#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } const std::vector> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}}; int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); } template std::pair operator+(const std::pair &l, const std::pair &r) { return std::make_pair(l.first + r.first, l.second + r.second); } template std::pair operator-(const std::pair &l, const std::pair &r) { return std::make_pair(l.first - r.first, l.second - r.second); } template std::vector sort_unique(std::vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template IStream &operator>>(IStream &is, std::vector &vec) { for (auto &v : vec) is >> v; return is; } template OStream &operator<<(OStream &os, const std::vector &vec); template OStream &operator<<(OStream &os, const std::array &arr); template OStream &operator<<(OStream &os, const std::unordered_set &vec); template OStream &operator<<(OStream &os, const pair &pa); template OStream &operator<<(OStream &os, const std::deque &vec); template OStream &operator<<(OStream &os, const std::set &vec); template OStream &operator<<(OStream &os, const std::multiset &vec); template OStream &operator<<(OStream &os, const std::unordered_multiset &vec); template OStream &operator<<(OStream &os, const std::pair &pa); template OStream &operator<<(OStream &os, const std::map &mp); template OStream &operator<<(OStream &os, const std::unordered_map &mp); template OStream &operator<<(OStream &os, const std::tuple &tpl); template OStream &operator<<(OStream &os, const std::vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } template std::istream &operator>>(std::istream &is, std::tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template OStream &operator<<(OStream &os, const std::tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } template OStream &operator<<(OStream &os, const std::unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::pair &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; } template OStream &operator<<(OStream &os, const std::map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl #define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr) #else #define dbg(x) ((void)0) #define dbgif(cond, x) ((void)0) #endif #include #include #include #include // Rerooting // Reference: // - https://atcoder.jp/contests/abc222/editorial/2749 // - https://null-mn.hatenablog.com/entry/2020/04/14/124151 template struct rerooting { int n_; std::vector par, visited; std::vector>> to; std::vector dp_subtree; std::vector dp_par; std::vector dpall; rerooting(const std::vector>> &to_) : n_(to_.size()), par(n_, -1), visited(n_, 0), to(to_) { for (int i = 0; i < n_; ++i) dp_subtree.push_back(g(e(), i)); dp_par = dpall = dp_subtree; } void run_connected(int root) { if (visited[root]) return; visited[root] = 1; std::vector visorder{root}; for (int t = 0; t < int(visorder.size()); ++t) { int now = visorder[t]; for (const auto &edge : to[now]) { int nxt = edge.first; if (visited[nxt]) continue; visorder.push_back(nxt); visited[nxt] = 1; par[nxt] = now; } } for (int t = int(visorder.size()) - 1; t >= 0; --t) { int now = visorder[t]; Ch ch = e(); for (const auto &edge : to[now]) { int nxt = edge.first; if (nxt == par[now]) continue; ch = merge(ch, f(dp_subtree[nxt], nxt, edge.second)); } dp_subtree[now] = g(ch, now); } std::vector left; for (int now : visorder) { int m = int(to[now].size()); left.assign(m + 1, e()); for (int j = 0; j < m; j++) { int nxt = to[now][j].first; const St &st = (nxt == par[now] ? dp_par[now] : dp_subtree[nxt]); left[j + 1] = merge(left[j], f(st, nxt, to[now][j].second)); } dpall[now] = g(left.back(), now); Ch rprod = e(); for (int j = m - 1; j >= 0; --j) { int nxt = to[now][j].first; if (nxt != par[now]) dp_par[nxt] = g(merge(left[j], rprod), now); const St &st = (nxt == par[now] ? dp_par[now] : dp_subtree[nxt]); rprod = merge(f(st, nxt, to[now][j].second), rprod); } } } void run() { for (int i = 0; i < n_; ++i) { if (!visited[i]) run_connected(i); } } const St &get_subtree(int root_, int par_) const { if (par_ < 0) return dpall.at(root_); if (par.at(root_) == par_) return dp_subtree.at(root_); if (par.at(par_) == root_) return dp_par.at(par_); std::exit(1); } }; using Subtree = pint; // (塗った、塗らない) using Child = pint; struct Edge {}; Child e() { return {0, 0}; } Child merge(Child x, Child y) { return x + y; } Child f(Subtree x, int, Edge) { return x; } Subtree g(Child x, int) { return {1 + x.second, max(x.first, x.second)}; } int main() { int N; cin >> N; vector>> to(N); REP(e, N - 1) { int a, b; cin >> a >> b; --a, --b; to.at(a).emplace_back(b, Edge{}); to.at(b).emplace_back(a, Edge{}); } rerooting tree(to); tree.run(); int ret = N; REP(i, N) { dbg(make_tuple(i, tree.dpall.at(i))); chmin(ret, tree.dpall.at(i).first); } cout << ret << '\n'; }