結果
| 問題 | No.1582 Vertexes vs Edges |
| ユーザー |
 nok0
|
| 提出日時 | 2021-07-02 22:42:40 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 29,207 bytes |
| コンパイル時間 | 4,632 ms |
| コンパイル使用メモリ | 285,860 KB |
| 実行使用メモリ | 11,264 KB |
| 最終ジャッジ日時 | 2024-06-29 12:34:42 |
| 合計ジャッジ時間 | 6,599 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | WA | - |
| testcase_01 | WA | - |
| testcase_02 | WA | - |
| testcase_03 | WA | - |
| testcase_04 | WA | - |
| testcase_05 | WA | - |
| testcase_06 | WA | - |
| testcase_07 | WA | - |
| testcase_08 | WA | - |
| testcase_09 | WA | - |
| testcase_10 | WA | - |
| testcase_11 | WA | - |
| testcase_12 | WA | - |
| testcase_13 | WA | - |
| testcase_14 | WA | - |
| testcase_15 | WA | - |
| testcase_16 | WA | - |
| testcase_17 | WA | - |
| testcase_18 | WA | - |
| testcase_19 | WA | - |
| testcase_20 | WA | - |
| testcase_21 | WA | - |
| testcase_22 | WA | - |
| testcase_23 | WA | - |
| testcase_24 | WA | - |
| testcase_25 | WA | - |
| testcase_26 | WA | - |
| testcase_27 | WA | - |
| testcase_28 | WA | - |
| testcase_29 | WA | - |
| testcase_30 | WA | - |
| testcase_31 | WA | - |
| testcase_32 | WA | - |
| testcase_33 | WA | - |
| testcase_34 | WA | - |
| testcase_35 | WA | - |
| testcase_36 | WA | - |
| testcase_37 | WA | - |
| testcase_38 | WA | - |
ソースコード
/**
* author: nok0
* created: 2021.07.02 22:09:27
**/
#ifdef LOCAL
#define _GLIBCXX_DEBUG
#endif
#include <bits/stdc++.h>
using namespace std;
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#endif
#pragma region Macros
// rep macro
#define foa(v, a) for(auto &v : a)
#define REPname(a, b, c, d, e, ...) e
#define REP(...) REPname(__VA_ARGS__, REP3, REP2, REP1, REP0)(__VA_ARGS__)
#define REP0(x) for(int i = 0; i < (x); ++i)
#define REP1(i, x) for(int i = 0; i < (x); ++i)
#define REP2(i, l, r) for(int i = (l); i < (r); ++i)
#define REP3(i, l, r, c) for(int i = (l); i < (r); i += (c))
#define REPSname(a, b, c, ...) c
#define REPS(...) REPSname(__VA_ARGS__, REPS1, REPS0)(__VA_ARGS__)
#define REPS0(x) for(int i = 1; i <= (x); ++i)
#define REPS1(i, x) for(int i = 1; i <= (x); ++i)
#define RREPname(a, b, c, d, e, ...) e
#define RREP(...) RREPname(__VA_ARGS__, RREP3, RREP2, RREP1, RREP0)(__VA_ARGS__)
#define RREP0(x) for(int i = (x)-1; i >= 0; --i)
#define RREP1(i, x) for(int i = (x)-1; i >= 0; --i)
#define RREP2(i, r, l) for(int i = (r)-1; i >= (l); --i)
#define RREP3(i, r, l, c) for(int i = (r)-1; i >= (l); i -= (c))
#define RREPSname(a, b, c, ...) c
#define RREPS(...) RREPSname(__VA_ARGS__, RREPS1, RREPS0)(__VA_ARGS__)
#define RREPS0(x) for(int i = (x); i >= 1; --i)
#define RREPS1(i, x) for(int i = (x); i >= 1; --i)
// name macro
#define pb push_back
#define eb emplace_back
#define SZ(x) ((int)(x).size())
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define popcnt(x) __builtin_popcountll(x)
template <class T = int>
using V = std::vector<T>;
template <class T = int>
using VV = std::vector<std::vector<T>>;
template <class T>
using pqup = std::priority_queue<T, std::vector<T>, std::greater<T>>;
using ll = long long;
using ld = long double;
using int128 = __int128_t;
using pii = std::pair<int, int>;
using pll = std::pair<long long, long long>;
// input macro
template <class T, class U>
std::istream &operator>>(std::istream &is, std::pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template <class T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
for(T &i : v) is >> i;
return is;
}
std::istream &operator>>(std::istream &is, __int128_t &a) {
std::string s;
is >> s;
__int128_t ret = 0;
for(int i = 0; i < s.length(); i++)
if('0' <= s[i] and s[i] <= '9')
ret = 10 * ret + s[i] - '0';
a = ret * (s[0] == '-' ? -1 : 1);
return is;
}
#if __has_include(<atcoder/all>)
std::istream &operator>>(std::istream &is, atcoder::modint998244353 &a) {
long long v;
is >> v;
a = v;
return is;
}
std::istream &operator>>(std::istream &is, atcoder::modint1000000007 &a) {
long long v;
is >> v;
a = v;
return is;
}
template <int m>
std::istream &operator>>(std::istream &is, atcoder::static_modint<m> &a) {
long long v;
is >> v;
a = v;
return is;
}
template <int m>
std::istream &operator>>(std::istream &is, atcoder::dynamic_modint<m> &a) {
long long v;
is >> v;
a = v;
return is;
}
#endif
namespace scanner {
void scan(int &a) { std::cin >> a; }
void scan(long long &a) { std::cin >> a; }
void scan(std::string &a) { std::cin >> a; }
void scan(char &a) { std::cin >> a; }
void scan(char a[]) { std::scanf("%s", a); }
void scan(double &a) { std::cin >> a; }
void scan(long double &a) { std::cin >> a; }
template <class T, class U>
void scan(std::pair<T, U> &p) { std::cin >> p; }
template <class T>
void scan(std::vector<T> &a) { std::cin >> a; }
void INPUT() {}
template <class Head, class... Tail>
void INPUT(Head &head, Tail &... tail) {
scan(head);
INPUT(tail...);
}
} // namespace scanner
#define VEC(type, name, size) \
std::vector<type> name(size); \
scanner::INPUT(name)
#define VVEC(type, name, h, w) \
std::vector<std::vector<type>> name(h, std::vector<type>(w)); \
scanner::INPUT(name)
#define INT(...) \
int __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#define LL(...) \
long long __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#define STR(...) \
std::string __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#define DOUBLE(...) \
double __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#define LD(...) \
long double __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
// output-macro
template <class T, class U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template <class T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &a) {
for(int i = 0; i < int(a.size()); ++i) {
if(i) os << " ";
os << a[i];
}
return os;
}
std::ostream &operator<<(std::ostream &dest, __int128_t &value) {
std::ostream::sentry s(dest);
if(s) {
__uint128_t tmp = value < 0 ? -value : value;
char buffer[128];
char *d = std::end(buffer);
do {
--d;
*d = "0123456789"[tmp % 10];
tmp /= 10;
} while(tmp != 0);
if(value < 0) {
--d;
*d = '-';
}
int len = std::end(buffer) - d;
if(dest.rdbuf()->sputn(d, len) != len) {
dest.setstate(std::ios_base::badbit);
}
}
return dest;
}
#if __has_include(<atcoder/all>)
std::ostream &operator<<(std::ostream &os, const atcoder::modint998244353 &a) { return os << a.val(); }
std::ostream &operator<<(std::ostream &os, const atcoder::modint1000000007 &a) { return os << a.val(); }
template <int m>
std::ostream &operator<<(std::ostream &os, const atcoder::static_modint<m> &a) { return os << a.val(); }
template <int m>
std::ostream &operator<<(std::ostream &os, const atcoder::dynamic_modint<m> &a) { return os << a.val(); }
#endif
template <class T>
void print(const T a) { std::cout << a << '\n'; }
template <class Head, class... Tail>
void print(Head H, Tail... T) {
std::cout << H << ' ';
print(T...);
}
template <class T>
void printel(const T a) { std::cout << a << '\n'; }
template <class T>
void printel(const std::vector<T> &a) {
for(const auto &v : a)
std::cout << v << '\n';
}
template <class Head, class... Tail>
void printel(Head H, Tail... T) {
std::cout << H << '\n';
printel(T...);
}
void Yes(const bool b = true) { std::cout << (b ? "Yes\n" : "No\n"); }
void No() { std::cout << "No\n"; }
void YES(const bool b = true) { std::cout << (b ? "YES\n" : "NO\n"); }
void NO() { std::cout << "NO\n"; }
void err(const bool b = true) {
if(b) {
std::cout << "-1\n", exit(0);
}
}
//debug macro
namespace debugger {
template <class T>
void view(const std::vector<T> &a) {
std::cerr << "{ ";
for(const auto &v : a) {
std::cerr << v << ", ";
}
std::cerr << "\b\b }";
}
template <class T>
void view(const std::vector<std::vector<T>> &a) {
std::cerr << "{\n";
for(const auto &v : a) {
std::cerr << "\t";
view(v);
std::cerr << "\n";
}
std::cerr << "}";
}
template <class T, class U>
void view(const std::vector<std::pair<T, U>> &a) {
std::cerr << "{\n";
for(const auto &p : a) std::cerr << "\t(" << p.first << ", " << p.second << ")\n";
std::cerr << "}";
}
template <class T, class U>
void view(const std::map<T, U> &m) {
std::cerr << "{\n";
for(const auto &p : m) std::cerr << "\t[" << p.first << "] : " << p.second << "\n";
std::cerr << "}";
}
template <class T, class U>
void view(const std::pair<T, U> &p) { std::cerr << "(" << p.first << ", " << p.second << ")"; }
template <class T>
void view(const std::set<T> &s) {
std::cerr << "{ ";
for(auto &v : s) {
view(v);
std::cerr << ", ";
}
std::cerr << "\b\b }";
}
template <class T>
void view(const T &e) { std::cerr << e; }
} // namespace debugger
#ifdef LOCAL
void debug_out() {}
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
debugger::view(H);
std::cerr << ", ";
debug_out(T...);
}
#define debug(...) \
do { \
std::cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \
debug_out(__VA_ARGS__); \
std::cerr << "\b\b]\n"; \
} while(false)
#else
#define debug(...) (void(0))
#endif
// vector macro
template <class T>
int lb(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::lower_bound((a).begin(), (a).end(), (x))); }
template <class T>
int ub(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::upper_bound((a).begin(), (a).end(), (x))); }
template <class T>
void UNIQUE(std::vector<T> &a) {
std::sort(a.begin(), a.end());
a.erase(std::unique(a.begin(), a.end()), a.end());
}
template <class T>
std::vector<T> press(std::vector<T> &a) {
auto res = a;
UNIQUE(res);
for(auto &v : a)
v = lb(res, v);
return res;
}
#define SORTname(a, b, c, ...) c
#define SORT(...) SORTname(__VA_ARGS__, SORT1, SORT0, ...)(__VA_ARGS__)
#define SORT0(a) std::sort((a).begin(), (a).end())
#define SORT1(a, c) std::sort((a).begin(), (a).end(), [](const auto x, const auto y) { return x c y; })
template <class T>
void ADD(std::vector<T> &a, const T x) {
for(auto &v : a) v += x;
}
template <class T>
void SUB(std::vector<T> &a, const T x = 1) {
for(auto &v : a) v -= x;
}
template <class T>
void MUL(std::vector<T> &a, const T x) {
for(auto &v : a) v *= x;
}
template <class T>
void DIV(std::vector<T> &a, const T x) {
for(auto &v : a) v /= x;
}
// math macro
template <class T, class U>
inline bool chmin(T &a, const U &b) { return a > b ? a = b, true : false; }
template <class T, class U>
inline bool chmax(T &a, const U &b) { return a < b ? a = b, true : false; }
template <class T>
T divup(T x, T y) { return (x + y - 1) / y; }
template <class T>
T POW(T a, long long n) {
T ret = 1;
while(n) {
if(n & 1) ret *= a;
a *= a;
n >>= 1;
}
return ret;
}
// modpow
long long POW(long long a, long long n, const int mod) {
long long ret = 1;
while(n) {
if(n & 1) (ret *= a) %= mod;
(a *= a) %= mod;
n >>= 1;
}
return ret;
}
// others
struct fast_io {
fast_io() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout << fixed << setprecision(15);
}
} fast_io_;
const int inf = 1e9;
const ll INF = 1e18;
#pragma endregion
#pragma region Graph Graph
#include <algorithm>
#include <cassert>
#include <deque>
#include <iostream>
#include <queue>
#include <tuple>
#include <utility>
#include <vector>
struct Edge {
int to;
long long cost;
Edge() = default;
Edge(int to_, long long cost_) : to(to_), cost(cost_) {}
bool operator<(const Edge &a) const { return cost < a.cost; }
bool operator>(const Edge &a) const { return cost > a.cost; }
friend std::ostream &operator<<(std::ostream &s, Edge &a) {
s << "to: " << a.to << ", cost: " << a.cost;
return s;
}
};
class Graph {
std::vector<std::vector<Edge>> edges;
template <class F>
struct rec_lambda {
F f;
rec_lambda(F &&f_) : f(std::forward<F>(f_)) {}
template <class... Args>
auto operator()(Args &&... args) const {
return f(*this, std::forward<Args>(args)...);
}
};
public:
inline const std::vector<Edge> &operator[](int k) const { return edges[k]; }
inline std::vector<Edge> &operator[](int k) { return edges[k]; }
int size() const { return edges.size(); }
void resize(const int n) { edges.resize(n); }
Graph() = default;
Graph(int n) : edges(n) {}
Graph(int n, int e, bool weight = 0, bool directed = 0, int idx = 1) : edges(n) { input(e, weight, directed, idx); }
const long long INF = 3e18;
void input(int e = -1, bool weight = 0, bool directed = false, int idx = 1) {
if(e == -1) e = size() - 1;
while(e--) {
int u, v;
long long cost = 1;
std::cin >> u >> v;
if(weight) std::cin >> cost;
u -= idx, v -= idx;
edges[u].emplace_back(v, cost);
if(!directed) edges[v].emplace_back(u, cost);
}
}
void add_edge(int u, int v, long long cost = 1, bool directed = false, int idx = 0) {
u -= idx, v -= idx;
edges[u].emplace_back(v, cost);
if(!directed) edges[v].emplace_back(u, cost);
}
// Ο(V+E)
std::vector<long long> bfs(int s) {
std::vector<long long> dist(size(), INF);
std::queue<int> que;
dist[s] = 0;
que.push(s);
while(!que.empty()) {
int v = que.front();
que.pop();
for(auto &e : edges[v]) {
if(dist[e.to] != INF) continue;
dist[e.to] = dist[v] + e.cost;
que.push(e.to);
}
}
return dist;
}
// Ο(V+E)
// constraint: cost of each edge is zero or one
std::vector<long long> zero_one_bfs(int s) {
std::vector<long long> dist(size(), INF);
std::deque<int> deq;
dist[s] = 0;
deq.push_back(s);
while(!deq.empty()) {
int v = deq.front();
deq.pop_front();
for(auto &e : edges[v]) {
assert(0LL <= e.cost and e.cost < 2LL);
if(e.cost and dist[e.to] > dist[v] + 1) {
dist[e.to] = dist[v] + 1;
deq.push_back(e.to);
} else if(!e.cost and dist[e.to] > dist[v]) {
dist[e.to] = dist[v];
deq.push_front(e.to);
}
}
}
return dist;
}
// Ο((E+V)logV)
// cannot reach: INF
std::vector<long long> dijkstra(int s) { // verified
std::vector<long long> dist(size(), INF);
const auto compare = [](const std::pair<long long, int> &a, const std::pair<long long, int> &b) { return a.first > b.first; };
std::priority_queue<std::pair<long long, int>, std::vector<std::pair<long long, int>>, decltype(compare)> que{compare};
dist[s] = 0;
que.emplace(0, s);
while(!que.empty()) {
std::pair<long long, int> p = que.top();
que.pop();
int v = p.second;
if(dist[v] < p.first) continue;
for(auto &e : edges[v]) {
if(dist[e.to] > dist[v] + e.cost) {
dist[e.to] = dist[v] + e.cost;
que.emplace(dist[e.to], e.to);
}
}
}
return dist;
}
// Ο(VE)
// cannot reach: INF
// negative cycle: -INF
std::vector<long long> bellman_ford(int s) { // verified
int n = size();
std::vector<long long> res(n, INF);
res[s] = 0;
for(int loop = 0; loop < n - 1; loop++) {
for(int v = 0; v < n; v++) {
if(res[v] == INF) continue;
for(auto &e : edges[v]) {
res[e.to] = std::min(res[e.to], res[v] + e.cost);
}
}
}
std::queue<int> que;
std::vector<int> chk(n);
for(int v = 0; v < n; v++) {
if(res[v] == INF) continue;
for(auto &e : edges[v]) {
if(res[e.to] > res[v] + e.cost and !chk[e.to]) {
que.push(e.to);
chk[e.to] = 1;
}
}
}
while(!que.empty()) {
int now = que.front();
que.pop();
for(auto &e : edges[now]) {
if(!chk[e.to]) {
chk[e.to] = 1;
que.push(e.to);
}
}
}
for(int i = 0; i < n; i++)
if(chk[i]) res[i] = -INF;
return res;
}
// Ο(V^3)
std::vector<std::vector<long long>> warshall_floyd() { // verified
int n = size();
std::vector<std::vector<long long>> dist(n, std::vector<long long>(n, INF));
for(int i = 0; i < n; i++) dist[i][i] = 0;
for(int i = 0; i < n; i++)
for(auto &e : edges[i]) dist[i][e.to] = std::min(dist[i][e.to], e.cost);
for(int k = 0; k < n; k++)
for(int i = 0; i < n; i++) {
if(dist[i][k] == INF) continue;
for(int j = 0; j < n; j++) {
if(dist[k][j] == INF) continue;
dist[i][j] = std::min(dist[i][j], dist[i][k] + dist[k][j]);
}
}
return dist;
}
// Ο(V) (using DFS)
// if a directed cycle exists, return {}
std::vector<int> topological_sort() { // verified
std::vector<int> res;
int n = size();
std::vector<int> used(n, 0);
bool not_DAG = false;
for(int i = 0; i < n; i++) {
rec_lambda([&](auto &&dfs, int k) -> void {
if(not_DAG) return;
if(used[k]) {
if(used[k] == 1) not_DAG = true;
return;
}
used[k] = 1;
for(auto &e : edges[k]) dfs(e.to);
used[k] = 2;
res.push_back(k);
})(i);
}
if(not_DAG) return std::vector<int>{};
std::reverse(res.begin(), res.end());
return res;
}
bool is_DAG() { return !topological_sort().empty(); } // verified
// Ο(V)
// array of the distance from each vertex to the most distant vertex
std::vector<long long> height() { // verified
auto vec1 = bfs(0);
int v1 = -1, v2 = -1;
long long dia = -1;
for(int i = 0; i < int(size()); i++)
if(dia < vec1[i]) dia = vec1[i], v1 = i;
vec1 = bfs(v1);
dia = -1;
for(int i = 0; i < int(size()); i++)
if(dia < vec1[i]) dia = vec1[i], v2 = i;
auto vec2 = bfs(v2);
for(int i = 0; i < int(size()); i++)
if(vec1[i] < vec2[i]) vec1[i] = vec2[i];
return vec1;
}
// O(V+E)
// vector<(int)(0 or 1)>
// if it is not bipartite, return {}
std::vector<int> bipartite_grouping() {
std::vector<int> colors(size(), -1);
auto dfs = [&](auto self, int now, int col) -> bool {
colors[now] = col;
for(auto &e : edges[now]) {
if(col == colors[e.to]) return false;
if(colors[e.to] == -1 and !self(self, e.to, !col)) return false;
}
return true;
};
for(int i = 0; i < int(size()); i++)
if(colors[i] == -1 and !dfs(dfs, i, 0)) return std::vector<int>{};
return colors;
}
bool is_bipartite() { return !bipartite_grouping().empty(); }
// Ο(V+E)
// ((v1, v2), diameter)
std::pair<std::pair<int, int>, long long> diameter() { // verified
auto vec = bfs(0);
int v1 = -1, v2 = -1;
long long dia = -1;
for(int i = 0; i < int(size()); i++)
if(dia < vec[i]) dia = vec[i], v1 = i;
vec = bfs(v1);
dia = -1;
for(int i = 0; i < int(size()); i++)
if(dia < vec[i]) dia = vec[i], v2 = i;
std::pair<std::pair<int, int>, long long> res = {{v1, v2}, dia};
return res;
}
// Ο(V+E)
// return {s, v1, v2, ... t}
std::vector<int> diameter_path() {
auto vec = bfs(0);
int v1 = -1, v2 = -1;
long long dia = -1;
for(int i = 0; i < int(size()); i++)
if(dia < vec[i]) dia = vec[i], v1 = i;
auto vec2 = bfs(v1);
dia = -1;
for(int i = 0; i < int(size()); i++)
if(dia < vec2[i]) dia = vec2[i], v2 = i;
vec = bfs(v2);
std::vector<int> ret;
auto dfs = [&](auto self, int now, int p) -> void {
ret.emplace_back(now);
if(now == v2) return;
for(auto &[to, cost] : (*this)[now]) {
if(vec[to] + vec2[to] == dia and to != p)
self(self, to, now);
}
};
dfs(dfs, v1, -1);
return ret;
}
// Ο(V+E)
// return subtree_size, root = root
std::vector<int> subtree_size(const int root) {
int n = size();
std::vector<int> ret(n, 1);
rec_lambda([&](auto &&dfs, int now, int p) -> void {
for(auto &[to, cost] : (*this)[now]) {
if(to == p) continue;
dfs(to, now);
ret[now] += ret[to];
}
})(root, -1);
return ret;
}
// Ο(ElogV)
long long prim() { // verified
long long res = 0;
std::priority_queue<Edge, std::vector<Edge>, std::greater<Edge>> que;
for(auto &e : edges[0]) que.push(e);
std::vector<int> chk(size());
chk[0] = 1;
int cnt = 1;
while(cnt < size()) {
auto e = que.top();
que.pop();
if(chk[e.to]) continue;
cnt++;
res += e.cost;
chk[e.to] = 1;
for(auto &e2 : edges[e.to]) que.push(e2);
}
return res;
}
// Ο(ElogE)
long long kruskal() { // verified
std::vector<std::tuple<int, int, long long>> Edges;
for(int i = 0; i < int(size()); i++)
for(auto &e : edges[i]) Edges.emplace_back(i, e.to, e.cost);
std::sort(Edges.begin(), Edges.end(), [](const std::tuple<int, int, long long> &a, const std::tuple<int, int, long long> &b) {
return std::get<2>(a) < std::get<2>(b);
});
std::vector<int> uf_data(size(), -1);
auto root = [&uf_data](auto self, int x) -> int {
if(uf_data[x] < 0) return x;
return uf_data[x] = self(self, uf_data[x]);
};
auto unite = [&uf_data, &root](int u, int v) -> bool {
u = root(root, u), v = root(root, v);
if(u == v) return false;
if(uf_data[u] > uf_data[v]) std::swap(u, v);
uf_data[u] += uf_data[v];
uf_data[v] = u;
return true;
};
long long ret = 0;
for(auto &e : Edges)
if(unite(std::get<0>(e), std::get<1>(e))) ret += std::get<2>(e);
return ret;
}
// O(V)
std::vector<int> centroid() {
int n = size();
std::vector<int> centroid, sz(n);
auto dfs = [&](auto self, int now, int per) -> void {
sz[now] = 1;
bool is_centroid = true;
for(auto &e : edges[now]) {
if(e.to != per) {
self(self, e.to, now);
sz[now] += sz[e.to];
if(sz[e.to] > n / 2) is_centroid = false;
}
}
if(n - sz[now] > n / 2) is_centroid = false;
if(is_centroid) centroid.push_back(now);
};
dfs(dfs, 0, -1);
return centroid;
}
// Ο(V+E)
// directed graph from root to leaf
Graph root_to_leaf(int root = 0) {
Graph res(size());
std::vector<int> chk(size(), 0);
chk[root] = 1;
auto dfs = [&](auto self, int now) -> void {
for(auto &e : edges[now]) {
if(chk[e.to] == 1) continue;
chk[e.to] = 1;
res.add_edge(now, e.to, e.cost, 1, 0);
self(self, e.to);
}
};
dfs(dfs, root);
return res;
}
// Ο(V+E)
// directed graph from leaf to root
Graph leaf_to_root(int root = 0) {
Graph res(size());
std::vector<int> chk(size(), 0);
chk[root] = 1;
auto dfs = [&](auto self, int now) -> void {
for(auto &e : edges[now]) {
if(chk[e.to] == 1) continue;
chk[e.to] = 1;
res.add_edge(e.to, now, e.cost, 1, 0);
self(self, e.to);
}
};
dfs(dfs, root);
return res;
}
// long long Chu_Liu_Edmonds(int root = 0) {}
};
struct tree_doubling {
private:
std::vector<std::vector<int>> parent;
std::vector<int> depth;
std::vector<long long> dist;
int max_jump = 1;
void build() {
for(int i = 0; i < max_jump - 1; i++) {
for(int v = 0; v < (int)dist.size(); v++) {
if(parent[i][v] == -1)
parent[i + 1][v] = -1;
else
parent[i + 1][v] = parent[i][parent[i][v]];
}
}
}
public:
tree_doubling() = default;
tree_doubling(const Graph &g, const int root = 0) : dist(g.size()), depth(g.size()) {
int n = g.size();
while((1 << max_jump) < n) max_jump++;
parent.assign(max_jump, std::vector<int>(n, -1));
auto dfs = [&](auto self, int now, int per, int d, long long cost) -> void {
parent[0][now] = per;
depth[now] = d;
dist[now] = cost;
for(auto &e : g[now])
if(e.to != per) self(self, e.to, now, d + 1, cost + e.cost);
};
dfs(dfs, root, -1, 0, 0LL);
build();
}
int lowest_common_ancestor(int u, int v) {
if(depth[u] < depth[v]) std::swap(u, v);
int k = parent.size();
for(int i = 0; i < k; i++)
if((depth[u] - depth[v]) >> i & 1) u = parent[i][u];
if(u == v) return u;
for(int i = k - 1; i >= 0; i--)
if(parent[i][u] != parent[i][v]) u = parent[i][u], v = parent[i][v];
return parent[0][u];
}
long long length_of_path(const int u, const int v) { return dist[u] + dist[v] - dist[lowest_common_ancestor(u, v)] * 2; }
int level_ancestor(int v, int level) {
assert(level >= 0);
for(int jump = 0; jump < max_jump and level; jump++) {
if(level & 1) v = parent[jump][v];
level >>= 1;
}
return v;
}
};
struct strongly_connected_components {
private:
enum { CHECKED = -1,
UNCHECKED = -2 };
const Graph &graph_given;
Graph graph_reversed;
std::vector<int> order, group_number; /* at the beginning of the building, 'group_number' is used as 'checked' */
void dfs(int now) {
if(group_number[now] != UNCHECKED) return;
group_number[now] = CHECKED;
for(auto &e : graph_given[now]) dfs(e.to);
order.push_back(now);
}
void rdfs(int now, int group_count) {
if(group_number[now] != UNCHECKED) return;
group_number[now] = group_count;
for(auto &e : graph_reversed[now]) rdfs(e.to, group_count);
}
void build(bool create_compressed_graph) {
for(int i = 0; i < (int)graph_given.size(); i++) dfs(i);
reverse(order.begin(), order.end());
group_number.assign(graph_given.size(), UNCHECKED);
int group = 0;
for(auto &i : order)
if(group_number[i] == UNCHECKED) rdfs(i, group), group++;
graph_compressed.resize(group);
groups.resize(group);
for(int i = 0; i < (int)graph_given.size(); i++) groups[group_number[i]].push_back(i);
if(create_compressed_graph) {
std::vector<int> edges(group, -1);
for(int i = 0; i < group; i++)
for(auto &vertex : groups[i])
for(auto &e : graph_given[vertex])
if(group_number[e.to] != i and edges[group_number[e.to]] != i) {
edges[group_number[e.to]] = i;
graph_compressed[i].emplace_back(group_number[e.to], 1);
}
}
return;
}
public:
std::vector<std::vector<int>> groups;
Graph graph_compressed;
strongly_connected_components(const Graph &g_, bool create_compressed_graph = false)
: graph_given(g_), graph_reversed(g_.size()), group_number(g_.size(), UNCHECKED) {
for(size_t i = 0; i < g_.size(); i++)
for(auto &e : graph_given[i]) graph_reversed[e.to].emplace_back(i, 1);
build(create_compressed_graph);
}
const int &operator[](const int k) { return group_number[k]; }
};
struct low_link {
private:
const Graph &graph_given;
int order_next;
void build() {
int n = graph_given.size();
order.resize(n, -1);
low.resize(n);
order_next = 0;
for(int i = 0; i < n; i++)
if(order[i] == -1) dfs(i);
}
void dfs(int now, int par = -1) {
low[now] = order[now] = order_next++;
bool is_articulation = false;
int cnt = 0, cnt_par = 0;
for(const auto &ed : graph_given[now]) {
const int &nxt = ed.to;
if(order[nxt] == -1) {
cnt++;
dfs(nxt, now);
if(order[now] < low[nxt]) bridge.push_back(std::minmax(now, nxt));
if(order[now] <= low[nxt]) is_articulation = true;
low[now] = std::min(low[now], low[nxt]);
} else if(nxt != par or cnt_par++ == 1) {
low[now] = std::min(low[now], order[nxt]);
}
}
if(par == -1 and cnt < 2) is_articulation = false;
if(is_articulation) articulation.push_back(now);
return;
}
public:
std::vector<int> order, low, articulation;
std::vector<std::pair<int, int>> bridge;
low_link() = default;
low_link(const Graph &g_) : graph_given(g_) { build(); }
};
struct two_edge_connected_components {
private:
const Graph &graph_given;
int group_next;
low_link li;
std::vector<int> group_number;
void build(bool create_compressed_graph) {
int n = graph_given.size();
group_number.resize(n, -1);
group_next = 0;
for(int i = 0; i < n; i++)
if(group_number[i] == -1) dfs(i);
groups.resize(group_next);
for(int i = 0; i < graph_given.size(); i++) groups[group_number[i]].push_back(i);
if(create_compressed_graph) {
graph_compressed.resize(group_next);
for(auto [u, v] : li.bridge) {
int x = group_number[u], y = group_number[v];
graph_compressed.add_edge(x, y);
}
}
}
void dfs(int now, int par = -1) {
if(par != -1 and li.order[par] >= li.low[now])
group_number[now] = group_number[par];
else
group_number[now] = group_next++;
for(const auto &e : graph_given[now])
if(group_number[e.to] == -1) dfs(e.to, now);
}
public:
Graph graph_compressed;
std::vector<std::vector<int>> groups;
two_edge_connected_components(const Graph &g_, bool create_compressed_graph = false)
: graph_given(g_), li(g_) {
build(create_compressed_graph);
}
const int &operator[](const int k) { return group_number[k]; }
};
struct heavy_light_decomposition {
public:
std::vector<int> sz, in, out, head, rev, par;
private:
Graph &g;
void dfs_sz(int v, int p = -1) {
par[v] = p;
if(!g[v].empty() and g[v].front().to == p) std::swap(g[v].front(), g[v].back());
for(auto &e : g[v]) {
if(e.to == p) continue;
dfs_sz(e.to, v);
sz[v] += sz[e.to];
if(sz[g[v].front().to] < sz[e.to]) std::swap(g[v].front(), e);
}
}
void dfs_hld(int v, int &t, int p = -1) {
in[v] = t++;
rev[in[v]] = v;
for(auto &e : g[v]) {
if(e.to == p) continue;
head[e.to] = (g[v].front().to == e.to ? head[v] : e.to);
dfs_hld(e.to, t, v);
}
out[v] = t;
}
void build(int root = 0) {
dfs_sz(root);
int t = 0;
head[root] = root;
dfs_hld(root, t);
}
public:
heavy_light_decomposition(Graph &g_, int root = 0) : g(g_) {
int n = g.size();
sz.resize(n, 1);
in.resize(n);
out.resize(n);
head.resize(n);
rev.resize(n);
par.resize(n);
build(root);
}
int level_ancestor(int v, int level) {
while(true) {
int u = head[v];
if(in[v] - level >= in[u]) return rev[in[v] - level];
level -= in[v] - in[u] + 1;
v = par[u];
}
}
int lowest_common_ancestor(int u, int v) {
for(;; v = par[head[v]]) {
if(in[u] > in[v]) std::swap(u, v);
if(head[u] == head[v]) return u;
}
}
// u, v: vertex, unit: unit, q: query on a path, f: binary operation ((T, T) -> T)
template <typename T, typename Q, typename F>
T query(int u, int v, const T &unit, const Q &q, const F &f, bool edge = false) {
T l = unit, r = unit;
for(;; v = par[head[v]]) {
if(in[u] > in[v]) std::swap(u, v), std::swap(l, r);
if(head[u] == head[v]) break;
l = f(q(in[head[v]], in[v] + 1), l);
}
return f(f(q(in[u] + edge, in[v] + 1), l), r);
}
// u, v: vertex, q: update query
template <typename Q>
void add(int u, int v, const Q &q, bool edge = false) {
for(;; v = par[head[v]]) {
if(in[u] > in[v]) std::swap(u, v);
if(head[u] == head[v]) break;
q(in[head[v]], in[v] + 1);
}
q(in[u] + edge, in[v] + 1);
}
std::pair<int, int> subtree(int v, bool edge = false) { return std::pair<int, int>(in[v] + edge, out[v]); }
};
#pragma endregion
int a[2];
void main_() {
INT(n);
Graph G(n, -1);
auto vec = G.bipartite_grouping();
REP(i, n) {
if(SZ(G[i]) > 1) {
a[vec[i]]++;
}
}
print(min(a[0], a[1]));
}
int main() {
int t = 1;
//cin >> t;
while(t--) main_();
return 0;
}