// #pragma GCC optimize ("Ofast")
// #pragma GCC target ("avx2")
#include <bits/stdc++.h>
using namespace std;
#ifdef LOCAL
#include <debug.h>
#else
#define debug(...)
#endif
#define ft front
#define bk back
#define st first
#define nd second
#define ins insert
#define ers erase
#define pb push_back
#define pf push_front
#define _pb pop_back
#define _pf pop_front
#define lb lower_bound
#define ub upper_bound
#define mtp make_tuple
#define bg begin
#define ed end
#define all(x) (x).bg(), (x).ed()
#define sz(x) (int)(x).size()
// #define int long long
typedef long long ll; typedef unsigned long long ull;
typedef double db; typedef long double ldb;
typedef pair<int, int> pi; typedef pair<ll, ll> pll;
typedef vector<int> vi; typedef vector<ll> vll; typedef vector<pi> vpi; typedef vector<pll> vpll;
typedef string str;
#define FOR(i, l, r) for (int i = (l); i <= (r); ++i)
#define FOS(i, r, l) for (int i = (r); i >= (l); --i)
#define FRN(i, n) for (int i = 0; i < (n); ++i)
#define FSN(i, n) for (int i = (n) - 1; i >= 0; --i)
#define EACH(i, x) for (auto &i : (x))
#define WHILE while
template<typename T> T gcd(T a, T b) { T d2 = (a | b) & -(a | b); a /= d2; b /= d2; WHILE(b) { a = a % b; swap(a, b); } return a * d2; }
template<typename T> T lcm(T a, T b) { return a / gcd(a, b) * b; }
void _assert(bool statement) { if (statement) return; cerr << "\n>> Assertion failed!\n"; exit(0); }
void _assert(bool statement, const str &message) { if (statement) return; cerr << "\n>> Assertion failed: " << message << '\n'; exit(0); }
void _error(const str &message) { cerr << "\n>> Error: " << message << '\n'; exit(0); }
#define file "TEST"
mt19937 rd(chrono::steady_clock::now().time_since_epoch().count());
ll rand(ll l, ll r) { return uniform_int_distribution<ll>(l, r)(rd); }
/*
----------------------------------------------------------------
END OF TEMPLATE
----------------------------------------------------------------
Tran The Bao - ghostwriter
Training for VOI23 gold medal
----------------------------------------------------------------
GOAT
----------------------------------------------------------------
*/
int n, m;
struct OnlineBridge {
#define matrix vector<vi>
int n;
vi h, s; // heights, size of the component
matrix adj, p; // adjacent matrix, sparse table parent
vpi e, bridge; // edges, vector that contains all the bridges
map<pi, bool> c; // markup map to mark all edge that's not bridge
OnlineBridge(int n) : n(n) { // 1 indexed
h.resize(n + 1, 0);
s.resize(n + 1, 0);
adj.resize(n + 1);
p.resize(n + 1);
FRN(i, n + 1) p[i].resize(17, 0);
FOR(i, 1, n) s[i] = 1;
}
int getp(int u) { // get parent of current components
FSN(j, 17)
if (p[u][j])
u = p[u][j];
return u;
}
void dfs(int u, int pn) { // reorder tree when a new edge is added (update all needed stat)
FOR(i, 1, 16) p[u][i] = p[p[u][i - 1]][i - 1];
EACH(j, adj[u]) {
int v = (e[j].st == u? e[j].nd : e[j].st);
if (v == pn) continue;
h[v] = h[u] + 1;
p[v][0] = u;
dfs(v, u);
}
}
int lca(int x, int y) { // find lowest common ancestor
if (h[x] > h[y]) swap(x, y);
int diff = h[y] - h[x];
FRN(i, 17)
if (diff & (1 << i))
y = p[y][i];
if (x == y) return x;
FSN(i, 17)
if (p[x][i] != p[y][i]) {
x = p[x][i];
y = p[y][i];
}
return p[x][0];
}
bool mark(int x, int y) { // mark edge (x, y), if (x, y) is already marked then return 0 else 1
if (x > y) swap(x, y);
if (c.count({x, y})) return 0;
c[{x, y}] = 1;
return 1;
}
void add(int x, int y) { // process new edge added to graph
int px = getp(x);
int py = getp(y);
if (px == py) {
int LCA = lca(x, y);
WHILE(y != LCA) {
int pn = p[y][0];
if (!mark(pn, y)) break;
y = pn;
}
WHILE(x != LCA) {
int pn = p[x][0];
if (!mark(pn, x)) break;
x = pn;
}
}
else {
if (s[px] < s[py]) {
swap(x, y);
swap(px, py);
}
adj[x].pb(sz(e));
adj[y].pb(sz(e));
e.pb({x, y});
h[y] = h[x] + 1;
p[y][0] = x;
dfs(y, x);
s[px] += s[py];
}
}
vpi getBridge() {
bridge.clear();
EACH(i, e) {
int u = i.st, v = i.nd;
if (u > v) swap(u, v);
if (!c.count({u, v})) bridge.pb({u, v});
}
return bridge;
}
};
void reinit(int test_id) {
}
void input(int test_id) {
cin >> n >> m;
}
void solve(int test_id) {
OnlineBridge ob(n);
WHILE(m--) {
int u, v;
cin >> u >> v;
ob.add(u, v);
}
vpi ans = ob.getBridge();
EACH(i, ans) cout << i.st << ' ' << i.nd << '\n';
}
signed main() {
ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
// freopen(file".inp", "r", stdin);
// freopen(file".out", "w", stdout);
int test_num = 1;
// cin >> test_num; // comment if the problem does not requires multitest
FOR(i, 1, test_num) {
input(i); // input in noninteractive sections for case #i
solve(i); // main function to solve case #i
reinit(i); // reinit global data to default used in case #i
}
#ifdef LOCAL
cerr << "\nTime: " << setprecision(5) << fixed << (ldb)clock() / CLOCKS_PER_SEC << "ms.\n";
#endif
return 0;
}
/*
----------------------------------------------------------------
From Benq:
stuff you should look for
* int overflow, array bounds
* special cases (n=1?)
* do smth instead of nothing and stay organized
* WRITE STUFF DOWN
* DON'T GET STUCK ON ONE APPROACH
----------------------------------------------------------------
*/
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
0 ms |
340 KB |
Output is correct |
| 2 |
Incorrect |
0 ms |
340 KB |
Wrong number of edges |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Incorrect |
10 ms |
1364 KB |
Wrong number of edges |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
391 ms |
1140 KB |
Output is correct |
| 2 |
Correct |
348 ms |
1108 KB |
Output is correct |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
767 ms |
2588 KB |
Output is correct |
| 2 |
Correct |
916 ms |
2524 KB |
Output is correct |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
1335 ms |
5864 KB |
Output is correct |
| 2 |
Runtime error |
1074 ms |
21080 KB |
Memory limit exceeded |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Runtime error |
3177 ms |
16644 KB |
Memory limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Execution timed out |
5005 ms |
20440 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Execution timed out |
5083 ms |
25056 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Execution timed out |
5079 ms |
25144 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Execution timed out |
5091 ms |
25344 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
