CP-templates
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test/lca_3.test.cpp
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- Last update: 2026-02-03 05:22:52+08:00
- Problem: https://judge.yosupo.jp/problem/lca
Depends on
default/t.cpp
Code
#define PROBLEM "https://judge.yosupo.jp/problem/lca"
#include "../default/t.cpp"
#include "../ds/RMQ.cpp"
#include "../tree/LCA.cpp"
signed main() {
ios::sync_with_stdio(false), cin.tie(NULL);
int n, q; cin >> n >> q;
vc<pii> e(n - 1);
for(int v = 1; auto &[x, y] : e) {
x = v++;
cin >> y;
}
LCA lc(e, 0);
while(q--) {
int u, v; cin >> u >> v;
cout << lc.lca(u, v) << '\n';
}
return 0;
}#line 1 "test/lca_3.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/lca"
#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 "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 6 "test/lca_3.test.cpp"
signed main() {
ios::sync_with_stdio(false), cin.tie(NULL);
int n, q; cin >> n >> q;
vc<pii> e(n - 1);
for(int v = 1; auto &[x, y] : e) {
x = v++;
cin >> y;
}
LCA lc(e, 0);
while(q--) {
int u, v; cin >> u >> v;
cout << lc.lca(u, v) << '\n';
}
return 0;
}