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#define PROBLEM "https://judge.yosupo.jp/problem/lca" #include "../../template/template.hpp" #include "../../graph/graph-template.hpp" #include "../../graph/tree/doubling-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); DoublingLowestCommonAncestor< 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-3.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/lca" #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-lca-3.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/doubling-lowest-common-ancestor.hpp" #line 4 "graph/tree/doubling-lowest-common-ancestor.hpp" /** * @brief Doubling-Lowest-Common-Ancestor(最小共通祖先) * @docs docs/doubling-lowest-common-ancestor.md */ template< typename T > struct DoublingLowestCommonAncestor : Graph< T > { public: using Graph< T >::g; vector< int > dep; vector< T > sum; vector< vector< int > > table; const int LOG; explicit DoublingLowestCommonAncestor(int n) : Graph< T >(n), LOG(32 - __builtin_clz(g.size())) {} explicit DoublingLowestCommonAncestor(const Graph< T > &g) : LOG(32 - __builtin_clz(g.size())), Graph< T >(g) {} void build(int root = 0) { dep.assign(g.size(), 0); sum.assign(g.size(), 0); table.assign(LOG, vector< int >(g.size(), -1)); dfs(root, -1, 0); for(int k = 0; k + 1 < LOG; k++) { for(int i = 0; i < (int)table[k].size(); i++) { if(table[k][i] == -1) table[k + 1][i] = -1; else table[k + 1][i] = table[k][table[k][i]]; } } } int lca(int u, int v) { if(dep[u] > dep[v]) swap(u, v); v = climb(v, dep[v] - dep[u]); if(u == v) return u; for(int i = LOG - 1; i >= 0; i--) { if(table[i][u] != table[i][v]) { u = table[i][u]; v = table[i][v]; } } return table[0][u]; } int climb(int u, int k) { if(dep[u] < k) return -1; for(int i = LOG - 1; i >= 0; i--) { if((k >> i) & 1) u = table[i][u]; } return u; } T dist(int u, int v) { return sum[u] + sum[v] - 2 * sum[lca(u, v)]; } private: void dfs(int idx, int par, int d) { table[0][idx] = par; dep[idx] = d; for(auto &to : g[idx]) { if(to != par) { sum[to] = sum[idx] + to.cost; dfs(to, idx, d + 1); } } } }; #line 7 "test/verify/yosupo-lca-3.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-3.test.cpp" int main() { Scanner in(stdin); Printer out(stdout); int N, Q; in.read(N, Q); DoublingLowestCommonAncestor< 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)); } }