#line 1 "test/yj_lca_squaring.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/lca"
#include <cstdio>
#line 1 "Graph/adjacency_list.cpp"
/**
* @brief 重みつきグラフの隣接リスト
* @author えびちゃん
*/
#include <cstddef>
#include <algorithm>
#include <type_traits>
#include <vector>
template <typename WeightType>
class weighted_edge {
public:
using size_type = size_t;
using weight_type = WeightType;
protected:
size_type M_src, M_dst;
weight_type M_weight;
public:
weighted_edge() = default;
weighted_edge(weighted_edge const&) = default;
weighted_edge(weighted_edge&&) = default;
weighted_edge(size_type s, size_type d, weight_type w):
M_src(s), M_dst(d), M_weight(w)
{}
weighted_edge& operator =(weighted_edge const&) = default;
weighted_edge& operator =(weighted_edge&&) = default;
bool operator <(weighted_edge const& other) const {
if (M_weight < other.M_weight) return true;
if (other.M_weight < M_weight) return false;
if (M_src != other.M_src) return M_src < other.M_src;
return M_dst < other.M_dst;
}
size_type source() const { return M_src; }
size_type target() const { return M_dst; }
weight_type weight() const { return M_weight; }
};
struct directed_tag {};
struct undirected_tag {};
template <typename Edge, typename Directedness>
class adjacency_list {
public:
using size_type = size_t;
using edge_type = Edge;
using weight_type = typename Edge::weight_type;
private:
std::vector<std::vector<edge_type>> M_g;
public:
adjacency_list() = default;
adjacency_list(adjacency_list const&) = default;
adjacency_list(adjacency_list&&) = default;
explicit adjacency_list(size_type n): M_g(n) {}
template <typename... Args>
void emplace(size_type src, size_type dst, Args... args) {
M_g[src].emplace_back(src, dst, args...);
if (std::is_same<Directedness, undirected_tag>::value)
M_g[dst].emplace_back(dst, src, args...);
}
void sort_by_index() {
auto cmp = [](auto const& e1, auto const& e2) {
return e1.target() < e2.target();
};
for (auto v: M_g) std::sort(v.begin(), v.end(), cmp);
}
size_type size() const { return M_g.size(); }
auto const& operator [](size_type i) const { return M_g[i]; }
};
#line 1 "Graph/lowest_common_ancestor_squaring.cpp"
/**
* @brief 最深共通祖先 (squaring)
* @author えびちゃん
*/
#line 11 "Graph/lowest_common_ancestor_squaring.cpp"
#include <tuple>
#include <utility>
#line 14 "Graph/lowest_common_ancestor_squaring.cpp"
#line 1 "utility/literals.cpp"
/**
* @brief ユーザ定義リテラル
* @author えびちゃん
*/
#line 10 "utility/literals.cpp"
#include <cstdint>
constexpr intmax_t operator ""_jd(unsigned long long n) { return n; }
constexpr uintmax_t operator ""_ju(unsigned long long n) { return n; }
constexpr size_t operator ""_zu(unsigned long long n) { return n; }
constexpr ptrdiff_t operator ""_td(unsigned long long n) { return n; }
constexpr int8_t operator ""_i8(unsigned long long n) { return n; }
constexpr int16_t operator ""_i16(unsigned long long n) { return n; }
constexpr int32_t operator ""_i32(unsigned long long n) { return n; }
constexpr int64_t operator ""_i64(unsigned long long n) { return n; }
constexpr uint8_t operator ""_u8(unsigned long long n) { return n; }
constexpr uint16_t operator ""_u16(unsigned long long n) { return n; }
constexpr uint32_t operator ""_u32(unsigned long long n) { return n; }
constexpr uint64_t operator ""_u64(unsigned long long n) { return n; }
#line 16 "Graph/lowest_common_ancestor_squaring.cpp"
class lowest_common_ancestor {
public:
using size_type = size_t;
private:
std::vector<size_type> M_d;
std::vector<std::vector<size_type>> M_p;
template <typename Tree>
void M_dfs(Tree const& g, size_type v, size_type p) {
for (auto const& e: g[v]) {
size_type u = e.target();
if (u == p) continue;
M_p[0][u] = v;
M_d[u] = M_d[v] + 1;
M_dfs(g, u, v);
}
}
void M_double() {
size_type n = M_p[0].size();
while (true) {
bool valid = false;
auto const& back = M_p.back();
std::vector<size_type> tmp(n, -1);
for (size_type i = 0; i < n; ++i) {
if (back[i] == -1_zu) continue;
tmp[i] = back[back[i]];
if (tmp[i] != -1_zu) valid = true;
}
if (!valid) break;
M_p.push_back(std::move(tmp));
}
}
public:
lowest_common_ancestor() = default;
lowest_common_ancestor(lowest_common_ancestor const&) = default;
lowest_common_ancestor(lowest_common_ancestor&&) = default;
template <typename Tree>
lowest_common_ancestor(Tree const& g, size_type r) {
size_type n = g.size();
M_d.assign(n, 0);
M_p.emplace_back(n, -1);
M_dfs(g, r, -1);
M_double();
}
lowest_common_ancestor& operator =(lowest_common_ancestor const&) = default;
lowest_common_ancestor& operator =(lowest_common_ancestor&&) = default;
size_type operator ()(size_type u, size_type v) const {
if (M_d[u] > M_d[v]) std::swap(u, v);
if (M_d[u] < M_d[v]) {
size_type d = M_d[v] - M_d[u];
for (size_type i = 0; i < M_p.size(); ++i)
if (d >> i & 1) v = M_p[i][v];
}
if (u == v) return u;
for (size_type i = M_p.size(); i--;) {
if (M_p[i][u] == M_p[i][v]) continue;
u = M_p[i][u];
v = M_p[i][v];
}
return M_p[0][u];
}
};
#line 7 "test/yj_lca_squaring.test.cpp"
int main() {
size_t n, q;
scanf("%zu %zu", &n, &q);
adjacency_list<weighted_edge<int>, undirected_tag> g(n);
for (size_t i = 1; i < n; ++i) {
size_t p;
scanf("%zu", &p);
g.emplace(i, p, 1);
}
lowest_common_ancestor lca(g, 0);
for (size_t i = 0; i < q; ++i) {
size_t u, v;
scanf("%zu %zu", &u, &v);
printf("%zu\n", lca(u, v));
}
}
test/yj_lca_squaring.test.cpp