This documentation is automatically generated by online-judge-tools/verification-helper
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/staticrmq
#include "../../template/template.hpp"
#include "../../graph/graph-template.hpp"
#include "../../graph/tree/pmormq-lowest-common-ancestor.hpp"
#include "../../graph/others/cartesian-tree.hpp"
int main() {
int N, Q;
cin >> N >> Q;
vector< int > A(N);
cin >> A;
auto t = cartesian_tree(A);
PMORMQLowestCommonAncestor< int > g(N);
int root = -1;
for(int i = 0; i < N; i++) {
if(t[i] == -1) {
root = i;
continue;
}
g.add_directed_edge(t[i], i);
}
g.build(root);
while(Q--) {
int l, r;
cin >> l >> r;
cout << A[g.lca(l, r - 1)] << "\n";
}
}
#line 1 "test/verify/yosupo-staticrmq-4.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/staticrmq
#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-staticrmq-4.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 2 "graph/others/cartesian-tree.hpp"
/**
* @brief Cartesian Tree
*
* @see https://kimiyuki.net/blog/2020/07/27/recursion-on-cartesian-tree/
*/
template <typename T>
vector<int> cartesian_tree(const vector<T> &v) {
int n = (int)v.size();
vector<int> par(n, -1);
stack<int> st;
for (int i = 0; i < n; i++) {
int last = -1;
while (!st.empty() && v[st.top()] >= v[i]) {
last = st.top();
st.pop();
}
if (!st.empty()) par[i] = st.top();
if (last >= 0) par[last] = i;
st.emplace(i);
}
return par;
}
#line 8 "test/verify/yosupo-staticrmq-4.test.cpp"
int main() {
int N, Q;
cin >> N >> Q;
vector< int > A(N);
cin >> A;
auto t = cartesian_tree(A);
PMORMQLowestCommonAncestor< int > g(N);
int root = -1;
for(int i = 0; i < N; i++) {
if(t[i] == -1) {
root = i;
continue;
}
g.add_directed_edge(t[i], i);
}
g.build(root);
while(Q--) {
int l, r;
cin >> l >> r;
cout << A[g.lca(l, r - 1)] << "\n";
}
}
Env | Name | Status | Elapsed | Memory |
---|---|---|---|---|
g++ | example_00 | AC | 7 ms | 4 MB |
g++ | max_random_00 | AC | 227 ms | 58 MB |
g++ | max_random_01 | AC | 223 ms | 58 MB |
g++ | max_random_02 | AC | 220 ms | 58 MB |
g++ | max_random_03 | AC | 228 ms | 58 MB |
g++ | max_random_04 | AC | 221 ms | 58 MB |
g++ | random_00 | AC | 181 ms | 46 MB |
g++ | random_01 | AC | 199 ms | 54 MB |
g++ | random_02 | AC | 98 ms | 9 MB |
g++ | random_03 | AC | 98 ms | 51 MB |
g++ | random_04 | AC | 84 ms | 34 MB |
g++ | small_00 | AC | 6 ms | 4 MB |
g++ | small_01 | AC | 6 ms | 4 MB |
g++ | small_02 | AC | 6 ms | 4 MB |
g++ | small_03 | AC | 6 ms | 4 MB |
g++ | small_04 | AC | 6 ms | 4 MB |
g++ | small_05 | AC | 6 ms | 4 MB |
g++ | small_06 | AC | 6 ms | 4 MB |
g++ | small_07 | AC | 6 ms | 4 MB |
g++ | small_08 | AC | 6 ms | 4 MB |
g++ | small_09 | AC | 6 ms | 4 MB |
g++ | small_width_query_00 | AC | 264 ms | 58 MB |
g++ | small_width_query_01 | AC | 265 ms | 58 MB |
g++ | small_width_query_02 | AC | 261 ms | 58 MB |
g++ | small_width_query_03 | AC | 251 ms | 58 MB |
g++ | small_width_query_04 | AC | 249 ms | 58 MB |
clang++ | example_00 | AC | 6 ms | 4 MB |
clang++ | max_random_00 | AC | 221 ms | 58 MB |
clang++ | max_random_01 | AC | 227 ms | 58 MB |
clang++ | max_random_02 | AC | 229 ms | 58 MB |
clang++ | max_random_03 | AC | 225 ms | 58 MB |
clang++ | max_random_04 | AC | 227 ms | 58 MB |
clang++ | random_00 | AC | 182 ms | 46 MB |
clang++ | random_01 | AC | 196 ms | 54 MB |
clang++ | random_02 | AC | 99 ms | 9 MB |
clang++ | random_03 | AC | 95 ms | 51 MB |
clang++ | random_04 | AC | 85 ms | 34 MB |
clang++ | small_00 | AC | 6 ms | 4 MB |
clang++ | small_01 | AC | 6 ms | 4 MB |
clang++ | small_02 | AC | 6 ms | 4 MB |
clang++ | small_03 | AC | 6 ms | 4 MB |
clang++ | small_04 | AC | 6 ms | 4 MB |
clang++ | small_05 | AC | 6 ms | 4 MB |
clang++ | small_06 | AC | 6 ms | 4 MB |
clang++ | small_07 | AC | 6 ms | 4 MB |
clang++ | small_08 | AC | 6 ms | 4 MB |
clang++ | small_09 | AC | 6 ms | 4 MB |
clang++ | small_width_query_00 | AC | 254 ms | 58 MB |
clang++ | small_width_query_01 | AC | 260 ms | 58 MB |
clang++ | small_width_query_02 | AC | 249 ms | 58 MB |
clang++ | small_width_query_03 | AC | 252 ms | 58 MB |
clang++ | small_width_query_04 | AC | 249 ms | 58 MB |