}
if(SZ - out_right < offset)
flush();
int cur = offset;
for(; x >= 1000; x /= mod) {
cur -= 4;
memcpy(out_tmp + cur, pre[x % mod], 4);
}
if(x >= 100) {
cur -= 3;
memcpy(out_tmp + cur, pre[x % mod] + 1, 3);
} else if(x >= 10) {
cur -= 2;
memcpy(out_tmp + cur, pre[x % mod] + 2, 2);
} else if(x >= 1) {
cur -= 1;
memcpy(out_tmp + cur, pre[x % mod] + 3, 1);
}
write_range(out_tmp + cur, offset - cur);
}
struct Dummy {
// プログラム終了時に出力
~Dummy() { flush(); }
} dummy;
} // namespace fastio
using fastio::write;
#line 4 "template.hpp"
// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
#line 8 "template.hpp"
using namespace std;
#ifdef LOCAL
#include <debug.hpp>
#else
#define debug(...)
#endif
template <Streamable T> void print_one(const T &value) { fastio::write(value); }
template <is_modint T> void print_one(const T &value) {
print_one(value.val());
}
void print() { print_one('\n'); }
template <class T, class... Ts> void print(const T &a, const Ts &...b) {
print_one(a);
((print_one(' '), print_one(b)), ...);
print();
}
template <ranges::range Iterable>
requires(!Streamable<Iterable>)
void print(const Iterable &v) {
for(auto it = v.begin(); it != v.end(); ++it) {
if(it != v.begin())
print_one(' ');
print_one(*it);
}
print();
}
#define all(v) begin(v), end(v)
template <class T> void UNIQUE(T &v) {
ranges::sort(v);
v.erase(unique(all(v)), end(v));
}
template <typename T> inline bool chmax(T &a, T b) {
return ((a < b) ? (a = b, true) : (false));
}
template <typename T> inline bool chmin(T &a, T b) {
return ((a > b) ? (a = b, true) : (false));
}
// https://trap.jp/post/1224/
template <class... T> constexpr auto min(T... a) {
return min(initializer_list<common_type_t<T...>>{a...});
}
template <class... T> constexpr auto max(T... a) {
return max(initializer_list<common_type_t<T...>>{a...});
}
void input() {}
template <class Head, class... Tail> void input(Head &head, Tail &...tail) {
#ifdef LOCAL
cin >> head;
#else
fastio::read(head);
#endif
input(tail...);
}
template <class T> void input(vector<T> &a) {
for(T &x : a)
input(x);
}
#define INT(...) \
int __VA_ARGS__; \
input(__VA_ARGS__)
#define LL(...) \
long long __VA_ARGS__; \
input(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
input(__VA_ARGS__)
#define REP1_0(n, c) REP1_1(n, c)
#define REP1_1(n, c) \
for(ll REP_COUNTER_##c = 0; REP_COUNTER_##c < (ll)(n); REP_COUNTER_##c++)
#define REP1(n) REP1_0(n, __COUNTER__)
#define REP2(i, a) for(ll i = 0; i < (ll)(a); i++)
#define REP3(i, a, b) for(ll i = (ll)(a); i < (ll)(b); i++)
#define REP4(i, a, b, c) for(ll i = (ll)(a); i < (ll)(b); i += (ll)(c))
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__)
ll inf = 3e18;
vl dx = {1, -1, 0, 0};
vl dy = {0, 0, 1, -1};
template <class T> constexpr T floor(T x, T y) noexcept {
return x / y - ((x ^ y) < 0 and x % y);
}
template <class T> constexpr T ceil(T x, T y) noexcept {
return x / y + ((x ^ y) >= 0 and x % y);
}
// yの符号に関わらず非負で定義 \bmod:texコマンド
template <class T> constexpr T bmod(T x, T y) noexcept {
T m = x % y;
return (m < 0) ? m + (y > 0 ? y : -y) : m;
}
template <std::signed_integral T> constexpr int bit_width(T x) noexcept {
return std::bit_width((uint64_t)x);
}
template <std::signed_integral T> constexpr int popcount(T x) noexcept {
return std::popcount((uint64_t)x);
}
constexpr bool kth_bit(auto n, auto k) { return (n >> k) & 1; }
#line 3 "data-structure/sparse-table.hpp"
/*
auto opには
[](int i,int j){return min(i,j);}や(int(*)(int,int))min
を渡す
↑このmin,std::minじゃないな
prod 単位元を渡していないので l==rは不可
*/
template <class T, auto op> struct SparseTable {
SparseTable(const vector<T> &vec) {
int n = vec.size();
int b = bit_width(unsigned(n));
v.resize(b);
v[0] = vec;
rep(i, b - 1) {
v[i + 1].resize(n - (1 << i));
rep(j, ssize(v[i]) - (1 << i)) {
v[i + 1][j] = op(v[i][j], v[i][j + (1 << i)]);
}
}
}
T prod(int l, int r) const {
if(l + 1 == r)
return v[0][l];
int b = bit_width(unsigned(r - l - 1)) - 1;
return op(v[b][l], v[b][r - (1 << b)]);
}
private:
vector<vector<T>> v;
};
#line 4 "tree/euler-tour.hpp"
// https://maspypy.com/euler-tour-%E3%81%AE%E3%81%8A%E5%8B%89%E5%BC%B7
// https://nyaannyaan.github.io/library/tree/euler-tour.hpp
template <class G> struct EulerTour {
int root, id;
vector<int> in, out, dep;
using pii = pair<int, int>; // depth,vartex
SparseTable<pii, [](pii a, pii b) { return a.first < b.first ? a : b; }>
rmq;
EulerTour(G &g, int root = 0)
: root(root), id(0), in(g.size(), -1), out(g.size(), -1),
dep(g.size(), 0), rmq([&] {
vector<pii> vec;
vec.reserve(2 * g.size());
dfs(g, root, -1, vec);
return vec;
}()) {}
int lca(int x, int y) const {
int ix = in[x], iy = in[y];
if(ix > iy)
swap(ix, iy);
return rmq.prod(ix, iy + 1).second;
}
int dist(int x, int y) const {
int l = lca(x, y);
return dep[x] + dep[y] - 2 * dep[l];
}
private:
void dfs(G &g, int now, int prev, vector<pii> &vec) {
vec.push_back({dep[now], now});
in[now] = id++;
for(auto nex : g[now]) {
if(nex == prev)
continue;
dep[nex] = dep[now] + 1;
dfs(g, nex, now, vec);
}
vec.push_back({dep[now] - 1, prev});
out[now] = id++;
}
};
#line 3 "tree/auxiliary-tree.hpp"
// https://smijake3.hatenablog.com/entry/2019/09/15/200200#%E3%82%BD%E3%83%BC%E3%83%882%E5%9B%9E%E3%81%AE%E6%96%B9%E6%B3%95
// https://nyaannyaan.github.io/library/tree/auxiliary-tree.hpp
template <class G> struct AuxiliaryTree {
G g;
EulerTour<G> et;
AuxiliaryTree(G &g) : g(g), et(g) {}
AuxiliaryTree(G &g, EulerTour<G> &et) : g(g), et(et) {}
// 頂点集合vsを受け取り
// {aux tree,vs:aux treeの頂点番号->gでの頂点番号}を返す
// aux tree : 親->子のみ含まれる
// N = size(g),M=size(vs)として
// 構築 O(N log N)
// クエリ O(M log M)
template <class T> pair<vector<vector<T>>, vector<T>> get(vector<T> vs) {
if(vs.empty())
return {};
auto comp = [&](T i, T j) { return et.in[i] < et.in[j]; };
sort(all(vs), comp);
for(int i = 1, sz = vs.size(); i < sz; i++) {
vs.push_back(et.lca(vs[i - 1], vs[i]));
}
sort(all(vs), comp);
vs.erase(unique(all(vs)), end(vs));
vector<vector<T>> aux(vs.size());
stack<T> st;
st.push(0);
rep(i, 1, vs.size()) {
while(et.out[vs[st.top()]] < et.in[vs[i]]) {
st.pop();
}
aux[st.top()].push_back(i);
st.push(i);
}
return {aux, vs};
}
};
指定された頂点たちの最小共通祖先関係を保って木を圧縮してできる補助的な木 (tree/auxiliary-tree.hpp)
data-structure/sparse-table.hpp