This documentation is automatically generated by online-judge-tools/verification-helper
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/lca
#include "../../template/template.hpp"
#include "../../graph/graph-template.hpp"
#include "../../graph/tree/pmormq-lowest-common-ancestor.hpp"
#include "../../other/scanner.hpp"
#include "../../other/printer.hpp"
int main() {
Scanner in(stdin);
Printer out(stdout);
int N, Q;
in.read(N, Q);
PMORMQLowestCommonAncestor< int > g(N);
for(int i = 1; i < N; i++) {
int x;
in.read(x);
g.add_directed_edge(x, i);
}
g.build();
for(int i = 0; i < Q; i++) {
int u, v;
in.read(u, v);
out.writeln(g.lca(u, v));
}
}
#line 1 "test/verify/yosupo-lca.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/lca
#line 1 "template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using int64 = long long;
const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;
struct IoSetup {
IoSetup() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(10);
cerr << fixed << setprecision(10);
}
} iosetup;
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
os << p.first << " " << p.second;
return os;
}
template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
for (int i = 0; i < (int)v.size(); i++) {
os << v[i] << (i + 1 != v.size() ? " " : "");
}
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (T &in : v) is >> in;
return is;
}
template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
return a < b && (a = b, true);
}
template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
return a > b && (a = b, true);
}
template <typename T = int64>
vector<T> make_v(size_t a) {
return vector<T>(a);
}
template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}
template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
t = v;
}
template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
for (auto &e : t) fill_v(e, v);
}
template <typename F>
struct FixPoint : F {
explicit FixPoint(F &&f) : F(forward<F>(f)) {}
template <typename... Args>
decltype(auto) operator()(Args &&...args) const {
return F::operator()(*this, forward<Args>(args)...);
}
};
template <typename F>
inline decltype(auto) MFP(F &&f) {
return FixPoint<F>{forward<F>(f)};
}
#line 4 "test/verify/yosupo-lca.test.cpp"
#line 2 "graph/graph-template.hpp"
/**
* @brief Graph Template(グラフテンプレート)
*/
template <typename T = int>
struct Edge {
int from, to;
T cost;
int idx;
Edge() = default;
Edge(int from, int to, T cost = 1, int idx = -1)
: from(from), to(to), cost(cost), idx(idx) {}
operator int() const { return to; }
};
template <typename T = int>
struct Graph {
vector<vector<Edge<T> > > g;
int es;
Graph() = default;
explicit Graph(int n) : g(n), es(0) {}
size_t size() const { return g.size(); }
void add_directed_edge(int from, int to, T cost = 1) {
g[from].emplace_back(from, to, cost, es++);
}
void add_edge(int from, int to, T cost = 1) {
g[from].emplace_back(from, to, cost, es);
g[to].emplace_back(to, from, cost, es++);
}
void read(int M, int padding = -1, bool weighted = false,
bool directed = false) {
for (int i = 0; i < M; i++) {
int a, b;
cin >> a >> b;
a += padding;
b += padding;
T c = T(1);
if (weighted) cin >> c;
if (directed)
add_directed_edge(a, b, c);
else
add_edge(a, b, c);
}
}
inline vector<Edge<T> > &operator[](const int &k) { return g[k]; }
inline const vector<Edge<T> > &operator[](const int &k) const { return g[k]; }
};
template <typename T = int>
using Edges = vector<Edge<T> >;
#line 2 "graph/tree/pmormq-lowest-common-ancestor.hpp"
#line 1 "structure/others/sparse-table.hpp"
/**
* @brief Sparse-Table(スパーステーブル)
*
*/
template <typename T, typename F>
struct SparseTable {
F f;
vector<vector<T> > st;
vector<int> lookup;
SparseTable() = default;
explicit SparseTable(const vector<T> &v, const F &f) : f(f) {
const int n = (int)v.size();
const int b = 32 - __builtin_clz(n);
st.assign(b, vector<T>(n));
for (int i = 0; i < v.size(); i++) {
st[0][i] = v[i];
}
for (int i = 1; i < b; i++) {
for (int j = 0; j + (1 << i) <= n; j++) {
st[i][j] = f(st[i - 1][j], st[i - 1][j + (1 << (i - 1))]);
}
}
lookup.resize(v.size() + 1);
for (int i = 2; i < lookup.size(); i++) {
lookup[i] = lookup[i >> 1] + 1;
}
}
inline T fold(int l, int r) const {
int b = lookup[r - l];
return f(st[b][l], st[b][r - (1 << b)]);
}
};
template <typename T, typename F>
SparseTable<T, F> get_sparse_table(const vector<T> &v, const F &f) {
return SparseTable<T, F>(v, f);
}
#line 2 "structure/others/plus-minus-one-rmq.hpp"
/**
* @brief Plus-Minus-One-RMQ
**/
template <typename T>
struct PlusMinusOneRMQ {
using F = function<int(int, int)>;
int backet;
vector<T> vs;
vector<int> bidx, bbit;
SparseTable<int, F> st;
vector<vector<vector<int> > > lookup;
explicit PlusMinusOneRMQ() = default;
explicit PlusMinusOneRMQ(const vector<T> &vs) : vs(vs) {
int n = (int)vs.size();
backet = max(1, (31 - __builtin_clz(n)) / 2);
int sz = (n + backet - 1) / backet;
bidx.assign(sz, -1);
bbit.assign(sz, 0);
for (int i = 0; i < sz; i++) {
int l = i * backet;
int r = min(l + backet, n);
bidx[i] = l;
for (int j = l + 1; j < r; j++) {
if (vs[j] < vs[bidx[i]]) bidx[i] = j;
if (vs[j - 1] < vs[j]) bbit[i] |= 1 << (j - l - 1);
}
}
F f = [&](int a, int b) { return vs[a] < vs[b] ? a : b; };
st = get_sparse_table(bidx, f);
lookup.assign(1 << (backet - 1),
vector<vector<int> >(backet, vector<int>(backet + 1)));
for (int i = 0; i < (1 << (backet - 1)); i++) {
for (int j = 0; j < backet; j++) {
int sum = 0, ret = 0, pos = j;
for (int k = j + 1; k <= backet; k++) {
lookup[i][j][k] = pos;
if (i & (1 << (k - 1)))
++sum;
else
--sum;
if (sum < ret) {
pos = k;
ret = sum;
}
}
}
}
}
pair<T, int> fold(int l, int r) const {
int lb = l / backet;
int rb = r / backet;
if (lb == rb) {
int pos = lb * backet + lookup[bbit[lb]][l % backet][r % backet];
return {vs[pos], pos};
}
int pos = lb * backet + lookup[bbit[lb]][l % backet][backet];
if (r % backet > 0) {
int sub = rb * backet + lookup[bbit[rb]][0][r % backet];
if (vs[sub] < vs[pos]) pos = sub;
}
if (lb + 1 == rb) {
return {vs[pos], pos};
} else {
int sub = st.fold(lb + 1, rb);
if (vs[sub] < vs[pos]) pos = sub;
return {vs[pos], pos};
}
}
};
#line 5 "graph/tree/pmormq-lowest-common-ancestor.hpp"
/**
* @brief PMORMQ-Lowest-Common-Ancestor(最小共通祖先)
*
**/
template <typename T = int>
struct PMORMQLowestCommonAncestor : Graph<T> {
public:
using Graph<T>::Graph;
using Graph<T>::g;
using F = function<int(int, int)>;
void build(int root = 0) {
ord.reserve(g.size() * 2 - 1);
dep.reserve(g.size() * 2 - 1);
in.resize(g.size());
dfs(root, -1, 0);
vector<int> vs(g.size() * 2 - 1);
iota(begin(vs), end(vs), 0);
st = PlusMinusOneRMQ<int>(dep);
}
int lca(int x, int y) const {
if (in[x] > in[y]) swap(x, y);
return ord[st.fold(in[x], in[y] + 1).second];
}
private:
vector<int> ord, dep, in;
PlusMinusOneRMQ<int> st;
void dfs(int idx, int par, int d) {
in[idx] = (int)ord.size();
ord.emplace_back(idx);
dep.emplace_back(d);
for (auto &to : g[idx]) {
if (to != par) {
dfs(to, idx, d + 1);
ord.emplace_back(idx);
dep.emplace_back(d);
}
}
}
};
#line 7 "test/verify/yosupo-lca.test.cpp"
#line 1 "other/scanner.hpp"
/**
* @brief Scanner(高速入力)
*/
struct Scanner {
public:
explicit Scanner(FILE *fp) : fp(fp) {}
template <typename T, typename... E>
void read(T &t, E &...e) {
read_single(t);
read(e...);
}
private:
static constexpr size_t line_size = 1 << 16;
static constexpr size_t int_digits = 20;
char line[line_size + 1] = {};
FILE *fp = nullptr;
char *st = line;
char *ed = line;
void read() {}
static inline bool is_space(char c) { return c <= ' '; }
void reread() {
ptrdiff_t len = ed - st;
memmove(line, st, len);
char *tmp = line + len;
ed = tmp + fread(tmp, 1, line_size - len, fp);
*ed = 0;
st = line;
}
void skip_space() {
while (true) {
if (st == ed) reread();
while (*st && is_space(*st)) ++st;
if (st != ed) return;
}
}
template <typename T, enable_if_t<is_integral<T>::value, int> = 0>
void read_single(T &s) {
skip_space();
if (st + int_digits >= ed) reread();
bool neg = false;
if (is_signed<T>::value && *st == '-') {
neg = true;
++st;
}
typename make_unsigned<T>::type y = *st++ - '0';
while (*st >= '0') {
y = 10 * y + *st++ - '0';
}
s = (neg ? -y : y);
}
template <typename T, enable_if_t<is_same<T, string>::value, int> = 0>
void read_single(T &s) {
s = "";
skip_space();
while (true) {
char *base = st;
while (*st && !is_space(*st)) ++st;
s += string(base, st);
if (st != ed) return;
reread();
}
}
template <typename T>
void read_single(vector<T> &s) {
for (auto &d : s) read(d);
}
};
#line 1 "other/printer.hpp"
/**
* @brief Printer(高速出力)
*/
struct Printer {
public:
explicit Printer(FILE *fp) : fp(fp) {}
~Printer() { flush(); }
template <bool f = false, typename T, typename... E>
void write(const T &t, const E &...e) {
if (f) write_single(' ');
write_single(t);
write<true>(e...);
}
template <typename... T>
void writeln(const T &...t) {
write(t...);
write_single('\n');
}
void flush() {
fwrite(line, 1, st - line, fp);
st = line;
}
private:
FILE *fp = nullptr;
static constexpr size_t line_size = 1 << 16;
static constexpr size_t int_digits = 20;
char line[line_size + 1] = {};
char *st = line;
template <bool f = false>
void write() {}
void write_single(const char &t) {
if (st + 1 >= line + line_size) flush();
*st++ = t;
}
template <typename T, enable_if_t<is_integral<T>::value, int> = 0>
void write_single(T s) {
if (st + int_digits >= line + line_size) flush();
st += to_chars(st, st + int_digits, s).ptr - st;
}
void write_single(const string &s) {
for (auto &c : s) write_single(c);
}
void write_single(const char *s) {
while (*s != 0) write_single(*s++);
}
template <typename T>
void write_single(const vector<T> &s) {
for (size_t i = 0; i < s.size(); i++) {
if (i) write_single(' ');
write_single(s[i]);
}
}
};
#line 10 "test/verify/yosupo-lca.test.cpp"
int main() {
Scanner in(stdin);
Printer out(stdout);
int N, Q;
in.read(N, Q);
PMORMQLowestCommonAncestor< int > g(N);
for(int i = 1; i < N; i++) {
int x;
in.read(x);
g.add_directed_edge(x, i);
}
g.build();
for(int i = 0; i < Q; i++) {
int u, v;
in.read(u, v);
out.writeln(g.lca(u, v));
}
}
Env | Name | Status | Elapsed | Memory |
---|---|---|---|---|
g++ | binary_00 | AC | 162 ms | 54 MB |
g++ | binary_01 | AC | 168 ms | 54 MB |
g++ | binary_02 | AC | 165 ms | 54 MB |
g++ | example_00 | AC | 7 ms | 4 MB |
g++ | line_00 | AC | 126 ms | 82 MB |
g++ | line_01 | AC | 143 ms | 97 MB |
g++ | line_02 | AC | 47 ms | 14 MB |
g++ | line_03 | AC | 95 ms | 90 MB |
g++ | line_04 | AC | 73 ms | 59 MB |
g++ | max_line_00 | AC | 157 ms | 104 MB |
g++ | max_line_01 | AC | 159 ms | 104 MB |
g++ | max_line_02 | AC | 161 ms | 104 MB |
g++ | max_random_00 | AC | 181 ms | 54 MB |
g++ | max_random_01 | AC | 184 ms | 54 MB |
g++ | max_random_02 | AC | 200 ms | 54 MB |
g++ | path_graph_root_centroid_00 | AC | 124 ms | 81 MB |
g++ | path_graph_root_centroid_01 | AC | 124 ms | 81 MB |
g++ | path_graph_root_centroid_02 | AC | 124 ms | 81 MB |
g++ | random_00 | AC | 131 ms | 43 MB |
g++ | random_01 | AC | 159 ms | 51 MB |
g++ | random_02 | AC | 46 ms | 9 MB |
g++ | random_03 | AC | 109 ms | 47 MB |
g++ | random_04 | AC | 64 ms | 32 MB |
clang++ | binary_00 | AC | 193 ms | 54 MB |
clang++ | binary_01 | AC | 177 ms | 54 MB |
clang++ | binary_02 | AC | 186 ms | 54 MB |
clang++ | example_00 | AC | 7 ms | 4 MB |
clang++ | line_00 | AC | 138 ms | 82 MB |
clang++ | line_01 | AC | 150 ms | 97 MB |
clang++ | line_02 | AC | 53 ms | 14 MB |
clang++ | line_03 | AC | 95 ms | 90 MB |
clang++ | line_04 | AC | 75 ms | 59 MB |
clang++ | max_line_00 | AC | 170 ms | 104 MB |
clang++ | max_line_01 | AC | 172 ms | 104 MB |
clang++ | max_line_02 | AC | 173 ms | 104 MB |
clang++ | max_random_00 | AC | 186 ms | 54 MB |
clang++ | max_random_01 | AC | 179 ms | 54 MB |
clang++ | max_random_02 | AC | 193 ms | 54 MB |
clang++ | path_graph_root_centroid_00 | AC | 130 ms | 81 MB |
clang++ | path_graph_root_centroid_01 | AC | 132 ms | 81 MB |
clang++ | path_graph_root_centroid_02 | AC | 131 ms | 81 MB |
clang++ | random_00 | AC | 131 ms | 43 MB |
clang++ | random_01 | AC | 161 ms | 51 MB |
clang++ | random_02 | AC | 53 ms | 9 MB |
clang++ | random_03 | AC | 114 ms | 47 MB |
clang++ | random_04 | AC | 71 ms | 32 MB |