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// LCA // Notes: // - Index from 0 // - Cannot use for queries like min edge in path u -> v // // Tested: // - https://judge.yosupo.jp/problem/lca #include "RMQ.h" struct LCA { const int n; vector<vector<int>> adj; const int root; using P = pair<int,int>; static P f(P x, P y) { return std::min(x, y); } LCA(int _n, const vector<vector<int>>& _adj, int _root) : n(_n), adj(_adj), root(_root) { assert(0 <= root && root < n); id.resize(n); depth.resize(n); order.reserve(2 * n); dfs(root, -1, 0); rmq = RMQ<P, f>(order); } int lca(int u, int v) { assert(0 <= u && u < n); assert(0 <= v && v < n); int x = id[u], y = id[v]; if (x > y) std::swap(x, y); return rmq.get(x, y+1).second; } // private: vector<int> id, depth; vector<P> order; RMQ<P, f> rmq; void dfs(int u, int fu, int d) { id[u] = order.size(); depth[u] = d; order.emplace_back(d, u); for (int v : adj[u]) { if (v == fu) continue; dfs(v, u, d + 1); order.emplace_back(d, u); } } };
#line 1 "DataStructure/LCA.h" // LCA // Notes: // - Index from 0 // - Cannot use for queries like min edge in path u -> v // // Tested: // - https://judge.yosupo.jp/problem/lca #line 1 "DataStructure/RMQ.h" // RMQ {{{ // // Sparse table // Usage: // RMQ<int, _min> st(v); // // Note: // - doesn't work for empty range // // Tested: // - https://judge.yosupo.jp/problem/staticrmq template<class T, T (*op) (T, T)> struct RMQ { RMQ() = default; RMQ(const vector<T>& v) : t{v}, n{(int) v.size()} { for (int k = 1; (1<<k) <= n; ++k) { t.emplace_back(n - (1<<k) + 1); for (int i = 0; i + (1<<k) <= n; ++i) { t[k][i] = op(t[k-1][i], t[k-1][i + (1<<(k-1))]); } } } // get range [l, r-1] // doesn't work for empty range T get(int l, int r) const { assert(0 <= l && l < r && r <= n); int k = __lg(r - l); return op(t[k][l], t[k][r - (1<<k)]); } private: vector<vector<T>> t; int n; }; template<class T> T _min(T a, T b) { return b < a ? b : a; } template<class T> T _max(T a, T b) { return a < b ? b : a; } // }}} #line 9 "DataStructure/LCA.h" struct LCA { const int n; vector<vector<int>> adj; const int root; using P = pair<int,int>; static P f(P x, P y) { return std::min(x, y); } LCA(int _n, const vector<vector<int>>& _adj, int _root) : n(_n), adj(_adj), root(_root) { assert(0 <= root && root < n); id.resize(n); depth.resize(n); order.reserve(2 * n); dfs(root, -1, 0); rmq = RMQ<P, f>(order); } int lca(int u, int v) { assert(0 <= u && u < n); assert(0 <= v && v < n); int x = id[u], y = id[v]; if (x > y) std::swap(x, y); return rmq.get(x, y+1).second; } // private: vector<int> id, depth; vector<P> order; RMQ<P, f> rmq; void dfs(int u, int fu, int d) { id[u] = order.size(); depth[u] = d; order.emplace_back(d, u); for (int v : adj[u]) { if (v == fu) continue; dfs(v, u, d + 1); order.emplace_back(d, u); } } };