#define PROBLEM "https://judge.yosupo.jp/problem/aplusb" // #include "../../template/template.hpp" // #include "../../tree/dynamic-diameter.hpp" using namespace Nyaan; // #include "../../graph/graph-utility.hpp" // #include "../../shortest-path/dijkstra.hpp" // #include "../../misc/rng.hpp" void test() { ll wmax = TEN(9); rep1(N, 50) { rep(_, 100) { WeightedGraph<ll> g; Edges<ll> es; rep1(i, N - 1) { int j = rng(0, i - 1); es.emplace_back(j, i, rng(0, wmax)); } auto gen = [&]() { g.clear(); g.resize(N); each(e, es) { g[e.src].emplace_back(e.src, e.to, e.cost); g[e.to].emplace_back(e.to, e.src, e.cost); } }; gen(); auto DP = DynamicDiameter(g); rep(t, 100) { // check auto [d, uv] = DP.get(); ll d2 = -1; { int u = 0; auto du = dijkstra(g, u); int v = max_element(all(du)) - begin(du); auto dv = dijkstra(g, v); int w = max_element(all(dv)) - begin(dv); d2 = dv[w]; } assert(uv.first != -1 and uv.second != -1); assert(d == d2); assert(d == dijkstra(g, uv.first)[uv.second]); if (N >= 2) { // update int e_num = rng(0, N - 2); int u = es[e_num].src, v = es[e_num].to; ll x = rng(0, wmax); DP.update(u, v, x); es[e_num].cost = x; gen(); } } } } trc2("OK"); } void q() { test(); int a, b; cin >> a >> b; cout << a + b << endl; } void Nyaan::solve() { int t = 1; // in(t); while (t--) q(); }
#line 1 "verify/verify-unit-test/dynamic-diameter.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/aplusb" // #line 2 "template/template.hpp" using namespace std; // intrinstic #include <immintrin.h> #include <algorithm> #include <array> #include <bitset> #include <cassert> #include <cctype> #include <cfenv> #include <cfloat> #include <chrono> #include <cinttypes> #include <climits> #include <cmath> #include <complex> #include <cstdarg> #include <cstddef> #include <cstdint> #include <cstdio> #include <cstdlib> #include <cstring> #include <deque> #include <fstream> #include <functional> #include <initializer_list> #include <iomanip> #include <ios> #include <iostream> #include <istream> #include <iterator> #include <limits> #include <list> #include <map> #include <memory> #include <new> #include <numeric> #include <ostream> #include <queue> #include <random> #include <set> #include <sstream> #include <stack> #include <streambuf> #include <string> #include <tuple> #include <type_traits> #include <typeinfo> #include <unordered_map> #include <unordered_set> #include <utility> #include <vector> // utility #line 1 "template/util.hpp" namespace Nyaan { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; template <typename T> using V = vector<T>; template <typename T> using VV = vector<vector<T>>; using vi = vector<int>; using vl = vector<long long>; using vd = V<double>; using vs = V<string>; using vvi = vector<vector<int>>; using vvl = vector<vector<long long>>; template <typename T> using minpq = priority_queue<T, vector<T>, greater<T>>; template <typename T, typename U> struct P : pair<T, U> { template <typename... Args> P(Args... args) : pair<T, U>(args...) {} using pair<T, U>::first; using pair<T, U>::second; P &operator+=(const P &r) { first += r.first; second += r.second; return *this; } P &operator-=(const P &r) { first -= r.first; second -= r.second; return *this; } P &operator*=(const P &r) { first *= r.first; second *= r.second; return *this; } template <typename S> P &operator*=(const S &r) { first *= r, second *= r; return *this; } P operator+(const P &r) const { return P(*this) += r; } P operator-(const P &r) const { return P(*this) -= r; } P operator*(const P &r) const { return P(*this) *= r; } template <typename S> P operator*(const S &r) const { return P(*this) *= r; } P operator-() const { return P{-first, -second}; } }; using pl = P<ll, ll>; using pi = P<int, int>; using vp = V<pl>; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template <typename T> int sz(const T &t) { return t.size(); } template <typename T, typename U> inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template <typename T, typename U> inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template <typename T> inline T Max(const vector<T> &v) { return *max_element(begin(v), end(v)); } template <typename T> inline T Min(const vector<T> &v) { return *min_element(begin(v), end(v)); } template <typename T> inline long long Sum(const vector<T> &v) { return accumulate(begin(v), end(v), 0LL); } template <typename T> int lb(const vector<T> &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template <typename T> int ub(const vector<T> &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } constexpr long long TEN(int n) { long long ret = 1, x = 10; for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1); return ret; } template <typename T, typename U> pair<T, U> mkp(const T &t, const U &u) { return make_pair(t, u); } template <typename T> vector<T> mkrui(const vector<T> &v, bool rev = false) { vector<T> ret(v.size() + 1); if (rev) { for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1]; } else { for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; } return ret; }; template <typename T> vector<T> mkuni(const vector<T> &v) { vector<T> ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template <typename F> vector<int> mkord(int N, F f) { vector<int> ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template <typename T> vector<int> mkinv(vector<T> &v) { int max_val = *max_element(begin(v), end(v)); vector<int> inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } vector<int> mkiota(int n) { vector<int> ret(n); iota(begin(ret), end(ret), 0); return ret; } template <typename T> T mkrev(const T &v) { T w{v}; reverse(begin(w), end(w)); return w; } template <typename T> bool nxp(T &v) { return next_permutation(begin(v), end(v)); } // 返り値の型は入力の T に依存 // i 要素目 : [0, a[i]) template <typename T> vector<vector<T>> product(const vector<T> &a) { vector<vector<T>> ret; vector<T> v; auto dfs = [&](auto rc, int i) -> void { if (i == (int)a.size()) { ret.push_back(v); return; } for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back(); }; dfs(dfs, 0); return ret; } // F : function(void(T&)), mod を取る操作 // T : 整数型のときはオーバーフローに注意する template <typename T> T Power(T a, long long n, const T &I, const function<void(T &)> &f) { T res = I; for (; n; f(a = a * a), n >>= 1) { if (n & 1) f(res = res * a); } return res; } // T : 整数型のときはオーバーフローに注意する template <typename T> T Power(T a, long long n, const T &I = T{1}) { return Power(a, n, I, function<void(T &)>{[](T &) -> void {}}); } template <typename T> T Rev(const T &v) { T res = v; reverse(begin(res), end(res)); return res; } template <typename T> vector<T> Transpose(const vector<T> &v) { using U = typename T::value_type; if(v.empty()) return {}; int H = v.size(), W = v[0].size(); vector res(W, T(H, U{})); for (int i = 0; i < H; i++) { for (int j = 0; j < W; j++) { res[j][i] = v[i][j]; } } return res; } template <typename T> vector<T> Rotate(const vector<T> &v, int clockwise = true) { using U = typename T::value_type; int H = v.size(), W = v[0].size(); vector res(W, T(H, U{})); for (int i = 0; i < H; i++) { for (int j = 0; j < W; j++) { if (clockwise) { res[W - 1 - j][i] = v[i][j]; } else { res[j][H - 1 - i] = v[i][j]; } } } return res; } } // namespace Nyaan #line 58 "template/template.hpp" // bit operation #line 1 "template/bitop.hpp" namespace Nyaan { __attribute__((target("popcnt"))) inline int popcnt(const u64 &a) { return __builtin_popcountll(a); } inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; } template <typename T> inline int gbit(const T &a, int i) { return (a >> i) & 1; } template <typename T> inline void sbit(T &a, int i, bool b) { if (gbit(a, i) != b) a ^= T(1) << i; } constexpr long long PW(int n) { return 1LL << n; } constexpr long long MSK(int n) { return (1LL << n) - 1; } } // namespace Nyaan #line 61 "template/template.hpp" // inout #line 1 "template/inout.hpp" namespace Nyaan { template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &p) { os << p.first << " " << p.second; return os; } template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &p) { is >> p.first >> p.second; return is; } template <typename T> ostream &operator<<(ostream &os, const vector<T> &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template <typename T> istream &operator>>(istream &is, vector<T> &v) { for (auto &x : v) is >> x; return is; } istream &operator>>(istream &is, __int128_t &x) { string S; is >> S; x = 0; int flag = 0; for (auto &c : S) { if (c == '-') { flag = true; continue; } x *= 10; x += c - '0'; } if (flag) x = -x; return is; } istream &operator>>(istream &is, __uint128_t &x) { string S; is >> S; x = 0; for (auto &c : S) { x *= 10; x += c - '0'; } return is; } ostream &operator<<(ostream &os, __int128_t x) { if (x == 0) return os << 0; if (x < 0) os << '-', x = -x; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } ostream &operator<<(ostream &os, __uint128_t x) { if (x == 0) return os << 0; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } void in() {} template <typename T, class... U> void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template <typename T, class... U, char sep = ' '> void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } struct IoSetupNya { IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupnya; } // namespace Nyaan #line 64 "template/template.hpp" // debug #line 1 "template/debug.hpp" namespace DebugImpl { template <typename U, typename = void> struct is_specialize : false_type {}; template <typename U> struct is_specialize< U, typename conditional<false, typename U::iterator, void>::type> : true_type {}; template <typename U> struct is_specialize< U, typename conditional<false, decltype(U::first), void>::type> : true_type {}; template <typename U> struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type { }; void dump(const char& t) { cerr << t; } void dump(const string& t) { cerr << t; } void dump(const bool& t) { cerr << (t ? "true" : "false"); } void dump(__int128_t t) { if (t == 0) cerr << 0; if (t < 0) cerr << '-', t = -t; string S; while (t) S.push_back('0' + t % 10), t /= 10; reverse(begin(S), end(S)); cerr << S; } void dump(__uint128_t t) { if (t == 0) cerr << 0; string S; while (t) S.push_back('0' + t % 10), t /= 10; reverse(begin(S), end(S)); cerr << S; } template <typename U, enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr> void dump(const U& t) { cerr << t; } template <typename T> void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) { string res; if (t == Nyaan::inf) res = "inf"; if constexpr (is_signed<T>::value) { if (t == -Nyaan::inf) res = "-inf"; } if constexpr (sizeof(T) == 8) { if (t == Nyaan::infLL) res = "inf"; if constexpr (is_signed<T>::value) { if (t == -Nyaan::infLL) res = "-inf"; } } if (res.empty()) res = to_string(t); cerr << res; } template <typename T, typename U> void dump(const pair<T, U>&); template <typename T> void dump(const pair<T*, int>&); template <typename T> void dump(const T& t, enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) { cerr << "[ "; for (auto it = t.begin(); it != t.end();) { dump(*it); cerr << (++it == t.end() ? "" : ", "); } cerr << " ]"; } template <typename T, typename U> void dump(const pair<T, U>& t) { cerr << "( "; dump(t.first); cerr << ", "; dump(t.second); cerr << " )"; } template <typename T> void dump(const pair<T*, int>& t) { cerr << "[ "; for (int i = 0; i < t.second; i++) { dump(t.first[i]); cerr << (i == t.second - 1 ? "" : ", "); } cerr << " ]"; } void trace() { cerr << endl; } template <typename Head, typename... Tail> void trace(Head&& head, Tail&&... tail) { cerr << " "; dump(head); if (sizeof...(tail) != 0) cerr << ","; trace(std::forward<Tail>(tail)...); } } // namespace DebugImpl #ifdef NyaanDebug #define trc(...) \ do { \ cerr << "## " << #__VA_ARGS__ << " = "; \ DebugImpl::trace(__VA_ARGS__); \ } while (0) #else #define trc(...) (void(0)) #endif #ifdef NyaanLocal #define trc2(...) \ do { \ cerr << "## " << #__VA_ARGS__ << " = "; \ DebugImpl::trace(__VA_ARGS__); \ } while (0) #else #define trc2(...) (void(0)) #endif #line 67 "template/template.hpp" // macro #line 1 "template/macro.hpp" #define each(x, v) for (auto&& x : v) #define each2(x, y, v) for (auto&& [x, y] : v) #define all(v) (v).begin(), (v).end() #define rep(i, N) for (long long i = 0; i < (long long)(N); i++) #define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--) #define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++) #define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--) #define reg(i, a, b) for (long long i = (a); i < (b); i++) #define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--) #define fi first #define se second #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define die(...) \ do { \ Nyaan::out(__VA_ARGS__); \ return; \ } while (0) #line 70 "template/template.hpp" namespace Nyaan { void solve(); } int main() { Nyaan::solve(); } #line 4 "verify/verify-unit-test/dynamic-diameter.test.cpp" // #line 2 "tree/dynamic-diameter.hpp" #line 9 "tree/dynamic-diameter.hpp" using namespace std; #line 2 "graph/graph-template.hpp" template <typename T> struct edge { int src, to; T cost; edge(int _to, T _cost) : src(-1), to(_to), cost(_cost) {} edge(int _src, int _to, T _cost) : src(_src), to(_to), cost(_cost) {} edge &operator=(const int &x) { to = x; return *this; } operator int() const { return to; } }; template <typename T> using Edges = vector<edge<T>>; template <typename T> using WeightedGraph = vector<Edges<T>>; using UnweightedGraph = vector<vector<int>>; // Input of (Unweighted) Graph UnweightedGraph graph(int N, int M = -1, bool is_directed = false, bool is_1origin = true) { UnweightedGraph g(N); if (M == -1) M = N - 1; for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; if (is_1origin) x--, y--; g[x].push_back(y); if (!is_directed) g[y].push_back(x); } return g; } // Input of Weighted Graph template <typename T> WeightedGraph<T> wgraph(int N, int M = -1, bool is_directed = false, bool is_1origin = true) { WeightedGraph<T> g(N); if (M == -1) M = N - 1; for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; T c; cin >> c; if (is_1origin) x--, y--; g[x].emplace_back(x, y, c); if (!is_directed) g[y].emplace_back(y, x, c); } return g; } // Input of Edges template <typename T> Edges<T> esgraph([[maybe_unused]] int N, int M, int is_weighted = true, bool is_1origin = true) { Edges<T> es; for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; T c; if (is_weighted) cin >> c; else c = 1; if (is_1origin) x--, y--; es.emplace_back(x, y, c); } return es; } // Input of Adjacency Matrix template <typename T> vector<vector<T>> adjgraph(int N, int M, T INF, int is_weighted = true, bool is_directed = false, bool is_1origin = true) { vector<vector<T>> d(N, vector<T>(N, INF)); for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; T c; if (is_weighted) cin >> c; else c = 1; if (is_1origin) x--, y--; d[x][y] = c; if (!is_directed) d[y][x] = c; } return d; } /** * @brief グラフテンプレート * @docs docs/graph/graph-template.md */ #line 2 "tree/static-top-tree-vertex-based.hpp" #line 6 "tree/static-top-tree-vertex-based.hpp" using namespace std; #line 2 "tree/convert-tree.hpp" #line 4 "tree/convert-tree.hpp" template <typename T> struct has_cost { private: template <typename U> static auto confirm(U u) -> decltype(u.cost, std::true_type()); static auto confirm(...) -> std::false_type; public: enum : bool { value = decltype(confirm(std::declval<T>()))::value }; }; template <typename T> vector<vector<T>> inverse_tree(const vector<vector<T>>& g) { int N = (int)g.size(); vector<vector<T>> rg(N); for (int i = 0; i < N; i++) { for (auto& e : g[i]) { if constexpr (is_same<T, int>::value) { rg[e].push_back(i); } else if constexpr (has_cost<T>::value) { rg[e].emplace_back(e.to, i, e.cost); } else { assert(0); } } } return rg; } template <typename T> vector<vector<T>> rooted_tree(const vector<vector<T>>& g, int root = 0) { int N = (int)g.size(); vector<vector<T>> rg(N); vector<char> v(N, false); v[root] = true; queue<int> que; que.emplace(root); while (!que.empty()) { auto p = que.front(); que.pop(); for (auto& e : g[p]) { if (v[e] == false) { v[e] = true; que.push(e); rg[p].push_back(e); } } } return rg; } /** * @brief 根付き木・逆辺からなる木への変換 */ #line 2 "tree/heavy-light-decomposition.hpp" #line 4 "tree/heavy-light-decomposition.hpp" template <typename G> struct HeavyLightDecomposition { private: void dfs_sz(int cur) { size[cur] = 1; for (auto& dst : g[cur]) { if (dst == par[cur]) { if (g[cur].size() >= 2 && int(dst) == int(g[cur][0])) swap(g[cur][0], g[cur][1]); else continue; } depth[dst] = depth[cur] + 1; par[dst] = cur; dfs_sz(dst); size[cur] += size[dst]; if (size[dst] > size[g[cur][0]]) { swap(dst, g[cur][0]); } } } void dfs_hld(int cur) { down[cur] = id++; for (auto dst : g[cur]) { if (dst == par[cur]) continue; nxt[dst] = (int(dst) == int(g[cur][0]) ? nxt[cur] : int(dst)); dfs_hld(dst); } up[cur] = id; } // [u, v) vector<pair<int, int>> ascend(int u, int v) const { vector<pair<int, int>> res; while (nxt[u] != nxt[v]) { res.emplace_back(down[u], down[nxt[u]]); u = par[nxt[u]]; } if (u != v) res.emplace_back(down[u], down[v] + 1); return res; } // (u, v] vector<pair<int, int>> descend(int u, int v) const { if (u == v) return {}; if (nxt[u] == nxt[v]) return {{down[u] + 1, down[v]}}; auto res = descend(u, par[nxt[v]]); res.emplace_back(down[nxt[v]], down[v]); return res; } public: G& g; int root, id; vector<int> size, depth, down, up, nxt, par; HeavyLightDecomposition(G& _g, int _root = 0) : g(_g), root(_root), id(0), size(g.size(), 0), depth(g.size(), 0), down(g.size(), -1), up(g.size(), -1), nxt(g.size(), root), par(g.size(), root) { dfs_sz(root); dfs_hld(root); } pair<int, int> idx(int i) const { return make_pair(down[i], up[i]); } template <typename F> void path_query(int u, int v, bool vertex, const F& f) { int l = lca(u, v); for (auto&& [a, b] : ascend(u, l)) { int s = a + 1, t = b; s > t ? f(t, s) : f(s, t); } if (vertex) f(down[l], down[l] + 1); for (auto&& [a, b] : descend(l, v)) { int s = a, t = b + 1; s > t ? f(t, s) : f(s, t); } } template <typename F> void path_noncommutative_query(int u, int v, bool vertex, const F& f) { int l = lca(u, v); for (auto&& [a, b] : ascend(u, l)) f(a + 1, b); if (vertex) f(down[l], down[l] + 1); for (auto&& [a, b] : descend(l, v)) f(a, b + 1); } template <typename F> void subtree_query(int u, bool vertex, const F& f) { f(down[u] + int(!vertex), up[u]); } int lca(int a, int b) { while (nxt[a] != nxt[b]) { if (down[a] < down[b]) swap(a, b); a = par[nxt[a]]; } return depth[a] < depth[b] ? a : b; } int dist(int a, int b) { return depth[a] + depth[b] - depth[lca(a, b)] * 2; } }; /** * @brief Heavy Light Decomposition(重軽分解) * @docs docs/tree/heavy-light-decomposition.md */ #line 10 "tree/static-top-tree-vertex-based.hpp" namespace StaticTopTreeVertexBasedImpl { enum Type { Vertex, Compress, Rake, Add_Edge, Add_Vertex }; template <typename G> struct StaticTopTreeVertexBased { const HeavyLightDecomposition<G>& hld; vector<vector<int>> g; int root; // 元の木の root int tt_root; // top tree の root vector<int> P, L, R; vector<Type> T; StaticTopTreeVertexBased(const HeavyLightDecomposition<G>& _hld) : hld(_hld) { root = hld.root; g = rooted_tree(hld.g, root); int n = g.size(); P.resize(n, -1), L.resize(n, -1), R.resize(n, -1); T.resize(n, Type::Vertex); build(); } private: int add(int l, int r, Type t) { if (t == Type::Compress or t == Type::Rake) { assert(l != -1 and r != -1); } if (t == Type::Add_Edge) { assert(l != -1 and r == -1); } assert(t != Type::Vertex and t != Type::Add_Vertex); int k = P.size(); P.push_back(-1), L.push_back(l), R.push_back(r), T.push_back(t); if (l != -1) P[l] = k; if (r != -1) P[r] = k; return k; } int add2(int k, int l, int r, Type t) { assert(k < (int)g.size()); assert(t == Type::Vertex or t == Type::Add_Vertex); if (t == Type::Vertex) { assert(l == -1 and r == -1); } else { assert(l != -1 and r == -1); } P[k] = -1, L[k] = l, R[k] = r, T[k] = t; if (l != -1) P[l] = k; if (r != -1) P[r] = k; return k; } pair<int, int> merge(const vector<pair<int, int>>& a, Type t) { assert(!a.empty()); if (a.size() == 1) return a[0]; int sum_s = 0; for (auto& [_, s] : a) sum_s += s; vector<pair<int, int>> b, c; for (auto& [i, s] : a) { (sum_s > s ? b : c).emplace_back(i, s); sum_s -= s * 2; } auto [i, si] = merge(b, t); auto [j, sj] = merge(c, t); return {add(i, j, t), si + sj}; } pair<int, int> compress(int i) { vector<pair<int, int>> chs; while (true) { chs.push_back(add_vertex(i)); if (g[i].empty()) break; i = g[i][0]; } return merge(chs, Type::Compress); } pair<int, int> rake(int i) { vector<pair<int, int>> chs; for (int j = 1; j < (int)g[i].size(); j++) chs.push_back(add_edge(g[i][j])); if (chs.empty()) return {-1, 0}; return merge(chs, Type::Rake); } pair<int, int> add_edge(int i) { auto [j, sj] = compress(i); return {add(j, -1, Type::Add_Edge), sj}; } pair<int, int> add_vertex(int i) { auto [j, sj] = rake(i); return {add2(i, j, -1, j == -1 ? Type::Vertex : Type::Add_Vertex), sj + 1}; } void build() { auto [i, n] = compress(root); assert((int)g.size() == n); tt_root = i; } }; template <typename G, typename Path, typename Point, typename Vertex, typename Compress, typename Rake, typename Add_edge, typename Add_vertex> struct DPonStaticTopTreeVertexBased { const StaticTopTreeVertexBased<G> tt; vector<Path> path; vector<Point> point; const Vertex vertex; const Compress compress; const Rake rake; const Add_edge add_edge; const Add_vertex add_vertex; DPonStaticTopTreeVertexBased(const HeavyLightDecomposition<G>& hld, const Vertex& _vertex, const Compress& _compress, const Rake& _rake, const Add_edge& _add_edge, const Add_vertex& _add_vertex) : tt(hld), vertex(_vertex), compress(_compress), rake(_rake), add_edge(_add_edge), add_vertex(_add_vertex) { int n = tt.P.size(); path.resize(n), point.resize(n); dfs(tt.tt_root); } Path get() { return path[tt.tt_root]; } void update(int k) { while (k != -1) _update(k), k = tt.P[k]; } private: void _update(int k) { if (tt.T[k] == Type::Vertex) { path[k] = vertex(k); } else if (tt.T[k] == Type::Compress) { path[k] = compress(path[tt.L[k]], path[tt.R[k]]); } else if (tt.T[k] == Type::Rake) { point[k] = rake(point[tt.L[k]], point[tt.R[k]]); } else if (tt.T[k] == Type::Add_Edge) { point[k] = add_edge(path[tt.L[k]]); } else { path[k] = add_vertex(point[tt.L[k]], k); } } void dfs(int k) { if (tt.L[k] != -1) dfs(tt.L[k]); if (tt.R[k] != -1) dfs(tt.R[k]); _update(k); } }; } // namespace StaticTopTreeVertexBasedImpl using StaticTopTreeVertexBasedImpl::DPonStaticTopTreeVertexBased; using StaticTopTreeVertexBasedImpl::StaticTopTreeVertexBased; /* // template using Path = ; using Point = ; auto vertex = [&](int i) -> Path { }; auto compress = [&](const Path& p, const Path& c) -> Path { }; auto rake = [&](const Point& a, const Point& b) -> Point { }; auto add_edge = [&](const Path& a) -> Point { }; auto add_vertex = [&](const Point& a, int i) -> Path { }; HeavyLightDecomposition hld{g}; DPonStaticTopTreeVertexBased<vector<vector<int>>, Path, Point, decltype(vertex), decltype(compress), decltype(rake), decltype(add_edge), decltype(add_vertex)> dp(hld, vertex, compress, rake, add_edge, add_vertex); */ /** * @brief Static Top Tree */ #line 13 "tree/dynamic-diameter.hpp" namespace DynamicDiameterImpl { template <typename T> struct HalfPath { T d; int u; friend HalfPath max(const HalfPath& lhs, const HalfPath& rhs) { if (lhs.d != rhs.d) return lhs.d > rhs.d ? lhs : rhs; return lhs.u > rhs.u ? lhs : rhs; } }; template <typename T> struct Path { T d; int u, v; friend Path max(const Path& lhs, const Path& rhs) { if (lhs.d != rhs.d) return lhs.d > rhs.d ? lhs : rhs; if (lhs.u != rhs.u) return lhs.u > rhs.u ? lhs : rhs; return lhs.v > rhs.v ? lhs : rhs; } }; template <typename T> struct L { Path<T> dia; HalfPath<T> d1, d2; }; template <typename T> struct H { Path<T> dia; HalfPath<T> pd, cd; T p_to_c; int p, c; }; template <typename T> H<T> vertex(T x, int i) { H<T> r; r.dia = {x, i, i}; r.pd = r.cd = {x, i}; r.p_to_c = x; r.p = r.c = i; return r; } template <typename T> H<T> compress(const H<T>& p, const H<T>& c) { H<T> r; r.dia = max(max(p.dia, c.dia), {p.cd.d + c.pd.d, p.cd.u, c.pd.u}); r.pd = max(p.pd, {p.p_to_c + c.pd.d, c.pd.u}); r.cd = max(c.cd, {c.p_to_c + p.cd.d, p.cd.u}); r.p_to_c = p.p_to_c + c.p_to_c; r.p = p.p, r.c = c.c; return r; } template <typename T> L<T> rake(const L<T>& a, const L<T>& b) { L<T> r; r.dia = max(a.dia, b.dia); if (a.d1.d > b.d1.d) { r.d1 = a.d1; r.d2 = max(a.d2, b.d1); } else { r.d1 = b.d1; r.d2 = max(b.d2, a.d1); } return r; } template <typename T> L<T> add_edge(const H<T>& a) { L<T> r; r.dia = a.dia; r.d1 = a.pd; r.d2 = {0, -1}; return r; } template <typename T> H<T> add_vertex(const L<T>& a, T x, int i) { H<T> r; r.dia = max(a.dia, {a.d1.d + x + a.d2.d, a.d1.u, a.d2.u}); r.pd = r.cd = {a.d1.d + x, a.d1.u}; r.p_to_c = x; r.p = r.c = i; return r; } template <typename T> struct Aux_Tree { int N, _buf; const WeightedGraph<T>& g; vector<vector<int>> aux; vector<T> w; map<pair<int, int>, int> e_to_id; Aux_Tree(const WeightedGraph<T>& _g) : g(_g) { N = g.size(); aux.resize(2 * N - 1); w.resize(2 * N - 1); _buf = N; dfs(0, -1); assert(_buf == 2 * N - 1); } void dfs(int c, int p) { for (auto& d : g[c]) { if (d == p) continue; int id = _buf++; aux[id].push_back(c), aux[c].push_back(id); aux[id].push_back(d), aux[d].push_back(id); w[id] = d.cost; e_to_id[minmax<int>(c, d)] = id; dfs(d, c); } } }; template <typename T> struct DynamicDiameter { const WeightedGraph<T>& g; int n; Aux_Tree<T> aux; HeavyLightDecomposition<vector<vector<int>>> hld; DPonStaticTopTreeVertexBased< vector<vector<int>>, H<T>, L<T>, function<H<T>(int)>, function<H<T>(const H<T>&, const H<T>&)>, function<L<T>(const L<T>&, const L<T>&)>, function<L<T>(const H<T>&)>, function<H<T>(const L<T>&, int)>> dp; DynamicDiameter(const WeightedGraph<T>& _g) : g(_g), n(g.size()), aux(g), hld(aux.aux), dp( hld, [&](int i) { return vertex(aux.w[i], i < n ? i : -1); }, [&](const H<T>& p, const H<T>& c) { return compress(p, c); }, [&](const L<T>& a, const L<T>& b) { return rake(a, b); }, [&](const H<T>& a) { return add_edge(a); }, [&](const L<T>& a, int i) { return add_vertex(a, aux.w[i], i < n ? i : -1); }) {} pair<T, pair<int, int>> get() { auto [d, u, v] = dp.get().dia; return make_pair(d, make_pair(u, v)); } void update(int u, int v, T x) { assert(aux.e_to_id.count(minmax(u, v))); int i = aux.e_to_id[minmax(u, v)]; aux.w[i] = x; dp.update(i); } }; } // namespace DynamicDiameterImpl using DynamicDiameterImpl::DynamicDiameter; #line 6 "verify/verify-unit-test/dynamic-diameter.test.cpp" using namespace Nyaan; // #line 2 "graph/graph-utility.hpp" #line 4 "graph/graph-utility.hpp" // 一般のグラフのstからの距離!!!! // unvisited nodes : d = -1 vector<int> Depth(const UnweightedGraph &g, int start = 0) { int n = g.size(); vector<int> ds(n, -1); ds[start] = 0; queue<int> q; q.push(start); while (!q.empty()) { int c = q.front(); q.pop(); int dc = ds[c]; for (auto &d : g[c]) { if (ds[d] == -1) { ds[d] = dc + 1; q.push(d); } } } return ds; } // Depth of Rooted Weighted Tree // unvisited nodes : d = -1 template <typename T> vector<T> Depth(const WeightedGraph<T> &g, int start = 0) { vector<T> d(g.size(), -1); auto dfs = [&](auto rec, int cur, T val, int par = -1) -> void { d[cur] = val; for (auto &dst : g[cur]) { if (dst == par) continue; rec(rec, dst, val + dst.cost, cur); } }; dfs(dfs, start, 0); return d; } // Diameter of Tree // return value : { {u, v}, length } pair<pair<int, int>, int> Diameter(const UnweightedGraph &g) { auto d = Depth(g, 0); int u = max_element(begin(d), end(d)) - begin(d); d = Depth(g, u); int v = max_element(begin(d), end(d)) - begin(d); return make_pair(make_pair(u, v), d[v]); } // Diameter of Weighted Tree // return value : { {u, v}, length } template <typename T> pair<pair<int, int>, T> Diameter(const WeightedGraph<T> &g) { auto d = Depth(g, 0); int u = max_element(begin(d), end(d)) - begin(d); d = Depth(g, u); int v = max_element(begin(d), end(d)) - begin(d); return make_pair(make_pair(u, v), d[v]); } // nodes on the path u-v ( O(N) ) template <typename G> vector<int> Path(G &g, int u, int v) { vector<int> ret; int end = 0; auto dfs = [&](auto rec, int cur, int par = -1) -> void { ret.push_back(cur); if (cur == v) { end = 1; return; } for (int dst : g[cur]) { if (dst == par) continue; rec(rec, dst, cur); if (end) return; } if (end) return; ret.pop_back(); }; dfs(dfs, u); return ret; } /** * @brief グラフユーティリティ * @docs docs/graph/graph-utility.md */ #line 9 "verify/verify-unit-test/dynamic-diameter.test.cpp" // #line 2 "shortest-path/dijkstra.hpp" #line 4 "shortest-path/dijkstra.hpp" // unreachable -> -1 template <typename T> vector<T> dijkstra(WeightedGraph<T> &g, int start = 0) { using P = pair<T, int>; int N = (int)g.size(); vector<T> d(N, T(-1)); priority_queue<P, vector<P>, greater<P> > Q; d[start] = 0; Q.emplace(0, start); while (!Q.empty()) { P p = Q.top(); Q.pop(); int cur = p.second; if (d[cur] < p.first) continue; for (auto dst : g[cur]) { if (d[dst] == T(-1) || d[cur] + dst.cost < d[dst]) { d[dst] = d[cur] + dst.cost; Q.emplace(d[dst], dst); } } } return d; } /** * @brief ダイクストラ法 * @docs docs/shortest-path/dijkstra.md */ #line 11 "verify/verify-unit-test/dynamic-diameter.test.cpp" // #line 2 "misc/rng.hpp" #line 2 "internal/internal-seed.hpp" #line 4 "internal/internal-seed.hpp" using namespace std; namespace internal { unsigned long long non_deterministic_seed() { unsigned long long m = chrono::duration_cast<chrono::nanoseconds>( chrono::high_resolution_clock::now().time_since_epoch()) .count(); m ^= 9845834732710364265uLL; m ^= m << 24, m ^= m >> 31, m ^= m << 35; return m; } unsigned long long deterministic_seed() { return 88172645463325252UL; } // 64 bit の seed 値を生成 (手元では seed 固定) // 連続で呼び出すと同じ値が何度も返ってくるので注意 // #define RANDOMIZED_SEED するとシードがランダムになる unsigned long long seed() { #if defined(NyaanLocal) && !defined(RANDOMIZED_SEED) return deterministic_seed(); #else return non_deterministic_seed(); #endif } } // namespace internal #line 4 "misc/rng.hpp" namespace my_rand { using i64 = long long; using u64 = unsigned long long; // [0, 2^64 - 1) u64 rng() { static u64 _x = internal::seed(); return _x ^= _x << 7, _x ^= _x >> 9; } // [l, r] i64 rng(i64 l, i64 r) { assert(l <= r); return l + rng() % u64(r - l + 1); } // [l, r) i64 randint(i64 l, i64 r) { assert(l < r); return l + rng() % u64(r - l); } // choose n numbers from [l, r) without overlapping vector<i64> randset(i64 l, i64 r, i64 n) { assert(l <= r && n <= r - l); unordered_set<i64> s; for (i64 i = n; i; --i) { i64 m = randint(l, r + 1 - i); if (s.find(m) != s.end()) m = r - i; s.insert(m); } vector<i64> ret; for (auto& x : s) ret.push_back(x); sort(begin(ret), end(ret)); return ret; } // [0.0, 1.0) double rnd() { return rng() * 5.42101086242752217004e-20; } // [l, r) double rnd(double l, double r) { assert(l < r); return l + rnd() * (r - l); } template <typename T> void randshf(vector<T>& v) { int n = v.size(); for (int i = 1; i < n; i++) swap(v[i], v[randint(0, i + 1)]); } } // namespace my_rand using my_rand::randint; using my_rand::randset; using my_rand::randshf; using my_rand::rnd; using my_rand::rng; #line 13 "verify/verify-unit-test/dynamic-diameter.test.cpp" void test() { ll wmax = TEN(9); rep1(N, 50) { rep(_, 100) { WeightedGraph<ll> g; Edges<ll> es; rep1(i, N - 1) { int j = rng(0, i - 1); es.emplace_back(j, i, rng(0, wmax)); } auto gen = [&]() { g.clear(); g.resize(N); each(e, es) { g[e.src].emplace_back(e.src, e.to, e.cost); g[e.to].emplace_back(e.to, e.src, e.cost); } }; gen(); auto DP = DynamicDiameter(g); rep(t, 100) { // check auto [d, uv] = DP.get(); ll d2 = -1; { int u = 0; auto du = dijkstra(g, u); int v = max_element(all(du)) - begin(du); auto dv = dijkstra(g, v); int w = max_element(all(dv)) - begin(dv); d2 = dv[w]; } assert(uv.first != -1 and uv.second != -1); assert(d == d2); assert(d == dijkstra(g, uv.first)[uv.second]); if (N >= 2) { // update int e_num = rng(0, N - 2); int u = es[e_num].src, v = es[e_num].to; ll x = rng(0, wmax); DP.update(u, v, x); es[e_num].cost = x; gen(); } } } } trc2("OK"); } void q() { test(); int a, b; cin >> a >> b; cout << a + b << endl; } void Nyaan::solve() { int t = 1; // in(t); while (t--) q(); }