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#define 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" #define PROBLEM "https://judge.yosupo.jp/problem/staticrmq" #line 1 "template/template.hpp" #include<bits/stdc++.h> using namespace std; using int64 = long long; const int mod = 1e9 + 7; 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) * @docs docs/sparse-table.md */ 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) * @docs docs/pmormq-lowest-common-ancestor.md **/ 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 * @docs docs/cartesian-tree.md * @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"; } }