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#pragma once #include "template.cpp" #include "graph/graph.cpp" class HLD { private: VI index, sz, par, rev; // last vertex in ascending heavy path VI nxt; public: HLD(Graph& graph) : index(graph.size()), sz(graph.size(), 1), par(graph.size(), -1), rev(graph.size()), nxt(graph.size()) { dfs_sz(graph, 0); dfs_hld(graph, 0); } private: void dfs_sz(Graph& graph, int v) { if (graph[v].size() >= 2 and graph[v][0] == par[v]) swap(graph[v][0], graph[v][1]); for (auto& c : graph[v]) if (c != par[v]) { par[c] = v; dfs_sz(graph, c); sz[v] += sz[c]; if (sz[c] > sz[graph[v][0]]) swap(c, graph[v][0]); } } void dfs_hld(const Graph& graph, int v) { static int t = 0; index[v] = t++; rev[index[v]] = v; for (auto c : graph[v]) if (c != par[v]) { nxt[c] = (c.to == graph[v][0].to ? nxt[v] : c.to); dfs_hld(graph, c); } assert(sz[v] == t - index[v]); } public: template <typename F> void path_vertex(int u, int v, F f) { while (true) { if (index[u] > index[v]) swap(u, v); // debug(u); debug(v); // debug(nxt[u]); debug(index[u]); f(max(index[nxt[v]], index[u]), index[v] + 1); if (nxt[u] != nxt[v]) v = par[nxt[v]]; else break; } } template <typename F> void path_edge(int u, int v, F f) { while (true) { if (index[u] > index[v]) swap(u, v); if (nxt[u] != nxt[v]) { f(index[nxt[v]], index[v] + 1); v = par[nxt[v]]; } else { if (u != v) f(index[u] + 1, index[v] + 1); break; } } } template <typename F> void subtree_vertex(int v, F f) { f(index[v], index[v] + sz[v]); } template <typename F> void subtree_edge(int v, F f) { f(index[v] + 1, index[v] + sz[v]); } int lca(int u, int v) { while (1) { if (index[u] > index[v]) swap(u, v); if (nxt[u] == nxt[v]) return u; v = par[nxt[v]]; } } int subtree_size(int v) { return sz[v]; } int vertex(int v) { return index[v]; } int parent(int v) { return par[v]; } int restore(int ix) { return rev[ix]; } };
#line 2 "tree/hld.cpp" #line 2 "template.cpp" #ifndef LOCAL #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #pragma GCC target("avx") #endif #include <algorithm> #include <bitset> #include <cassert> #include <cmath> #include <functional> #include <iostream> #include <map> #include <numeric> #include <queue> #include <set> #include <stack> using namespace std; using ll = long long; using ull = unsigned long long; using VI = vector<int>; using VVI = vector<vector<int>>; using VLL = vector<ll>; using VVLL = vector<vector<ll>>; using VB = vector<bool>; using PII = pair<int, int>; using PLL = pair<ll, ll>; constexpr int INF = 1000000007; constexpr ll INF_LL = 1'000'000'000'000'000'007; #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) #define newl '\n' // loops rep(until) / rep(var, until) / rep(var, from, until) / repr (reversed order) #define OVERLOAD3(_1, _2, _3, name, ...) name #define rep(...) OVERLOAD3(__VA_ARGS__, REPEAT_FROM_UNTIL, REPEAT_UNTIL, REPEAT)(__VA_ARGS__) #define REPEAT(times) REPEAT_CNT(_repeat, __COUNTER__, times) #define REPEAT_CNT(_repeat, cnt, times) REPEAT_CNT_CAT(_repeat, cnt, times) #define REPEAT_CNT_CAT(_repeat, cnt, times) REPEAT_FROM_UNTIL(_repeat ## cnt, 0, times) #define REPEAT_UNTIL(name, times) REPEAT_FROM_UNTIL(name, 0, times) #define REPEAT_FROM_UNTIL(name, from, until) for (int name = from, name ## __until = (until); name < name ## __until; name++) #define repr(...) OVERLOAD3(__VA_ARGS__, REPR_FROM_UNTIL, REPR_UNTIL, REPEAT)(__VA_ARGS__) #define REPR_UNTIL(name, times) REPR_FROM_UNTIL(name, 0, times) #define REPR_FROM_UNTIL(name, from, until) for (int name = (until)-1, name ## __from = (from); name >= name ## __from; name--) template <typename T, typename U> bool chmin(T& var, U x) { if (var > x) { var = x; return true; } else return false; } template <typename T, typename U> bool chmax(T& var, U x) { if (var < x) { var = x; return true; } else return false; } ll power(ll e, ll t, ll mod = INF_LL) { ll res = 1; for (; t; t >>= 1, (e *= e) %= mod) if (t & 1) (res *= e) %= mod; return res; } ll choose(ll n, int r) { chmin(r, n-r); if (r < 0) return 0; ll res = 1; rep(i, r) res *= n-i, res /= i+1; return res; } template <typename T, typename U> T divceil(T m, U d) { return (m + d - 1) / d; } template <typename T> vector<T> make_v(size_t a, T b) { return vector<T>(a, b); } template <typename... Ts> auto make_v(size_t a, Ts... ts) { return vector<decltype(make_v(ts...))>(a, make_v(ts...)); } // debugging stuff #pragma GCC diagnostic push #pragma GCC diagnostic ignored "-Wmisleading-indentation" #define repi(it, ds) for (auto it = ds.begin(); it != ds.end(); it++) class DebugPrint { public: template <typename T> DebugPrint& operator <<(const T& v) { #ifdef LOCAL cerr << v; #endif return *this; } } debugos; template <typename T> DebugPrint& operator<<(DebugPrint& os, const vector<T>& vec) { os << "{"; for (int i = 0; i < vec.size(); i++) os << vec[i] << (i + 1 == vec.size() ? "" : ", "); os << "}"; return os; } template <typename T, typename U> DebugPrint& operator<<(DebugPrint& os, const map<T, U>& map_var) { os << "{"; repi(itr, map_var) { os << * itr; itr++; if (itr != map_var.end()) os << ", "; itr--; } os << "}"; return os; } template < typename T> DebugPrint& operator<<(DebugPrint& os, const set<T>& set_var) { os << "{"; repi( itr, set_var) { os << *itr; itr++; if (itr != set_var.end()) os << ", "; itr--; } os << "}"; return os; } template <typename T, typename U> DebugPrint& operator<<(DebugPrint& os, const pair<T, U>& p) { os << "(" << p.first << ", " << p.second << ")"; return os; } void dump_func( ) { debugos << newl; } template <class Head, class... Tail> void dump_func(Head &&head, Tail &&... tail) { debugos << head; if (sizeof...(Tail) > 0) { debugos << ", "; } dump_func(forward <Tail>(tail)...); } #ifdef LOCAL #define dump(...) debugos << " " << string(#__VA_ARGS__) << ": " << "[" << to_string(__LINE__) \ << ":" << __FUNCTION__ << "]" << newl << " ", dump_func(__VA_ARGS__) #else #define dump(...) ({}) #endif #pragma GCC diagnostic pop #line 2 "graph/graph.cpp" #line 4 "graph/graph.cpp" struct Edge { int to; ll cost; Edge(int _to) : to(_to), cost(1) {} Edge(int _to, ll _cost) : to(_to), cost(_cost) {} operator int() const { return to; } }; using Graph = vector<vector<Edge>>; #line 5 "tree/hld.cpp" class HLD { private: VI index, sz, par, rev; // last vertex in ascending heavy path VI nxt; public: HLD(Graph& graph) : index(graph.size()), sz(graph.size(), 1), par(graph.size(), -1), rev(graph.size()), nxt(graph.size()) { dfs_sz(graph, 0); dfs_hld(graph, 0); } private: void dfs_sz(Graph& graph, int v) { if (graph[v].size() >= 2 and graph[v][0] == par[v]) swap(graph[v][0], graph[v][1]); for (auto& c : graph[v]) if (c != par[v]) { par[c] = v; dfs_sz(graph, c); sz[v] += sz[c]; if (sz[c] > sz[graph[v][0]]) swap(c, graph[v][0]); } } void dfs_hld(const Graph& graph, int v) { static int t = 0; index[v] = t++; rev[index[v]] = v; for (auto c : graph[v]) if (c != par[v]) { nxt[c] = (c.to == graph[v][0].to ? nxt[v] : c.to); dfs_hld(graph, c); } assert(sz[v] == t - index[v]); } public: template <typename F> void path_vertex(int u, int v, F f) { while (true) { if (index[u] > index[v]) swap(u, v); // debug(u); debug(v); // debug(nxt[u]); debug(index[u]); f(max(index[nxt[v]], index[u]), index[v] + 1); if (nxt[u] != nxt[v]) v = par[nxt[v]]; else break; } } template <typename F> void path_edge(int u, int v, F f) { while (true) { if (index[u] > index[v]) swap(u, v); if (nxt[u] != nxt[v]) { f(index[nxt[v]], index[v] + 1); v = par[nxt[v]]; } else { if (u != v) f(index[u] + 1, index[v] + 1); break; } } } template <typename F> void subtree_vertex(int v, F f) { f(index[v], index[v] + sz[v]); } template <typename F> void subtree_edge(int v, F f) { f(index[v] + 1, index[v] + sz[v]); } int lca(int u, int v) { while (1) { if (index[u] > index[v]) swap(u, v); if (nxt[u] == nxt[v]) return u; v = par[nxt[v]]; } } int subtree_size(int v) { return sz[v]; } int vertex(int v) { return index[v]; } int parent(int v) { return par[v]; } int restore(int ix) { return rev[ix]; } };